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Global Systems Science University of California, Berkeley Lawrence Hall of Science http://lawrencehallofscience.org/gss A CHANGING COSMOS Global Systems Science based on Hands-On Universe Units by TERC Edited by Alan Gould Telescope Images by Vivian Hoette A Changing Cosmos 2009 Edition 1 Global Systems Science (GSS) and Hands-On Universe (HOU) are projects of the Lawrence Hall of Science (LHS), University of California, Berkeley. GSS is also an activity of the Museum of Science in Boston, Massachusetts, which provides assistance in revising and disseminating the program. Global Systems Science (GSS) is an integrated, interdisciplinary course for schools, grades 9–12. GSS consists of 10 student books (see back cover), teacher guides, and Image Analysis software. Each GSS book deals with a societal issue that requires science for full understanding. GSS may be used in designing an integrated interdisciplinary science course or serve as supplementary materials for existing biology, physics, chemistry, Earth science, or social studies courses. To obtain latest revised editions of GSS books through University of California, Lawrence Hall of Science, please visit the GSS website: http://lhs.berkeley.edu/gss/ Hands-On Universe (HOU; http://www.handsonuniverse.org) is an educational program that enables students to investigate the Universe while applying tools and concepts from science, math, and technology. Using the Internet, HOU participants around the world request observations from observatories, download images from a large image archive, and analyze them with user-friendly image processing software. Sources of Support NIGEC. Development and publication of the Global Systems Science series was funded by the U.S. Department of Energy’s (DOE) National Institute for Global Environmental Change (NIGEC) through the NIGEC Western Regional Center (WESTGEC) at the University of California, Davis (DOE Cooperative Agreement No. DE-FC03-90ER61010). Noreen Dowling, Joseph Knox, Linda Ono, and Thomas Suchanek provided assistance to this project on behalf of NIGEC and WESTGEC. NSF. The opportunity to involve high school teachers in the development of this project was made possible by a grant from the Teacher Enhancement Program of the National Science Foundation (Grant #TPE 9155393). This grant enabled us to invite 125 teachers to test these materials with their students, then come to Berkeley for three weeks, where they reported on trial test results, suggested improvements in the printed materials, and developed new laboratory activities. We are indebted to Larry G. Enochs and Wayne Sukow, Program Directors of the National Science Foundation, as well as to many teachers and students whose insights, ideas, and hard work have helped bring the GSS series to fruition. NASA. Support from NASA’s Earth Science Enterprise (ESE) has included printing and distribution of the GSS Books under a Memorandum of Understanding between NASA and the University of California at Berkeley. Nahid Khazenie provided assistance on behalf of NASA/ESE. NASA ESE also funded the enhancement of GSS to make it part of the Digital Library for Earth System Education (http://www.dlese.org/) Major portions of this book are adaptations of Hands-On Universe high school modules developed by Jodi Asbell-Clark and Tim Barclay © 1995-2000 by TERC. Financial support does not constitute an endorsement by DOE, NSF, or NASA of the views expressed in this book. 2 © 2007 by The Regents of the University of California. All rights reserved. Printed in the United States of America. This work may not be reproduced by mechanical or electronic means without written permission from the Lawrence Hall of Science, except for pages to be used in classroom activities and teacher workshops. For permission to copy portions of this material for other purposes, please write to: Global Systems Science, Lawrence Hall of Science, University of California, Berkeley, CA Global Systems Science A Changing Cosmos 94720-5200 or e-mail [email protected]. Based on Hands-On Universe Units by TERC (Jodi Asbell-Clarke, Tim Barclay) edited by Alan Gould HOU Telescope Images by Vivian Hoette, Yerkes Observatory Contents 1. Cosmic Cataclysms....................................................................... 2 2. Astronomers' Tools........................................................................ 8 3. Cosmic Engines.......................................................................... 22 4. Fathoming Huge Distances ........................................................ 30 5. Color, Temperature, and Age....................................................... 42 6. Dramatic Change in Stars........................................................... 60 7. Planet-Star Systems.................................................................... 72 8. Search for Habitable Planets....................................................... 86 9. Cosmos Begins...and Ends?....................................................... 90 List of Investigations........................................................................ 96 References...................................................................................... 97 Acknowledgments........................................................................... 98 News and updates are available at the GSS website http://www.lhs.berkeley.edu/GSS/ through the "Staying Up To Date” section. Global Systems Science A Changing Cosmos 1 Chapter 1 1. Cosmic Cataclysms Asteroid Collision We normally think of things in space as remote and not really able to affect things around us much. But there are some types of events in our changing cosmos that could really mess things up badly for us. In fossil records, there are many instances of species going extinct—apparently unable to cope with some change in environment. At certain times in Earth's history, not just one species has died off, but lots of species have died off, in mass extinctions. The latest such mass extinction happened 65 million years ago, when the Age of Reptiles ended and the Age of Mammals began. The question, “What caused the mass extinction at the end of the dinosaur age?” made scientists disagree and squabble for quite a while. The candidates for the cause of the extinction were: a. The theory of gradual change — mass extinctions took place over thousands or maybe millions of years, possibly due to long term climate change. Fossil evidence indicates that prior to sixty-five million years ago the dinosaurs were beginning to decline and many dinosaur species had already become extinct. b. The impact theory — set forth by Geologist Walter Alvarez from the University of California at Berkeley. He was studying a thin layer of clay between rock layers of the Cretaceous Period (Age of Reptiles) and the Tertiary Period (containing no dinosaurs fossils). The clay layer contained very large amounts of the rare element iridium, which is common in meteorites but uncommon in the Earth’s crust. This suggested a sudden large influx—perhaps one really huge meteor struck the Earth at about that time. An underground crater found near Chixulub (pronounced Chi’-shooloob), Mexico, was found to be about 65 million years old. The clay layer contained tiny pieces of minerals (shocked quartz) and glassy rocks (tektites), which are found at nuclear test sites and large meteor impact sites, as well as soot—indicative of continent-sized forest fires. An asteroid in the 10 kilometer diameter size range could have caused the event. 2 Global Systems Science The Chixulub Crater is buried underground, so it cannot be directly photographed. This is a 3-D graph made with equipment normally used to search for oil. It shows gravitational attraction of underground structures. Photo courtesy of Virgil L. Sharpton, Center for Advanced Space Studies, Houston, Texas, USA A Changing Cosmos Chapter 1: Cosmic Cataclysms c. The volcanic eruption theory—A huge series of lava flows in India, named the Deccan Traps, which covers 10,000 square kilometers and is in some places more than 2 kilometers thick, is evidence of a period of volcanic activity that spanned about half a million years—including the period of the mass extinction at the end of the Cretaceous Period. The volcanic eruption theory is in agreement with paleontologists’ original idea that the extinction of species was gradual, or at least occurred in several steps, over hundreds of thousands of years. When a 10 km-sized asteroid strikes the ground, it buries itself in the Earth and coverts its tremendous energy of motion into heat in a period of only seconds. It opens a crater that reaches a diameter of 100 miles and a depth of fifteen miles. Red hot rock debris streams outward, forming a plume heading into the sky. The plume can go so high it sends hot debris into orbit that eventually rain back all over Earth. On the ground, you would feel an effect very similar to an oven on broil for about an hour. As a result of this thermal radiation, even green vegetation would dry out and begin to burst into flames spontaneously, causing global forest fires. The Deccan Traps are extensive lava flows in India. Source: © Dr. Keith G. Cox, University of Oxford, Oxford, England. Which Theory is Right? Will Earth be Hit by a Large Asteroid? It may well be that we will never know for sure if either a large impact or massive volcanism caused the death of the dinosaurs. Eventually, it is likely. But the odds of one hitting tomorrow, or next week, or in the next few thousand years are quite low. Of course tons of smaller bodies (sand grain size) enter Earth’s atmosphere every day. But the larger the body, the rarer it is. The Barringer Meteor Crater near Winslow, Arizona, is as deep as a 60 story building and more than a kilometer across. It was created about 30,000 years ago by a rocky object about 30 meters in diameter traveling at 40,000 miles per hour. The impact had an explosive energy equivalent to over a million tons of TNT. It is 1/100 the size of the crater in Chixulub, Mexico. Source: Yerkes Observatory. Chapter 1: Cosmic Cataclysms Asteroids are not the only menace. Evidence of comets crashing into planets was dramatically seen in 1994 when the large comet ShoemakerLevy 9 fragmented and created huge explosions when it struck the planet Jupiter at more than 20 different sites. We’ll find out more about this event at the end of Chapter 3. It would behoove us to seek advance warning of such an approaching body. An asteroid could come in quickly, but it may be technically possible to deflect an asteroid from an Earth impact course if there is enough advance warning. Hands-On Universe 3 The Search for Near Earth Asteroids (NEOs) Asteroids must be discovered and their orbits tracked. At this point in time North American Aerospace Defense Command (NORAD) has a limited number of people monitoring the skies for asteroids. There is also a project called Space Guard which is an international network of telescopes and people working together to discover and track asteroids, with the idea of providing lots of advance warning if an asteroid is found to be on a collision course with Earth, so that an effort could be made to divert it. Currently, NASA carries out the “Spaceguard Survey” to find NEOs greater than 140 meters in diameter, and this program was budgeted at $4.1 million per year for FY 2006 through FY 2012. In chapter 7, we'll learn more about asteroids, as well as other bodies in the solar system. Supernova It is in the darkness before dawn on July 4, 1054 A.D. Chinese astronomers are greatly excited by the appearance of a “guest star”—a new star in the sky, never seen before. As the Earth spins, half a day later on July 5, it is predawn in Navajo lands of what is now northern Arizona. The Anasazi, the “ancient ones” of this region, have spotted that same new star and are equally excited. The legacy of that “guest star” continues to this day. Each culture records the event in its own way. Anasazi etch a rock drawing—a petroglyph— on a rock overhang, depicting a circle next to a crescent Moon as it appeared to them that morning. Petroglyphs in Navaho Canyon and White Mesa, Arizona, as well as in the Chaco Canyon National Park of New Mexico are lasting records left by those Anasazi skywatchers. Mimbres Indian ceramic art from New Mexico also apparently depicted the supernova. Japanese and Chinese astronomers record that the “guest star” shone at least as bright as 4 Global Systems Science the maximum brightness of planet Venus. Some said it was about four times brighter than Venus, which was nearly a hundred times brighter than the brightest stars in the sky (aside from the Sun). It was visible in broad daylight for 23 days, and in the night sky it shone for 653 days to the naked eye. Its location was in a part of the sky that we now call the constellation Taurus. Six hundred and seventy seven years later, in 1731, a nebulous cloud was spotted in the constellation Taurus by John Bevis through his telescope. Charles Messier observed the nebula again through a telescope on August 28, 1758, and first thought it was a comet. He recorded it in a catalog he was compiling to help him distinguish comets which he eagerly sought to discover from “comet impostors” which stayed always in the same places in the sky. In 1844, the 3rd Earl of Rosse, at Birr Castle in Ireland, examined and made a detailed drawing of the nebula using his giant 6 foot diameter, 56 foot long telescope. The drawing of the nebula resembled a "Crab" which A Changing Cosmos Chapter 1: Cosmic Cataclysms has been the name of the nebula ever since. The Crab Nebula, or M1 in Charles Messier’s catalog of “comet impostors,” is in the exact same spot as the recorded position of the “guest star” of 1054. But it wasn’t until 1928 that Edwin Hubble measured the rate of expansion of the Crab nebula which led him to conclude that it had been expanding for about 900 years. The connection with the “guest star” of 1054 was clear. The “guest star” was actually a supernova—exploding star— and the Crab nebula, the supernova remnant, consists of the material ejected in the supernova explosion which has been spread over a volume approximately 10 light years in diameter and is still expanding at the very high velocity of about 1,800 km/sec. A supernova is an unimaginably powerful explosive event. It occurs when a very large star, over eight times the Sun's mass, has burned most of its nuclear fuel. When such a star's central fires go out, its core collapses releasing a huge amount of gravitational energy. A blast wave ejects the star's outer layers into space. The Crab nebula supernova remnant is incredibly bright, even though it looks quite dim at our distance from it—6,300 light-years. If we were to observe it from much closer, we would find that it puts out 1000 times as much visible light as our Sun. In 1948, the Crab nebula was found to be an even stronger source of radio wave radiation, and in 1964, observations with a high-altitude rocket showed that the energy emitted in X-rays by the Crab nebula is about 100 times more than that emitted in visual light. Taking into account all energies of radiation, the Crab nebula is putting out over 100,000 times more energy than our Sun. Another indication of the violence of a supernova explosion is that in some cases all that is left is a neutron star, which is an extremely dense object. It is denser than an atomic nucleus, concentrating more than the entire mass of the Sun in a volume only 30 kilometers (20 miles) across. On November 9, 1968, a pulsating radio source was discovered in the Crab nebula by astronomers using a 300-meter radio telescope in Arecibo, Puerto Rico. It pulses about 30 times per second! It’s that neutron star (pulsar) rotating 30 times per second and putting out 100,000 times more energy than our Sun. Chapter 1: Cosmic Cataclysms Image of M1, the Crab Nebula, the aftermath of a supernova explosion. From the Grasslands Observatory near Tucson, Arizona. If the Crab nebula pulsar is pumping out that much energy now, over 900 years after the supernova explosion, how much energy did the supernova release at its peak? At its brightest, a supernova can put out the energy of 10 billion suns! Could Our Sun Become a Supernova? Not a chance! Our Sun is not large enough to become a supernova of any sort. Besides, it will take another 5 billion years before our Sun's supply of hydrogen is depleted. At that time it will begin its dying process and eventually become a white dwarf with a surrounding shell of material much like the Ring Nebula (M57) in the constellation of Lyra! Can a Nearby Supernova Affect Us on Earth? Yes, if it’s near enough, within several dozen light-years. The intense influx of radiation could kill all life on Earth, sterilizing the planet. However, the odds of this happening are extremely small, especially in the short life-span of us humans. The most important effects of more distant supernovae are extreme excitement among astronomers who study supernovae to understand cosmology—the history and fate of the Universe. We will be learning a great deal more about supernova in chapter 3. Hands-On Universe 5 The Sun Engulfs the Earth If you have read the book or seen the movie “The Time Machine” by H.G. Wells, you may know of the eerie landscape that the Time Traveller (Alexander Hartdegen) saw near the end of his time travels. The passage here is from Chapter 11 of H.G. Wells’s The Time Machine as serialized in the New Review, cut from the book, but later published as a short story, “The Grey Man.” “I have already told you of the sickness and confusion that comes with time travelling. ...when I brought myself to look at the dials again I was amazed to find where I had arrived. One dial records days, another thousands of days, another millions of days, and another thousands of millions. ...the thousands hand was sweeping round as fast as the seconds hand of a watch— into futurity. "...I stopped. ...The time was midday, the orange sun, shorn of its effulgence, brooding near the meridian in a sky of drabby grey. "...I rose to my feet, and stared at this grotesque monster. I can only describe it by comparing it to a centipede. It stood about three feet high, and had a long segmented body, perhaps thirty feet long, with curiously overlapping greenishblack plates. It seemed to crawl upon a multitude of feet, looping its body as it advanced. Its blunt round head with a polygonal arrangement of black eye spots, carried two flexible, writhing, horn-like antennae. It was coming along, I should judge, at a pace of about eight or ten miles an hour, and it left me little time for thinking. "...When I gained the machine the monster was scarce fifty yards away. It was certainly not a vertebrated animal. "...But I did not care for a nearer view. "...As I drove on, a peculiar change crept over the appearance of things. The unwonted greyness grew lighter; then—though I was travelling with prodigious velocity—the blinking succession of day and night, which was usually indicative of a slower pace, returned, and grew more and more marked. This puzzled me very much at first. The alternations of night and day grew slower and slower, and so did the passage of the sun across the sky, until they seemed to stretch through centuries. 6 Global Systems Science "At last a steady twilight brooded over the earth, a twilight only broken now and then when a comet glared across the darkling sky. The band of light that had indicated the sun had long since disappeared; for the sun had ceased to set—it simply rose and fell in the west, and grew ever broader and more red. All trace of the moon had vanished. The circling of the stars, growing slower and slower, had given place to creeping points of light. "At last, some time before I stopped, the sun, red and very large, halted motionless upon the horizon, a vast dome glowing with a dull heat, and now and then suffering a momentary extinction. At one time it had for a little while glowed more brilliantly again, but it speedily reverted to its sullen red-heat. I perceived by this slowing down of its rising and setting that the work of the tidal drag was done. The earth had come to rest with one face to the sun, even as in our own time the moon faces the earth.” Wells described how our Sun might appear not after thousands of years, or even millions of years, but after a few billion years. Current theories for progression of the Sun in its lifetime predict that when the nuclear furnace at its core runs out of fuel, it will begin a stage of expansion and surface cooling that will make it huge and its A Changing Cosmos Chapter 1: Cosmic Cataclysms surface red—a red giant star. The surface could swell up big enough to engulf the current orbit of Earth. Even if the gravitational pull of the Sun will have weakened by then from loss of mass, so that Earth migrates to a larger orbit, Earth still will get hot enough for the oceans to evaporate to space, and our biosphere will be destroyed. The good news is the enormous time span before this particular fate occurs. Humans may not even be recognizable as humans by then, in terms of species adaptations. Understanding, Helplessness, and Empowerment Understanding the three ways that life on Earth is threatened can invoke various reactions. In the case of the threat of the Sun in its red giant stage, we are pretty much helpless for now, but not too many people are worrying a whole lot in any practical terms about what will be happening in 5 billion years. In the case of a nearby supernova explosion, we are also pretty much helpless, since protecting the Earth from a huge influx of planet-wide radiation is a bit much to contemplate in practical terms. However, we can learn about what the probabilities are for such a scenario, and for the time being, the likelihood of that kind of disaster is exceedingly low, almost vanishingly so. The likelihood of Earth being hit by a large body, such as an asteroid, is much, much higher than our being saturated by radiation from a supernova. It is nearly inevitable—only a matter of time, though we do not know if it will be today, tomorrow, or in many millions of years. But in this scenario, we certainly are not helpless. If we are able to detect a body that is hurtling towards Earth with enough advance warning, there are a number of strategies proposed to avert disaster. It's tempting to try blowing the thing up with nuclear weapons, a typical video game-style mentality, that unfortunately, at best, would create a number of smaller bodies that would still continue on their trajectories and impact Earth with devastating effect. Other ideas are mostly different ways of nudging the asteroid to deflect it into a path that will not strike Earth. This book is devoted to better understanding various astronomical ideas, many of which relate directly or indirectly with the challenge of early detection of "near Earth asteroids," as well as other intriguing aspects of our "changing cosmos." Chapter 1: Cosmic Cataclysms Find late breaking news and information about Cosmic Cataclysms at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Hands-On Universe 7 Chapter 2 2. Astronomers' Tools Astronomers are very limited in ability to actually visit and explore their objects of interest. Humans have personally visited only one other body in the cosmos other than Earth: the Moon. We have sent spacecraft to most of the planets in our own solar system and received treasure troves of data and information about those places, including their moons, some asteroids, and comets. But when it comes down to more distant objects—and most of the Universe—we basically have only the light we receive from those objects and our imagination and ingenuity to analyze and interpret that light. Fortunately, we are not restricted to visible light only. We have detectors for all types of electromagnetic radiation: infrared light, ultraviolet light, x-rays, gamma rays, and radio waves. Mapping Space and Time One of the simplest tools of astronomy is something to help find things in the sky: a star map. There are a wide variety of these, ranging from those ideal for beginning stargazers to highly detailed maps and computer programs for advanced amateur or professional astronomers. One kind of star map, the planisphere, is adjustable to show what the sky looks like any time of night and any time of year. Caution—it’s common and easy to confuse these terms: Rotate—think of something spinning on its own axis. Revolve—think of something orbiting (going around) something else. These terms are verbs, but similarly, people often confuse the corresponding nouns: rotation and revolution. 8 Global Systems Science Kyle Cudworth controlling the Yerkes Observatory 40" telescope—the largest refractor telescope in the world. Motion Defines Time Time often seems so subjective—while listening to a boring lecture, it seems like time drags on endlessly. When spending an enjoyable or exciting evening with friends, time flies. When we need to actually measure time, the sky is a great reference—it seems to move “like clockwork” with the different ways that the Earth is moving: Rotation—Earth spinning on its axis makes the sky seem to move from east to west. Revolution—Earth orbiting around the Sun makes the sky seem to shift each day so that the part of the sky is visible to us without the Sun blocking it in daytime Precession—the wobbling of the Earth’s rotation axis, so the direction that Earth's axis points in the sky slowly drifts over thousands of years— 26,000 years for one complete wobble. Earth’s axis currently points to within a degree of the star Polaris (North Star). In about 10,000 years it will point closer to the very bright star Vega, in the constellation Lyra. A Changing Cosmos Chapter 2: Astronomers’ Tools In the investigation on the next page, Star Maps, you can construct your own star map and use it not only to find things in the sky, but to show how the sky changes with time. Coordinates For Earth and Sky To roughly locate things in the sky, we can identify groups of stars, called constellations. But to specify exactly where an object is in the sky, we use celestial coordinates. Celestial coordinates are to the sky, as geographical coordinates (latitude and longitude) are to the Earth. Review of Geographical Coordinates The Earth’s spin determines special locations on Earth. The spin axis goes through the North and South Poles, and midway between them, is the equator. Latitude—To indicate how far north or south we are on Earth, we use degrees (°) of latitude. The equator is neither north nor south and is 0° latitude. Latitude lines range between 90°S, which is the latitude of the South pole, and 90°North, the latitude of the North Pole. Longitude—To indicate how far east or west we are, we use longitude in degrees. Longitude lines are perpendicular to the latitude lines and go from the North Pole to the South Pole. As Earth spins, longitude lines swing under the Sun “like clock-work.” A zero longitude line was arbitrarily chosen to go through Greenwich, England. Longitude lines are numbered to 180 degrees east of Greenwich and 180 degrees west of Greenwich. For telling more precise locations, each degree of latitude or longitude is subdivided into 60 minutes, often called minutes of arc (measure of angle, not time). Each minute is further divided into 60 seconds of arc. An apostrophe (') is the symbol for minutes of arc, and a quote mark (") is the symbol for seconds of arc. Example: San Francisco, California is 122° 26' west of Greenwich and 37°46' north of the equator. These geographical coordinates are abbreviated 37°46' N 122°26' W. Celestial Coordinates Long ago, people believed that there was a giant sphere to which the stars were attached—the celestial sphere. Imagine extending the Earth’s axis infinitely into space, north and south. It would pierce that sphere in two places: the celestial north pole and the celestial south pole. If Earth’s equator were extended infinitely outward to the celestial sphere, it would become the celestial equator. Even though we know there is no physical sphere out there holding up the stars, we still find it convenient to think of an imaginary celestial sphere to specifying locations of things in the sky. The “celestial latitude lines” are called declination. As with latitude on Earth, declination in the sky increases from 0°at the celestial equator to 90° at the celestial North or South pole. As with latitude on Earth, each degree has 60 minute divisions (') and each minute is further divided into 60 seconds ("). Chapter 2: Astronomers' Tools Right Ascension is the name of the celestial coordinate that corresponds to longitude on Earth. Unlike longitude, which is measured in degrees and minutes, right ascension is measured in hours and minutes. There are 24 hours of right ascension corresponding to the full sweep of 360 degrees around the celestial equator. Simple division will tell you that each hour of right ascension must be equivalent to 15 degrees of arc. As you might expect by now, each hour has 60 minute divisions (') and each minute is further divided into 60 seconds ("). Hands-On Universe 9 Investigation Using Star Maps Standing here on Earth which is rotating, we see everything in the sky wheeling around us once every 24 hours. Each object in the sky appears to move 15° westward every hour as Earth rotates. (15°/hr = 360°/24 hrs) Make “Uncle Al's HOU Sky Wheel” to demonstrate this motion. [Print the "Coordinate Sky Wheel" and "Sky Wheel Holder" from http://lhs.berkeley.edu/starclock/ skywheel.html.] Follow the instructions on the printed starwheel sheet, and when it is cut out and assembled, set the Sky Wheel for near the end of the school year, June 1, at shortly after sunset, say 9 p.m. Notice the Big Dipper is high in the sky and the tip of the handle is near Right Ascension 14 hours, which in turn points close to the word “Southern” in “Southern Horizon” on the Star Wheel Holder. The times on the Star Wheel Holder are always standard time, so you may need to take that into account if your clock is set to daylight savings time. Rotate the Star Wheel FORWARD 2 hours (to 11 p.m. standard time on June 1). 2.1 What Right Ascension line now points to the word “Southern” in Southern Horizon? 2.2 What constellation just rose, almost due east? 2.3 What constellation is setting in the northwest? 2.4 What constellation is closest to the zenith (highest place in the sky; center of the map)? Rotate the Star Wheel FORWARD by another 2 hours (to 1 am standard time on June 1). 2.5 What Right Ascension line now points to the “Southern” in Southern Horizon? 2.6 What constellation is closest to the zenith? 2.7 What constellation is rising, almost due east? 2.8 What constellation is setting in the west? Rotate the Star Wheel FORWARD another 2 hours (to 3 am standard time, June 1). 2.9 What Right Ascension line now points to 10 Global Systems Science the "S" in Southern Horizon? 2.10 What constellation is closest to the zenith? 2.11 What constellation is rising in the northeast? 2.12 What constellation is setting in the northwest? Notice that there is one star in the sky which does not seem to change its position ever. It's at the tip of the handle of the Little Dipper, (Ursa Minor) and is called Polaris, or the North Star. Now some more questions to test your Star Wheel driving skill: 2.13 What constellation is near the zenith on New Year's Eve at 11 p.m.? 2.14 In what month is the Big Dipper (Ursa Major) highest in the sky at midnight? 2.15 About what time is Leo setting (in the northwest) on the summer solstice (about June 21)? A Changing Cosmos Chapter 2: Astronomers’ Tools Earth Rotating on Its Axis and Revolving Around the Sun Rotating the Star Wheel can represent both rotation (spinning) of Earth and revolution (orbiting) of Earth around the Sun. To imagine Earth’s rotation, keep your attention focused on one date and watch the hours go by that date as you turn the wheel. To imagine Earth revolving around the Sun, keep your attention focused on a particular hour of the night and imagine that you are coming out each night to see that sky at that particular hour of night. You can then watch the days and months go by from the perspective of that particular time of night. The Sun appears to creep Eastward in the sky each day by approximately one degree, or about 30 degrees (2 hours right ascension) per month. 2.16 How many degrees does the sky shift in one month? The Trifid Nebula, the 20th entry in Charles Messier’s catalog, commonly referred to as M20. Photo courtesy Richard Bennion, Ewell Observatory, Belmont, CA. http://www.ewellobservatory.com Find Messier Objects Charles Messier, a French comet hunter, created a catalog of interesting sky objects that might look a little like comets, but are not. They are actually a variety of objects including star clusters, galaxies, and nebulae (clouds of gas). If you find a table that has the coordinates of the Messier objects, you can mark them on your own star map. For example, the Owl Nebula is a Planetary Nebula 1630LY from us, whose coordinates are RA 11h14.8m; DEC +55°01' 2.17 In which constellation is the Owl Nebula? You can download the HOU Messier Object Excel spreadsheets at http://www. handsonuniverse.org/activities/uncleal. You might choose to mark the BRIGHTEST Messier objects on your Coordinate Star Wheel, or perhaps the CLOSEST Messier objects. 2.18 Get image(s) of Messier object(s). In book(s) or searching the worldwide web, find Messier objects of the following types: nebulae (gas clouds), globular star clusters, open star clusters, galaxies. Print one for wall decoration or save for a computer screen display. Moving Planets, Asteroids, and Comets Most things we see in the solar system— planets, asteroids, and comets—generally move across the sky through the night along with the “fixed” stars. However, most of them very slowly drift relative to stars from west to east as they orbit the Sun. The movements of the planets range from Mercury’s fast orbit motion (as much as 2 degrees per day eastward in the sky) to Pluto’s slow orbit motion (about 1.5 degree per year eastward against the background stars). August 2007: Google announced the roll-out of its Google Sky software for exploring celestial objects. best if you make those marks in pencil so you can erase and update their positions as needed. Good ways to find planets include: • Get a “planetarium program” that computes celestial coordinates of planets. See http://astro.nineplanets.org/astrosoftware.html • Que Tal in the Current Sky -- http://currentsky.com • Magazines: Sky & Telescope or Astronomy magazine • Observers Handbook (Royal Astronomical Society of Canada) • Guy Ottwell's Astronomical Calendar (Dept. of Physics, Furman University, Greenville, S.C.) You can also get an ephemeris of the Planet's Coordinates which is a table of celestial coordinates pinpointing the object's location at specific time intervals as it moves in the sky. You can find an Ephemeris generator at the NASA Jet Propulsion Lab (JPL) website, http://ssd.jpl.nasa. gov/horizons.cgi. You can mark the positions of planets on your Coordinate Star Wheel, but since they change, it’s Chapter 2: Astronomers' Tools Hands-On Universe 11 Telescopes Since astronomical objects are so far away, detecting light from those objects is one of the most important ways we have to learn anything at all about them. For the most part, we can’t physically go out there and get samples of material or poke around. The first telescopes were built in the time of Galileo, in 1608, by Jan Lippershey, an eyeglass maker in an area of Europe that is now Holland. Two key functions of a telescope are (1) to gather light from dim objects and (2) to make things look bigger. These are two powers of a telescope: light-gathering power to make dim objects look brighter, and magnifying power to make distant objects look bigger. Generally speaking there are two types of telescopes: one type, called a refractor telescope, depends on a large lens of curved glass to gather light and focus the light towards a smaller lens (or system of lenses) called the eyepiece. The other type of telescope, called a reflector, depends on a large curved mirror to gather light and focus it towards the eyepiece. Today there are many types of telescopes, but most of the largest ones are reflectors—they depend on mirrors for light-gathering. Galileo Galilei, in 1609, was the first person to do serious observations of sky objects with a telescope. Galileo’s telescope was very simple: two lenses, one at each end of a tube. It was one of the first refractor telescopes. Telescope Timeline 1608 - Invention of the refracting telescope 1609 - Galileo Galilei builds his first refracting telescope 1668 - Isaac Newton constructs the first reflecting telescope 1672 - Laurent Cassegrain designs the Cassegrain reflecting telescope 1757 - John Dollond invents the achromatic lens 1789 - William Herschel builds a 49-inch (1.2-meter) optical reflecting telescope, located in Slough, England 1840 - Invention of astronomical photography — J.W. Draper photographs the Moon 1845 - Lord Rosse finishes the Birr Castle 72-inch optical reflecting telescope, located in Parsonstown, Ireland 1859 - Invention of spectroscopy (Kirchoff and Bunsen) 1872 - Henry Draper invents astronomical spectral photography and photographs the spectrum of Vega 1897 - Alvan Clark finishes the Yerkes 40-inch optical refracting telescope, located in Williams Bay, Wisconsin 1917 - Mount Wilson 100-inch optical reflecting telescope begins operation, located in Mount Wilson, California 1934 - Bernhard Schmidt finishes the first 14-inch Schmidt optical reflecting telescope Sir Isaac Newton and a replica of his reflector telescope 1941 - Dmitri Maksutov invents the Maksutov telescope 1949 - Palomar 200-inch optical reflecting telescope (Hale telescope) begins regular operation, located in Palomar, California 1979 - NASA Infrared Telescope Facility[1] 120-inch infrared reflecting telescope begins operation, located at Mauna Kea, Hawaii 1993 - Keck 10-meter optical/infrared reflecting telescope begins operation, located at Mauna Kea, Hawaii 1996 - Keck 2 10-meter optical/infrared reflecting telescope begins operation, located at Mauna Kea, Hawaii 2005 - First light at SALT, the largest optical telescope in the southern hemisphere, with a primary mirror diameter of 11 meters. 12 Global Systems Science A Changing Cosmos Chapter 2: Astronomers’ Tools Cameras and Detectors For about 400 years, people have been putting their eyes up close to the eyepieces of telescopes and enjoying magnificent views of heavenly objects. In 1727, Johann Heinrich Schulze discovered that silver nitrate darkened upon exposure to light— laying the groundwork for the invention of photography. In 1840, John William Draper started the discipline of astrophotography and made the first photograph of the Moon. Chemical reactions on photographic film are much more sensitive than the human eye, largely because many many photons can be collected from very faint objects in a photographic exposure of many minutes. Astrophotography can capture faint details that the eye cannot detect. Electronic photography was ushered in after the CCD (charge coupled device) was invented in 1969 by Willard Boyle and George E. Smith at AT&T Bell Labs. CCDs have the ability to transfer electric charge along the surface of a semiconductor and can receive charge by converting light energy to electrical energy through the photoelectric effect. In this way electronic images are created. The Keck Observatory has two telescopes, each with a 10 meter diameter primary mirror to collect light. The mirrors are each made of 36 hexagonal segments, each 1.8 meters wide. Courtesy W. M. Keck Observatory. Computers and Software With the advent of digital images of sky objects captured by CCD cameras on telescopes, the opportunity to use computers and image processing software is irresistible and in modern astronomy, indispensable. CCD chip being prepared for the NASA Kepler mission photometer. Chapter 2: Astronomers' Tools To study astronomical objects, we really have little more than the light from those objects to reveal their qualities and their essence. The light is made of up tiny packets we call photons, and in a CCD, each photon that strikes the CCD is converted into an electrical pulse that is stored and recorded in computer memory. The CCD is made up of rows and columns of tiny sensors that capture each tiny element of the picture. These picture elements are called pixels. Hands-On Universe 13 Investigation CCD Image Color Coding The images from the HOU telescopes are generated using a CCD camera. This kind of camera uses an electronic chip rather than the photosensitive chemical films used by regular cameras. The electronic chip is divided into many small areas that collect and record light. Each pixel on the screen is then given a number based on the amount of light from that particular area of the CCD chip. The more light at a pixel, the larger the number. The computer assigns a shade of gray or a color (when using a false color palette) at each pixel to produce the image you view on the screen. Below is a grid that simulates a CCD image with each pixel assigned a number between 0 and 9 to represent the amount of light at that pixel. Using only four different colored markers, develop a color coding scale for the ten different brightness values, 0 to 9. Indicate your color code in the Key at the bottom of the screen. Using your color scale, color each pixel with its proper color. Tape your sheet on the wall with everyone else’s and compare the result of using different color scales to represent the same data. Color Key Brightness Key <--- Make a copy of this grid 1. What is different and what is the same as you look at the collection of grids? 2. How does this activity relate to Min/Max settings in the image processing program? 3. Did anyone simulate a log scale in his or her color coding scale? If so, what difference did it make? If not, what difference do you believe it would have made? 4. Each coding scale can be thought of as a different color palette. Compare the grid images in terms of the pros and cons of using different palettes. 14 Global Systems Science A Changing Cosmos Chapter 2: Astronomers’ Tools Investigation Browsing the Universe There is a myriad variety of celestial objects. Astronomers delight in describing, classifying, and naming them, but also grapple with trying to explain why they look the way they do. Materials • HOU Image Processing (IP 2.0) software* • Images: browser1 through browser7; galaxy1 through galaxy8 • Pencil and paper for worksheet(s) * There are differences between old HOU IP and HOU IP 2.0. For details see http://www.handsonuniverse.org/ip/ Part I: Browse 2.19. Using each of the files, browser1 through browser7, use and familiarize yourself with the following HOU IP functions: See diagram of “HOU Image Processing Screen at the bottom of this page. • Open the image (file folder icon or “Open” in File menu). • Use Zoom Factor (in the View menu) or Zoom icon (in Tools Palette on left of screen) to enlarge the image. • Use Color Palette to change colors. • Drag the sliders. • Adjust Min/Max settings to change contrast, brightness and improve the appearance of the image. • Enter new values in the boxes at either side. • Try the Log scaling function (View menu). a. Get or create worksheets on which to write a detailed description of the appearance of each object. See sample worksheets on next page. b. For each object, make a hypothesis about what type it is and why it looks the way it does. The following are a few questions to think about. They may not all apply to each object, and you may choose other questions to explore. Min/Max values can be changed two ways: Is it solid or gaseous? Why is it dark or bright in certain areas? Are we looking at it from a side view or top down view? c. Pick your favorite of the images, select the best color palette for the image, adjust with the Min and Max tool, and set Log Scaling. Then record your settings for the best display of this image. Optional: Print out or save your image (both options are under the File menu). If your printer is a black and white one, you probably HOU Image Processing Screen should use the grey or igrey palettes. Zoom Open Sliders for Min-Max Min-Max Log Indicator Color Palette Image displayed here. This one is “browser3.fts” Chapter 2: Astronomers' Tools Hands-On Universe 15 2. My h Date: ______________ ypothe it looks sis on what ty p the wa y it doe e each objec browse t might s. r1: be Name: ____________________________ Worksheet: Browser’s Guide to the Universe 1. Detailed description of the appearance of each object. and wh y browse r2: browser1: browse r3: s t e e h s k le Wor browser2: browser3: browser4: browse r4: Samp browse r5: browse r6: browser5: browse r7: browser6: 3. Sett browser7: ings fo r my fa vorite image: Image file nam e: ____ ______ Min/Ma _____ x: ____ Color p ______ alette: _____ ______ Log sca ______ ling: ____ yes no Part II: Galaxy Features If you are fortunate enough to view the sky from a place far from city lights—the mountains, desert, or a remote area—you may see the largest and most beautiful sky object visible without a telescope: a large cloud-like band where there are many more stars than anywhere else in the sky. It is called the Milky Way, and astronomers have studied it, concluding that we live in a galaxy—a huge collection of billions of stars—that we call the Milky Way Galaxy. If we could go outside our galaxy, , it would look like this: In the 20th century, astronomers discovered other galaxies than our own, some larger than our Milky Way Galaxy, many smaller. There are different types of galaxies. Our own looks like a spiral galaxy. Spiral galaxies have a lot of dust and gas with stars forming in them. The famous Orion Nebula is a star-forming region in our own galaxy. Galaxies NGC 4636 and NGC 4697 Side View Top View 16 Global Systems Science These two images are really not the Milky Way— noone could have taken pictures like that of our galaxy because we live inside it. The right image is galaxy NGC 4565 and the left one is galaxy NGC 6946. Both photos courtesy Richard Bennion, Ewell Observatory, Belmont, CA. http://www.ewellobservatory.com A Changing Cosmos Chapter 2: Astronomers’ Tools in the “Galaxy Atlas” on the next page are not like spirals. They are simply a lot of stars clumped into the same region of space with no measurable interstellar dust or gas and no new stars forming now. They look like ellipses, so astronomers call them elliptical galaxies. Finally, there are peculiar galaxies. They are not spiral or elliptical. Sometimes galaxies crash into each other. The two peculiar galaxies in this unit, NGC 2146 and NGC 3034, are interesting because they have an enormous amount of dust and gas, so many stars are being born in them right now. 2.20. Describe and categorize eight galaxies. Get or create a worksheet like the sample on the page after the Galaxy Atlas. With your computer, open images galaxy1, galaxy2, etc. one at a time. [All images came from the Leuschner Observatory which is operated by the Astronomy Department of the University of California at Berkeley.]. On your worksheet, draw a quick sketch of the galaxy and compare it to the ones in the Galaxy Atlas. Decide whether it is a spiral galaxy, an elliptical galaxy, or a peculiar galaxy and record that on the worksheet. Then identify different features—see if any of the ones described below are present. Change the Min, Max, and Log settings to better bring out its features. Sometimes selecting Log and moving the ‘Min’ up a little is best with galaxy images. Changing color palettes is often very helpful, too. 1. Galaxy nucleus: Almost all galaxies have a nucleus. It is the bright central part of the galaxy. Galaxy nuclei are made of millions of stars and tons of dust and gas (if available). There is reason to believe there might even be enormous black holes in the center of galaxy nuclei. 2. Foreground Stars: You know what stars look like. They are the bright points of light in your image. Foreground stars are ones inside our own galaxy that lie between us and other galaxies. They are not part of the galaxy in the image. We have so many stars in our Milky Way galaxy that all of the images in our collection include foreground stars. 3. Spiral Arms: These are the features that give spiral galaxies their name. Only spiral galaxies have them. They are spiral shaped regions of dust, gas, and stars where star formation is occurring. 4. Bar: An interesting feature in many spiral galaxies is a bar running through the middle of the galaxy nucleus. While there are many theories about why this feature forms, astronomers are not completely sure why they do. There are many things in astronomy that are not known. 5. Ring: Similar to the bar, except that this looks like a ring around the galaxy nucleus in some spiral galaxies. Like galaxy bars, astronomers are not 100% sure why the rings form or why they form in some galaxies and not in others. 6. H II Regions (pronounced “H 2 Regions”): Areas of star formation. Young, hot stars heat the dust and gas around them, causing the dust and gas to radiate light. These appear as faint balls of light. Elliptical galaxies do not have H II regions because there is little dust and gas in these galaxies. HII Regions are made up of ionized hydrogen, the nuclei without its electron. 7. Dust Lanes: Dark bands of dust that block the light from a galaxy. If you look closely at the two peculiar galaxies, you will see that both have dust lanes. 8. Companion Galaxies: A galaxy that orbits around another galaxy the way the Earth orbits the Sun. These galaxies can interact with their parent galaxy and change the parent galaxy’s appearance. Galaxy Nucleus HII Regions Spiral Arm Bar Chapter 2: Astronomers' Tools Hands-On Universe 17 GALAXY ATLAS Spiral Galaxies: NGC 4321 (M100) N.A. Sharp/ NOAO/ AURA/NSF NGC 3351 (M95) NOAO/ AURA/NSF NGC 2841 NGC 5194 (M51) T.A. Rector and Monica Ramirez/ NOAO/AURA/ NSF Elliptical Galaxies: NGC 4636 Courtesy Digital Sky Survey M 82 Peculiar Galaxies: NGC 2146 NOAO/ AURA/NSF 18 NGC 4697 Daniel Verschatse Observatorio Antilhue Global Systems Science Mark Westmoquette (University College London), Jay Gallagher (University of WisconsinMadison), Linda Smith (University College London), WIYN//NSF, NASA/ESA A Changing Cosmos Chapter 2: Astronomers’ Tools ets Galaxy Date: ______________ Name: __________________ 5: Disp Sample Worksh e Answer Sheet lay: M in: ___ Name (s Max: _ ee Gala __ LogGalaxy Features Unit xy Atla s): ___ Feature ______ s used Rough Min: ___ Max: ___ Log ______Galaxy 1: Display: Sketch to iden _____ : tify gala ______ ______ xy: ___ ______ ______Name (see Galaxy Atlas): ____________________ ______ _____ Galaxy ______ Type:_ ______ Features used to identify galaxy: ______________ ______ _____ ______ Spiral A ______ rms B ______ _________________________________________ ar _____ Dust La Ring ne H Galaxy Type:______________________________ II Regio ns Compa nion G Spiral Arms Bar Ring alaxy Foregro Dust Lane HII Regions und Sta rs Companion Galaxy Foreground Stars Galaxy 6: Disp lay: M in: ___ Name (s Max: _ ee Gala Galaxy 2: Display: Min: ___ Max: ___ Log __ Log xy Atla s): ___ Feature ______ s used ugh SGalaxy NameRo(see ______ to iden ketch:Atlas): ____________________ _____ tify gala ______ ______ xy: ___ Features used to identify galaxy: ______________ ______ ______ ______ _____ Galaxy ______ Type:_ ______ ______ _____ _________________________________________ ______ Spiral A ______ rms B ______ Galaxy Type:______________________________ ar _____ Dust La Ring ne H Spiral Arms Bar Ring II Regio ns Compa nion G alaxy Dust Lane HII Regions Foregro und Sta Companion Galaxy Foreground Stars rs Galaxy 7: Disp lay: M in : ___ M Name (s ax: ___ ee Gala Galaxy 3: Display: Min: ___ Max: ___ Log xy Atla Log s): ___ Feature ______ s used Rough ______ to iden NameSk(see Atlas): ____________________ etchGalaxy _____ : tify gala ______ ______ xy: ___ ______ ______ Features used to identify galaxy: ______________ _ _ ______ ____ Galaxy ______ Type:_ ______ ______ _________________________________________ ____ ______ Spiral A ______ rms B ______ ar Galaxy Type:______________________________ _____ Dust La Ring ne H II Regio Spiral Arms Bar Ring ns Compa nion G alaxy Dust Lane HII Regions Foregro und Sta Companion Galaxy Foreground Stars rs Galaxy 8: Disp lay: M in: ___ Name (s Max: _ ee Gala __ Log xy Atla s): ___ Feature ______ s used ______ to iden _____ ti ______ fy gala ______ xy: ___ ______ ______ ______ _____ Galaxy ______ Type:_ ______ ______ _____ ______ Spiral A _ ______ rms B ______ ar ____ Dust La Ring ne H II Regio ns Compa nion G alaxy Foregro und Sta rs Galaxy 4: Display: Min: ___ Max: ___ Log Rough Sketch: Rough Sketch: Rough Sketch: Rough Sketch: Rough S Name (see Galaxy Atlas): ____________________ kFeatures etch: used to identify galaxy: ______________ _________________________________________ Galaxy Type:______________________________ Spiral Arms Bar Dust Lane Ring HII Regions Companion Galaxy Foreground Stars Part III: Image Data vs Image Display Pick any image of the ones you have opened, and open it twice. For example, if you open browser6 twice, you will get two windows titled browser6:1 and browser6:2. Choose an appropriate zoom size so that you can put the two windows side by side on your computer screen. a. In the View menu, there are two “bars” (Toolbar and Control Bar) and a palette (Tools Palette). Toggle these on and off to see what each name refers to. 2.20 With progressively larger and larger values for Zoom, at what zoom value do you clearly discern the individual picture elements—pixels—as little squares? Within each square, does the color or shading vary? Chapter 2: Astronomers' Tools Toggle these off and on And if you Zoom the image even more, does that color within each pixel change? b.About the Image Contrast—Min/Max tool: This controls the shading (or the coloring). If you set the palette color as Grey, pixels dimmer than Min will be black and pixels brighter than Max white. Everything in between will be a shade of grey. The software assigns shades of Hands-On Universe 19 grey or colors across the range of brightness between the Min and Max. Changing the values to make the range narrower brings out more detail in the parts of the image whose brightness is within that narrower range. c. Cursor Information: The (x,y) coordinates and the brightness in “Counts” for the cursor’s position are displayed in the Pixel Coordinates area of the Control Bar [Status Bar in old HOU IP]. Each (x,y) pair of coordinates identifies a specific location—picture element—or pixel for short. Control Bar Coordinates of Cursor Brightness in “Counts” 2.21 What are the dimensions of your “Display Region” (in pixels of the image displayed without scrolling)? Find the (x,y) coordinates of the bottom left corner of the window and then the (x,y) coordinates of the top right corner of the window. What are the window’s dimensions? 2.22 How do the dimensions of the Display Region change when you change the Zoom Factor to other values? Since you have two windows of the same image open, you can easily compare different zoom values. 2.23 Does the position image data (x,y coordinates in the status bar) of a particular star or feature on your image change when you change zoom value? Change zoom factor; find the star or feature; click the cursor on it, and read “x,y” in the Pixel Coordinates. 2.24 Does the brightness data (Counts in the Pixel Coordinates area) change when you change the image display functions with the Min/Max tool or the Log scaling check-box? • You can return to original Min-Max settings by selecting “Reset Default Min/Max” in the View menu. • Log Scaling (in View menu) brings out detail in dimmer parts of an image. You may need to adjust Min/Max to enhance the features you are interested in. Did you note the better detail in the lower part of the image? d.With Log Scaling in one image and normal linear scaling in the other, the two images look very different. The Log On/Off indicator is at the right end of the Control Bar. e. From Tool Palette, choose Color Palette Bar. With the same image in two windows, you compare changes in settings. The Display Controls Bar and Color Palette Bar only refer to the active window, the one with its title bar highlighted. The Color Palette Bar bar shows the range of colors in the active window and shows the relationship between the colors brightness in Counts. 2.26 When you change Min-Max settings or turn on Log Scaling, does relationship of colors and brightness shown in the Color Palette Bar change? If so, how? 2.25 Does the brightness data (Counts in the Pixel Coordinates area) change when you turn on Log Scaling? With two windows open with the same image, check brightness value in same place on each image. 20 Global Systems Science A Changing Cosmos Chapter 2: Astronomers’ Tools Detectors of Invisible Energies Even though we generally only have the light from astronomical objects to learn what we can from them, the amount of information contained in that light can be quite rich. Light energies can be described in terms of numbers of photons which is essentially brightness. But each photon also has an intrinsic energy that we usually describe in the language of waves: wavelength (how long the waves are) and frequency (how fast the waves vibrate). Lower energy photons are longer wavelength and lower frequency. Higher energy photons are shorter wavelength and higher frequency. Chandra X-Ray Observatory Colors of visible light range rainbow-like from red colors with long wavelengths (low frequency) to violet colors (short wavelengths). Higher energies than violet go from ultraviolet light to x-rays to gamma rays. Lower energy photons go from infrared light to microwaves to radio waves. Spitzer Infrared Observatory Astronomers have worked with engineers to create special telescopes and detectors for sensing these invisible energies. On this page you see some photos of some such telescopes. In the next chapter, we look in a bit more depth about how we can find out a lot about stars just by cleverly analyzing the light from those stars. The Greenbank Radio Telescope, West Virginia Photon Wavelengths—Electromagnetic Spectrum Find late breaking news and information about Astronomers’ Tools at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 2: Astronomers' Tools Hands-On Universe 21 Chapter 3 3. Cosmic Engines Photo of M42, Great Nebula in Orion, courtesy Richard Bennion, Ewell Observatory, Belmont, CA. http:// www.ewellobservatory.com At the beginning of this book, two of the three ways to “end life as we know it” were caused by dramatic changes that can happen at certain stages in the life of a star: at the end of a star’s life, it can swell up to enormous size in a red giant stage, or it can blow up in a supernova explosion. The beginning of a star’s life happens in a gigantic cloud of gas (nebula), many examples of which are found in Charles Messier’s catalog that we spoke of in the Investigation Using Star Maps in the previous chapter. The way that a nebula becomes a star is by the gravity force from each individual molecule in the gas cloud acting on other molecules causing the whole cloud to contract and shrink in size. In that process, molecules move faster and faster as the cloud shrinks, and as you probably know, faster moving molecules means hotter and hotter gas. This gravitational generation of heat energy is one of the fundamental “engines” of cosmic energy. When the gas gets to a certain “magic” temperature and pressure, and amazing thing happens—atoms start transforming and a star is born. A good place to study this is in the nearest star to us: our own Sun! What Is the Secret of the Sun’s Furnace? Using instruments called spectrometers that analyze the color of light from the Sun, astronomers found that it is composed mostly of hydrogen (70%) and helium (28%). Just 2% of the Sun is composed of heavier elements, and almost none of it is of the variety that will generate energy by radioactive decay. In 1920, at a meeting of the British Association for the Advancement of Science, Sir Arthur Eddington, who was already a famous English physicist, speculated about the source of energy that powered the Sun. His idea turned out to be an amazingly accurate prediction. In his presentation, he referred to measurements that had been made by his colleague, Francis Aston, which showed that when the nuclei of four hydrogen atoms were combined, or fused, to form one nucleus of helium, a bit of matter was apparently “lost.” This fact—plus his knowledge of the Law of Conservation of Energy—is what Eddington needed to speculate about the source of energy in the Sun. Aston has further shown conclusively that the mass of the helium atom is even less than the masses of the four hydrogen atoms which enter into it—and in this, at any rate, the chemists agree with him. There is a loss of mass in the synthesis amounting to 1 part in 120, the atomic weight of hydrogen being 1.008 and that of helium just 4. Now mass cannot be annihilated, and the deficit can only represent the mass of the electrical energy set free in the transmutation of hydrogen into helium, other particles and a release of energy. We can therefore at once calculate the quantity of energy liberated when helium is made out of hydrogen.... If, indeed, the sub-atomic [nuclear] energy in stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race—or for its suicide. 22 Global Systems Science —Sir Arthur Eddington, 1929 A Changing Cosmos Chapter 3: Cosmic Engines Eddington noted that the amount of energy liberated when mass is apparently “lost” can be calculated from Einstein’s famous equation: E = mc2 This equation means that a certain amount of energy (E) is equivalent to a certain amount of mass (m) multiplied by the speed of light times itself. The speed of light is about 300,000 kilometers per second. If you could go that fast, you could go around the world seven times in a single second. This is a very large number, and when it is squared it is even bigger! So the tiny bit of mass that is lost when four hydrogen atoms combine to form one helium nucleus is converted into a relatively large amount of energy. In the core of the Sun, about five billion kilograms of hydrogen is turned into helium every second. If 1/120 of that mass is converted to energy—that’s about 50 million kg/sec.—enough to account for the Sun’s production of energy. The Sun has been fusing hydrogen at this rate for about five billion years, and there is enough hydrogen fuel to keep the Sun “burning” for another five billion years. The combination of four hydrogen nuclei into a single helium nucleus is called nuclear fusion. The details of this process were worked out in 1938 by Hans Bethe in the United States and Carl von Weizsacher, working independently in Germany. It is now widely accepted that this process is at work in the core of the Sun, producing the energy that we need to live. In the late 1930’s, experimenters in the United States, England, and Germany were conducting experiments in which they created fission reactions in the laboratory. This was the time when Hitler was in power in Nazi Germany, and World War II was brewing. Scientists around the world saw the implications of nuclear power for the making of powerful weapons, and both the U.S. and Germany started research projects to create nuclear weapons. The first “atomic bombs” which used a fission reaction were dropped by U.S. warplanes on the cities of Hiroshima and Nagasaki in 1945, killing over a hundred thousand people. A much more powerful “hydrogen bomb,” which used a fusion reaction, was exploded at test sites on Pacific Islands by the United States Chapter 3: Cosmic Engines Image of the Sun from the TRACE spacecraft. Courtesy NASA. Nuclear Fusion Four protons This diagram (hydrogen nuclei) represents nuclear P P reactions going on in the core of the P P Sun. In reality, there is not one nuclear reaction, but a series of several different nuclear reactions, two of which are shown on the next page. Energy Helium nucleus in the early 1950’s, and shortly thereafter by the Soviet Union. The ensuing “arms race,” which occupied the world for the next few decades, gave chilling meaning to the last words in Eddington’s speech. Hands-On Universe 23 Particles Involved in Nuclear Reactions: Proton-proton nuclear reaction P P p = proton; positively charged; relatively massive; nucleus of the hydrogen atom. n = neutron; no charge; very slightly more massive than the proton. e- = electron; negative charge; very light (1/1840 times the mass of the proton). Deuteron-proton nuclear reaction P N P proton deuteron e+ = positron; antiparticle to electron—same mass but positive charge. N/P = deuteron; composed of a proton and a neutron bound together; has same positive charge as the proton; nucleus of deuterium (heavy hydrogen), an isotope of hydrogen. ν neutrino N P deuteron Sunspots Prominence y γ ra e+ positron ν = neutrino; massless and chargeless; very little interaction with matter; can pass through a whole planet or star without interacting. γ = gamma ray; a photon—packet of electromagnetic energy—much like ordinary light, but with much higher energy and very short wavelength. The prominences seem to float upwards from darker regions of the Sun, called sunspots. These sunspots look black from Earth, but from your current vantage point you can see that they are only slightly cooler and less luminous than the surrounding areas. Photosphere 3 P Helium N P nucleus Chromosphere (just above photosphere) Earth (to scale by size but not distance) Granulation Convection Zone Sunspots Core Sun’s Surface 24 Global Systems Science Radiation Zone Sun’s Interior A Changing Cosmos Chapter 3: Cosmic Engines Investigation Size and Scale of the Sun I. How Big is that Prominence? Materials: a. Use the HOU Image Processing software to open the image eclipse1.fts. This image of the longest total solar eclipse of the 20th century was taken in Hawaii in 1991 by an HOU team. Look around the rim of the Sun (often called the limb of the Sun) and see if you can find prominences—cloud-like or flame-like structures extending into the corona of the Sun (the Sun’s atmosphere). A prominence forms in a time period of about a day, but stable ones can last many days or even months. The bright eruption at the bottom of the eclipse1 image is an example of a prominence. • HOU Image Processing software • Images: eclipse1.fts hemma.jpg m51.fts jupiter.fts moon.fits ringnebula.fts fireballShoemakerLevy.fts fireballShoemakerLevy2.fts b. Try some color palettes such as RAIN.PAL and WRMB.PAL. Adjust the contrast using Min/Max so you can see the Sun’s rim. See if Log scaling helps. The big bright blob with the “spike” sticking through it is probably not a prominence. It’s more likely a feature of a total solar eclipse called the diamond ring effect, which happens either right at the beginning or end of totality (totality is when the Moon completely obscures the disk of the Sun). A tiny piece of the Sun’s surface is shining through and over-exposing some of the CCD pixels. c. Find the prominence that is nearly on the opposite side of the Sun from the diamond ring blob and zoom in on it to get as large a display of the prominence as possible that still fits on the screen (with no scroll bars on window). d. Using the cursor and the Pixel Coordinates, find the height in pixels of the prominence above the Sun’s rim. Also find the diameter of the Sun. e. Use the fact that the Sun’s diameter is 1,390,000 km to compute height of the prominence in kilometers. 3.1. How many Earths could fit under the prominence? (Earth’s diameter = 12,756 km) f. Another way to measure size is to use the Slice tool (in Analyze menu). Draw three slice lines: one across the prominence to show its width, one out from the Sun to show it height, and third one all the way across the Sun. Be sure your slice lines include parts of the image beyond the prominence. Chapter 3: Cosmic Engines g.Make a sketch of your 3 graphs. Drag in one of the graph windows so the distance and brightness coordinates are shown and a small box appears on the slice line in the image. Drag the cursor to the place on the graph corresponding to the left or outside edge of the prominence. In the image window does the box showing where you are along the slice also appear to be at the edge of the prominence? Often it does not. h.Increase the value for Max until the prominence almost whites out. Make another slice on top of one of slices you made in step g. 3.2. Compare these two Slice graphs. What is different? What is the same? What is the distance in pixels between the apparent edge of the prominence in the image and the edge shown on the graph? Hands-On Universe 25 II. Measuring Plate Scale of an Image Each pixel on a CCD image, e.g. of the Sun, represents a very small portion of the sky and is colored or shaded to represent the amount of light received through the telescope from that part of the sky. The entire sky is like a 360° sphere surrounding us, and the field of view of the telescope covers a tiny angle on that sphere with each pixel of the CCD covering an even tinier angle in the sky. That angle determines a quality known as the plate scale of telescope-CCD system. The pixel angles are very small: seconds of arc (see box “What is an angle of 1 arcsec?). For instance, for a certain CCD camera on the 30-inch telescope at Leuschner Observatory near Lafayette, California, where most of the images for our investigations were taken, the plate scale was 0.99 arcsecs/pixel. Each pixel on those images is nearly 1 arcsec/pixel in angular size. When we got a new CCD camera to put on the 30-inch telescope, the plate scale of the new system became 0.67 arcsecs/pixel. With that new system, each pixel on the image is 0.67 arc seconds in the sky. Using Angles to Measure Size: The Small Angle Approximation The angle covered by an object depends on both its actual size and the distance to the object. Consider the diagram at right that shows a circle with radius (r) representing the distance between the observer and an object. The width (or size) of the object is D, and q is the angle subtended by the object. The arc length subtended by the object is s. The arc length of a full circle is the circumference (2πr). The angle q may be expressed in degrees, which most people are familiar with. But another unit of angle is the radian. The angle q is one radian when arc length s = radius r, or s = r. Since 360° = 2π radians, that means 1° = 2π/360 radians = 0.017 radians and conversely, What is an angle of 1 arcsec? 1° is 1/360th of a circle 1° = 60 arc minutes (written 60’) 1’ = 60 arc seconds (written 60”) therefore 1” = 1/3600°, which is a VERY small angle. The angle covered by a star or even a galaxy is much smaller than a degree. Size of astronomical objects are usually measured in arc seconds and occasionally in arc minutes for very large objects. Some of the largest objects are the Sun and Moon, both of which are about 1/2 degree (30 arcminutes) in diameter. The angle q is one radian when the arc length equals the radius, or q s=r s D r 1° = 0.017 radians 1 radian = 57.3° 1 radian = 206,265" 1 radian = 57.3° = 206,265” The relationship between s and r can be written more generally in terms of any angle q that is measured in radians: s = r x q when q is measured in radians. As q becomes smaller, the arc length s has less curvature and can therefore be approximated by a straight line of length D. When q is much less than 1 radian, the lengths of D and s become almost equal, which gives us the Small Angle Approximation: D=rxq or Small Angle Approximation: For very small angles s ≈ D and the angle in radians is roughly equal to the ratio of the width of the object to its distance away q = D/r where r is the distance away from the object, D is the size of the object in the same units as r, and q is the angle in Observer q radians. Object D r 26 Global Systems Science A Changing Cosmos Chapter 3: Cosmic Engines You need to be very careful to keep your units of measurement straight when working with plate scales and the Small Angle Approximation. In order to measure sizes of the objects on CCD images, there are four steps: 1) Measure the number of pixels covered by the object. 2) Use the plate scale for the image to calculate the actual angle in the sky covered by the object. 3) Convert this angle to radians. 4) Use the Small Angle Approximation to calculate the size of the object given its angle in radians and distance away. Find Plate Scale of eclipse1 In the image eclipse1 of a solar eclipse in 1991, the angle covered in the sky by both the Sun and the Moon is 1/2°. a. Use cursor readings in the Pixel Coordinates or use Slice under Analyze menu to measure the number of pixels across the width of the Moon in the image. b. Calculate the ratio of the angle covered by the Moon in the sky when looking at it with your naked eyes to the number of pixels covered by the Moon in the image. This is the plate scale of this image in units of degrees per pixel. c. Plate scales of CCD images are commonly expressed in arcsecs/pixel. Use the conversion factor, 1 degree = 3600” (A double quotation mark, “, is the common symbol for arc seconds) to calculate the plate scale of the image of the eclipse in arcsecs/pixel. III. Measuring Size on a CCD Image Open image hemma.png or hemma.gif. The image is of Hemma, HOU student/ assistant, sitting at her computer. You can use the Rotate or Flip option under Manipulation to make the image right side up. If your computer is slow, rotating it may take a few minutes. Astronomers usually look at astronomical images where you can’t tell which way is sideways. For this Earthly image, you may want to use the rotate function of your Image Processing software...or not. a. Use cursor readings in the Pixel Coordinates to determine the number of pixels in the width of the screen on Hemma’s computer. b. Given the following data: The height of the active area of Hemma’s screen = 9.5 inches The distance of the camera from the screen = 36 inches ...use the Small Angle Approximation to calculate the angle covered by Hemma’s screen as observed by the camera. (See the Measuring Size with Images Discussion Sheet for an explanation of the Small Angle Approximation). This angle is rather large for the Small Angle Approximation but will suffice for this activity. Chapter 3: Cosmic Engines c. Calculate the plate scale of the hemma image in arcsecs/pixel. (1 radian = 206,265”) Hands-On Universe 27 IV. Measuring the Size of Astronomical Objects In this activity, you may first need to do some image processing (using the Min/Max adjustment and Log scaling) to make sure you are measuring the entire width of the object. Open the following images one at a time and a. find object width or length in pixels b. use the plate scale to calculate the angle in arcseconds c. use the distance to find the actual size, assuming small angle approximation applies. A. moon.fts Object: any one of the craters Plate Scale: 0.45”/pixel Distance to the Moon: 3.84 x 108 m 3.3. Could a house fit inside this crater? Your city or town? B. jup1.fts Object: Jupiter Plate scale = 0.45”/pixel Average distance to Jupiter = 7.8 x 1011 m 3.4. How many times bigger is Jupiter than the moon crater you measured? C. eclipse1.fts Object: Sun Plate scale = 3.0”/pixel Average distance to the Sun = 1.5 x 1011 m 3.5. How does the size of the Sun compare with the size of Jupiter? D. 3ringnebula.fts Definition Object: the Crab Nebula (a planetary nebula; gas from a dying star) Plate scale = 0.63”/pixel L ight- ye a r : t h e distance light travels in one year Distance = 2.300 light years (ly) You need to convert the distance to the Ring Nebula from light years to meters: 1 ly = 9.5 x 1015 m. 3.6 How does the width of the Ring Nebula compare to the Earth-Sun distance? 28 Global Systems Science A Changing Cosmos Chapter 3: Cosmic Engines E. m51.fts Object: M51, a spiral galaxy Plate scale = 0.99”/pixel Distance to the galaxy M51 = 30 million ly 3.7a. How wide are the spiral arms in light years? 3.7b. How wide is the entire galaxy? 3.7c. How does this compare to the width of the Crab Nebula? Extra Challenge: Determine the field of view for one of the images used in this section (IV). The field of view is the angle covered by the entire image. V. Comet Crash Open image fireballShoemakerLevy.fts and flip it vertically. The fireball was made by a piece of the comet Shoemaker-Levy 9 in July 1994. The piece was called Fragment G, and it was probably about two miles (three or four kilometers) across. It hit on the back side of Jupiter, where no one could see it, but Jupiter’s very fast rotation (period = 10 hrs) brought it into view in only a few minutes. The fireball was visible for only minutes. This picture was taken with the largest telescope in the world, the 10-meter Keck telescope on Mauna Kea in Hawaii. 3.8 How big is that fireball? Are we talking about a bonfire or something really serious? How big is the fireball compared to the Earth? [Hint: Jupiter is 11 times the diameter of Earth.] Every object has energy by virtue of its motion—that’s called kinetic energy. Kinetic energy of an object depends on its mass and how fast it is moving. Specifically: E = (1/2)mv2 where E is energy; m is mass; v is velocity. Fragment G was moving at over 30,000 m/ sec, so the square of that is a huge number. The mass of comet Fragment G was also huge: about 100-trillion (1014)kg. So its kinetic energy was really huge. The energy released when Fragment G crashed into Jupiter was hundreds of times more than all the nuclear weapons on Earth -- all going off at once. Think what an explosion of that much energy would do to Earth. Open fireballShoemakerLevy2 and flip it vertically. The spots in the lower left were made by three earlier comet fragments. They are thought to be clouds of dust and sulfur containing gases left over from the explosion of rocky comet chunks. 3.11. How big are the spots? Jupiter’s famous red spot is to the right and above the three spots. It was there long before the impacts—first seen hundreds of years ago. Find late breaking news and information about Cosmic Engines at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 3: Cosmic Engines Hands-On Universe 29 Chapter 4 4. Fathoming Huge Distances Star Motion If our galaxy as viewed by beings outside it looks like a big spiral, might it not be spinning like a big pinwheel? Indeed it is. But since the galaxy is made of billions of stars (plus assorted gases, dust, and heaven knows what), that means for the galaxy to spin, each star must orbit the center of the galaxy. They don’t all move in perfectly synchronized orbits though, so from our vantage point stars seems to move very slowly with respect to each other. The motion has two components to it: lateral (sideways) movement and movement towards or away from us. The sideways motion is called proper motion, though no one seems to know anymore what’s proper about it. When we measure a star’s velocity towards or away from us, it’s called radial velocity (as in change of length of a radius line of a circle where we’re at the center and the star is on the circle). Distance To Things in Our Solar System For relatively nearby things, like airplanes, we can use radar waves to measure how far away they are. Radar waves are like the radio waves that your radios and TVs at home receive. Air traffic controllers at airports use radar systems to measure distances to airplanes. Radio waves are sent out, and they bounce off airplanes. The amount of time the wave takes to return tells the controller how far away the airplane is. The longer the time the wave takes to return, the farther away the airplane is. Radar at airports measure distances to airplanes that may be a few hundred kilometers away. Astronomical things are much farther. The most accurate distances to the Moon, Sun, planets and other objects in the solar system are measured by timing waves sent to and from spacecraft. Speed of those waves is 300,000 kilometers per second (same as the speed of light). At that speed, it takes about one and a half seconds for the wave to get to the moon, and another one and a half seconds to get back, so 30 Global Systems Science there is a distinct lag time in conversation when you’re talking by radio to someone on the Moon: 3 seconds. Rather than express huge distances in hundreds of thousands, millions, or trillions of kilometers, it’s handy to describe those distances in terms of the time it takes radio or light signals to travel that distance. A light-second is the distance that light or radio waves travel in one second. Light-second might sound like a unit of time, but don’t be confused—it’s really a unit of distance. In the case of the Moon, we could say that the Moon’s distance is about one and a half light-seconds away from Earth. Mars is usually over 100 million kilometers away, and as Mars orbits the Sun, there are times when it is over 15 light-minutes away from us. There would be about a half hour roundtrip delay time between us and someone on Mars. Neptune, in the outer reaches of the solar system, is over 4 billion kilometers away—over 3 light-hours away. A Changing Cosmos Chapter 4: Fathoming Huge Distances 4.1 If the distance to the Moon is about 1.5 light seconds, how far is that in km? Look up the actual distance to the Moon in km. How accurate is the statement, “The Moon is 1.5 light-seconds away from Earth?” Distance By Parallax The position of an object seems to change when you change your point of view. This is the basis for another distance measuring method. Imagine that your thumb is a “star” and hold your “star’ out at arm’s length. Look at your star against the background of the other more distant things. Without moving your arm or head, look at your star first through one eye and then the other eye. Does the star seem to shift position against the background stars? The shift in position is known as parallax. Now try holding your star closer by bending your elbow, so that the star is about half an arm’s length away. Do the same thing as before: without moving the star or your head, look at your star first through one eye and then the other eye. Does the star’s position seem to shift less than before? The parallax shift should be greater, the shorter the distance you make to your “star.” The first people who tried this observed stars from different cities very far from each other, but they saw no shift at all. The stars were too far away for any parallax shift in position to be noticeable. They were able to measure the parallax shift for the Moon hundreds of years before radar was invented. In 150 BC, the Greek astronomer Hipparchus used parallax to measure a distance to the moon that was only a percent different from the number we can measure today. Pretty good for someone 17 centuries before the invention of the telescope! Measuring the parallax of the planets required much better angle-measuring techniques, and it wasn’t until 1672 that French astronomers just barely succeeded in measuring the parallax of Mars, and at last we knew how big the solar system is. The Sun is 150 million kilometers away! Measuring distance to the Moon required a baseline distance hundreds or thousands of kilometers apart on Earth. But any baseline on Earth was not long enough for making a parallax measurement to determine distances to stars. Chapter 4: Fathoming Huge Distances Hands-On Universe 31 Investigation Parallax To see how parallax works, we’ll observe and measure the parallax angle of a relatively distant object such as a tree or a flagpole and use that angle to determine the distance to the object. Materials: ruler, meter stick, Parallax Diagram C Target (pole) Refer to the Parallax Diagram for these steps: B q b d A I. Locate a target object, like a pole or tree, whose parallax and distance you want to measure. 4.2 Make an estimate of the distance to the target object in meters, and record your estimate. This will allow you to appreciate how well you q' D can visualize distances that are beyond your reach. It will also help in determining whether your result at the end is reasonable or not. II. Find an area where you can lay out a baseline about 10 meters long with these qualities: (a) you can sight the target at approximately either end of the baseline, points A and B a. Hold the ruler in front of your eye and on the diagram, measure the distance (x) between C and D. (b) from near point A you can sight on the b.At the same time have a partner with a meter target and line up an easily seen object in stick measure the distance (y) from your eye the far distance, preferably a few miles or to the ruler you are holding. Have more than more behind the target, point C, and one pair of people do this measurement for (c) from the other end of the baseline, near the most reliable result. point B, you can line up the target with c. Compute the parallax angle another, easily seen object in the far q' = (x/y) * 57.3 degrees. distance, point D. 4.4. Calculate the distance, d, to the pole. Assume III. Mark positions A and B and measure the the angle is fairly small, so you can use the baseline distance (b) between A and B in following approximation: meters. It should be in the range of 5–10 d = b (57.3°/ q’) meters. Record that distance on the diagram 4.5. Compare your measured distance to the value (letter b). you estimated in question 4.2 above. Do you 4.3. Measure the parallax angle of the target believe your measured result is reasonable? by standing somewhere along the baseline Explain. where you can view both points C and D in the distance. The closer you are to the center of the baseline, the better, but any point along the baseline will work. With the help of a partner, measure the angle between points C and D (angle p’ on the diagram), as follows: 32 Global Systems Science 4.5 Which step of the procedure do you believe had the most potential for error? Without doing a major error analysis, approximately what percent error do you feel there is in your result of distance to the pole? A Changing Cosmos Chapter 4: Fathoming Huge Distances Investigations on Measuring Distances to Asteroids Two investigations, developed by HOU teacher Rich Lohman, on using the parallax technique to find distance to asteroids, Distance to Asteroid 1998wt and The Parallax of Asteroid “Austria,” are at the Staying Up To Date pages for A Changing Cosmos, Chapter 4: http://lhs.berkeley.edu/gss/uptodate/10acc Images for the investigation on Asteroid 1998wt are in the folder MoreTelescopeImages/AsteroidParallax Distances to Stars By Parallax After many failures in attempting to measure distance to stars by the parallax technique, a breakthrough came when astronomers realized the Earth itself changes position in space as it travels around the Sun. As the Earth travels around the Sun each year, we change our point of view by over 300 million kilometers! That’s the kind of baseline we need to see the parallax of a star. When astronomers take pictures of the same region of sky six months apart, some stars—the closest ones to us—change position! Astronomers tried to use parallax on the stars in the 15th, 16th, 17th, and 18th century: and they all failed. Even with the enormous baseline of the diameter of the Earth’s orbit, the parallax to the brightest (and presumably nearest) stars always came out to be 0 degrees. They were back to having to assume all the stars were infinitely far away. Finally in 1838 Friedrich Bessel, after a year and a half of observations of one star, 61 Cygni, succeeded in measuring the parallax to a star. The parallax was less than one 10-thousandth of one degree! No wonder it was so hard to measure. Bessel calculated that 61 Cygni, one of the nearest stars to us, was an incredible 25 TRILLION kilometers away. That’s 25 thousand billion kilometers! Measuring distance to a nearby star required a baseline distance the entire diameter of Earth’s orbit. The Light-Year As a Unit of Distance A convenient unit for describing such large distances is not kilometers,or even light seconds, light minutes, or light hours, but light years. Astronomers have found that the star which makes the biggest jump every six months is Alpha Centauri. It is “only” 10 trillion kilometers away. 4.6. How many light years is the distance to Alpha Centauri? How many light years away is 61 Cygni? The Parsec Distance Unit The technique of measuring distances to stars by parallax led to another convenient unit for expressing distance. The baseline for such measurements is the diameter of Earth’s orbit, or twice the radius of Earth’s orbit. The average distance from Earth to Sun is often called an Astronomical Unit or AU. A parsec is a unit of distance for which one parsec is the distance to Chapter 4: Fathoming Huge Distances an object that has a parallax angle of 1 arcsec with a baseline of 1 AU. The word, “parsec”, comes from a combination of “parallax” and “arcsecond.” 1 parsec (pc) ≈ 31 trillion km ≈ 3.26 light years Star Brightness and Magnitude For really faraway stars, yet another clever distance finding method had to be found. The next trick to determine star distances was to compare their brightness. If you observe two stars that put out the same amount of light and are equal distances away from you, the two stars appear to have the same brightness. However, if one of the stars is twice as far away from you, that star would appear much dimmer. Hands-On Universe 33 Investigation A Law of Brightness A basic physics lab activity using a light sensor to measure brightness of light source(s) at various distances. Materials: Computer light sensor or Photo cell and ohmmeter Light bulb(s) Meter stick • Hook the photocell to the ohmmeter, and check that the reading on the ohmmeter changes as light to the cell changes (you can do this by turning off the lights or by shielding the cell with your hand). • Place a lit light bulb in an otherwise darkened room. It is important not to have any background light behind the light bulb or objects obstructing light from the light bulb. • Hold the light sensor or photocell one meter away from the light bulb and take a reading of brightness from the light. 4.7. Record your light brightness reading, and then before taking additional readings at new distances, make predictions for what you would expect at two and three meters. Take readings at two and three meters, record your data, and compare these with your predictions. • Gather and record data for five additional distances. 4.8. Plot your data (there should be at least eight points) on a graph with distance on the horizontal axis and light reading on the vertical axis. Draw a smooth curve that approximately connects the points. 4.9. On the basis of your graph, which of the following relationships between brightness, B, and distance, D, can you rule out? (a) B D (b) B 2 D (c) B (d) B 1/D 1/D A.What is the slope of this line? 2 What function most matches this curve ? 34 Global Systems Science 4.10. Square each of your distance measurements. Plot light reading vs. distance squared. Draw a straight line through the points on the graph. B.What is the math function for the light reading in terms of the distance? A Changing Cosmos Chapter 4: Fathoming Huge Distances The Magnitude Scale An ancient Greek astronomer, Hipparchus, devised a system to classify stars according to their brightness. He divided all of the stars he could see on a dark, clear night into six groups with magnitude 1 stars being the brightest group and magnitude 6 stars being the dimmest. Hipparchus did not have a telescope back in those days, so the stars he classified were only those visible to the naked eye. Astronomers still use the magnitude scale to describe the brightness of stars. Since human eyes see light in a logarithmic fashion, the mathematics of the magnitude scale is based on logs. When astronomers considered the stars that Hipparchus must have seen when creating his magnitude scale, they found the magnitude 1 stars are about 100 times brighter than the magnitude 6 stars. In order to make this true mathematically, each change of one in magnitude must correspond to an increase in brightness by a factor of about 2.51 since 2.51 x 2.51 x 2.51 x 2.51 x 2.51 equals approximately 100. mag 1 = (2.51)1 times brighter than mag 2 -or- Ba = 2.51 x Bb when mb - ma = 1 mag 1 = (2.51)2 times brighter than mag 3 -or- Ba = 6.30 x Bb when mb - ma = 2 mag 1 = (2.51)3 times brighter than mag 4 -or Ba = 15.8 x Bb when mb - ma = 3 mag 1 = (2.51)4 times brighter than mag 5 -or- Ba = 39.7 x Bb when mb - ma = 4 mag 1 = (2.51)5 times brighter than mag 6 -or- Ba = 99.6 x Bb when mb - ma = 5 (B is brightness, m is magnitude, and subscripts a and b are for two stars.) By the same principle each half magnitude corresponds to a brightness factor of 1.6 (1.6 x 1.6 roughly equals 2.5). Some of the brightest stars in the sky were not visible in Hipparchus’ region, so new magnitudes had to be created to accommodate them. Thus, we now have negative numbers on the magnitude scale to describe very bright objects. When measuring a star on a CCD image, you get its brightness in Counts. To see the magnitude scale in terms of this brightness value, let’s assume a magnitude 0 star has brightness = 10000 (note: we are just using an arbitrary value to demonstrate the scale). Based on this brightness value, the following magnitudes would have the associated brightness: Magnitude Brightness -1 25000 0 10000 1 4000 2 1600 3 640 4 256 5 102.4 10 1.0 15 0.01 Chart: A Magnitude-Brightness Example Chapter 4: Fathoming Huge Distances The chart points out an interesting problem. The brightest star in the night sky in the Northern Hemisphere is Sirius, a magnitude -1 star. On the above scale Sirius would have a brightness of 25000, which is near the upper limit of the CCD and the image processing software. In the same image, with Sirius at the upper limit of the CCD, a magnitude 15 star or even a magnitude 10 star is so dim that the software would not even identify it as a star. To see dim stars you need to choose a longer exposure time but bright stars will be overexposed. Hands-On Universe 35 Investigation Star Magnitudes I. The Magnitude Scale Using magnitude scale definitions on the previous page, the following are examples of determining how many times brighter one star is than another: • A 10th magnitude object compared to a 20th magnitude object. A 10th magnitude object is 100 times brighter than a 15th magnitude object, and a 15th magnitude object is 100 times brighter than a 20th magnitude object. So a 10th magnitude object is 100 x 100 = 10,000 times brighter than a 20th magnitude object. • A 7th magnitude star compared to a 14th magnitude star. A 7th magnitude object is 100 times brighter than a 12th magnitude object; a 12th magnitude object is 2.5 times brighter than a 13th magnitude object; and a 13th magnitude object is 2.5 times brighter than a 14th magnitude object. So a 7th magnitude object is 100 x 2.5 x 2.5 = 625 times brighter than a 14th magnitude object. A 5th magnitude star compared to a 11.5 magnitude star. A 5th magnitude object is 100 times brighter than a 10th magnitude object; a 10th magnitude object is 2.5 times brighter than a 11th magnitude object; and a 11th magnitude object is 1.6 times brighter than a 11.5 magnitude object. So a 5th magnitude object is 100 x 2.5 x 1.6 = 400 times brighter than a 11.5 magnitude object. • A negative 5th (-5th) magnitude star compared to a 7th magnitude star is 100 x 100 x 2.5 x 2.5 = 62,500 times brighter. Now, you try a few: How many times brighter is: 4.11. A 5th magnitude star than a 10th magnitude star? 4.12. A 7th magnitude star than a 17th magnitude star? 4.13. A 3rd magnitude star than a 5th magnitude star? 4.14. A 3rd magnitude star than a 6.5 magnitude star? 4.15. A 12th magnitude star than a 22.5 magnitude star? 4.16. Our sun (-26 magnitude) than a 15th magnitude star? Ask the reverse question. Here are some examples. What is the magnitude of the star if: It is 100 times brighter than a 15th magnitude star. A difference of five magnitudes means a difference of 100 times in brightness. Also, a lower number means a brighter star, so the star must be a magnitude 10 star. It is 10,000 times dimmer than a 15th magnitude star. A difference of 10 magnitudes means a difference of 10,000 times in brightness. Also a higher number means a dimmer star so the star must be a magnitude 25 star. 36 Global Systems Science It is 250 times brighter than a 14th magnitude star. A difference of 6 magnitudes: 8th magnitude. It is 625 times brighter than a 9th magnitude star. A difference of 7 magnitudes: 2nd magnitude. Now you try a few. What is the magnitude of a star if: 4.17. It is 100 times dimmer than a 12th magnitude star? 4.18. It is 10,000 times brighter than a 12th magnitude star? 4.19. It is 625 times brighter than a 11th magnitude star? 4.20. It is 25,000 times dimmer than a -5 magnitude star? 4.21. It is 100,000,000 times brighter than a 5th magnitude star? A Changing Cosmos Chapter 4: Fathoming Huge Distances II. Comparing the Magnitudes of Stars It is a common practice in astronomy to compare the brightness of stars on the same image or on two different images. The ratio of brightness can be expressed as a difference in magnitudes. • Open the image Mgclust. The brightest star on this image has magnitude, m(v) = 8.0. • Using Find, get the brightness of stars in a small part of the image. Try another part to see if the range of dim stars is similar. 4.22 Knowing the apparent magnitude of the brightest star, use Equation 2 at the bottom of the box to the right to calculate the apparent magnitude of each of the stars in one of your samples. A spreadsheet is one way to do these calculations. 4.23 How much brighter is the brighter dim star than the dimmest? Calculate this two ways: one based on the difference in magnitudes and one based on the ratio of Counts. These two values are probably not the same. Why not? If we have two stars of brightness B1 and B2 and magnitudes m1 and m2, we know that if m1 - m2 = 1, then B2 = (2.5)1 x B1 and in general, if m1 - m2 = n, then B2 = (2.5)n x B1 Using log base 10: m1 - m2 = 2.5 log(B2/B1) [Equation 1] When comparing two stars on the same image, the ratio of Counts for those stars is equivalent to the ratio of brightness, so: m1 - m2 = 2.5 log(C2/C1) where C1 & C2 = Counts of star1 & star2. Solving for m1: m1 = m2 + 2.5 log(C2/C1) [Equation 2] III. Absolute Magnitude So far we have been dealing with apparent magnitudes, which are how bright stars appear to us on Earth. Absolute magnitude is how bright the star is intrinsically, independent of its distance away. This is related to luminosity of a star, which is the amount of energy it emits per second. The apparent brightness of a star 10 pc away is: (luminosity)/4π(10pc)2 Using the Equation 1 above: m1 - m2 = 2.5 log(B2/B1), we get m - M = 2.5 log [(L/4π(10pc)2) / (L/4πd2)] where m = the apparent magnitude of the star M = the absolute magnitude of the star L = the luminosity of the star d = the distance to the star in parsecs The absolute magnitude of a star can be obtained from the apparent magnitude if the distance to the star is known. Absolute magnitude is defined to be the apparent magnitude that a star would have if it were 10 parsecs (pc) from Earth. 4.24. Use algebra and the rules for logarithms to derive the following equation, called the distance modulus, for the difference between apparent and apparent brightness = (luminosity)/4πd2 absolute magnitude: The apparent brightness of a star can be calculated as follows: where d = the distance to the star and 4πd2 is the surface area of the sphere over which the light is spread. The absolute magnitude, M, is defined as the apparent brightness of a star 10 pc away. Chapter 4: Fathoming Huge Distances m – M = 5 log (d) – 5 4.25. If a star is 2000 pc away and has an apparent magnitude of 7.0, what is its absolute magnitude? 4.26. If the star measured in Part II is 1400 pc away, what is its absolute magnitude? Hands-On Universe 37 Cepheid Variable Stars as Distance Indicators In 1784 a star in the constellation Cepheus was observed night after night by John Goodricke, and he noted that the star became brighter and then dimmer. The fluctuation in brightness repeated over and over again approximately every five days. This was the discovery of the first Cepheid variable star. In 1908 at Harvard College Observatory, Henrietta Leavitt was examining many photographic images of two small galaxies orbiting the Milky Way, called the Magellanic Clouds. She was studying the Cepheid variable stars in the Magellanic Clouds and noticed a pattern in their brightness fluctuations: the brightest Cepheids had the longest fluctuation cycles and the dimmest stars the shortest fluctuation cycles. Since the Cepheids were all in the Magellanic clouds, all at the same distance from us, comparing their apparent brightness was equivalent to comparing their luminosity. Leavitt arrived at a general relationship between luminosity and period which she published in 1917. It is now called the period-luminosity relationship, illustrated in the diagram in the Cepheids investigation on the next two pages. The period-luminosity diagram allows an astronomer to infer the luminosity of a Cepheid simply by measuring the period of its brightness fluctuation. Since luminosity generally cannot be measured directly, knowing luminosity from the period of a Cepheid variable is incredibly valuable for determining distance. Leavitt’s discovery of the periodluminosity relationship is a milestone in astronomy. Before her research, no one had a reliable tool for measuring the distance to objects farther away than the closest stars. The technique for determining the distance of a Cepheid requires three basic steps: 1) Measure the period of fluctuation and infer the luminosity of the Cepheid. 2) Use a standard star to calibrate the image and determine the Cepheid’s apparent brightness. 3) Use the equation for apparent brightness to calculate the distance to the star, d: apparent brightness = luminosity/4πd2 To measure the period of fluctuation, the Cepheid must be observed at least every few nights for several weeks. The number of Counts measured for a Cepheid will change from night to night for two reasons: 1) the changing observing conditions and 2) the changing luminosity of the star. In order to get a plot of the Cepheid’s changing luminosity you must remove the effects of the atmosphere by including a reference star. Since the Cepheid star and the reference star are on the same image, the observing conditions are the same for both stars. If the observing conditions 38 Global Systems Science did not change from night to night, the reference star would appear just as bright each night. In general, observing conditions do change, so the number of Counts measured for the reference star will increase or decrease depending on how much light the atmosphere lets through. If the atmosphere blocks out a large amount of light on one night, both stars will appear dimmer; on a clear night, both stars will appear brighter. If the Cepheid had constant luminosity, the ratio of Counts between the Cepheid and the reference star would remain constant. A Cepheid is not constant, however. As the luminosity of the Cepheid increases because of internal changes in the star, the ratio of Counts measured for the Cepheid to the Counts measured for the reference star will increase. By measuring this ratio for each image, you can plot the true brightness fluctuation of the Cepheid. A Changing Cosmos Chapter 4: Fathoming Huge Distances Investigation A Cepheid Variable Star I. Plotting the Light Curve for a Cepheid A Cepheid was monitored for a 15-day time span, but on only eight of those nights were the skies clear enough to get good images. You are to measure the brightness of the star on each image and create a light curve for the star. A light curve is a plot with brightness on the vertical axis and time (days) on the horizontal axis. Perform the following procedure on each of the images listed below. The name of the file gives you the date of observation. If you want to try working may06cepheid, may08cepheid, may10cepheid, on data from other Cepheid may11cepheid, may14cepheid, may15cepheid, variable stars, look in the folder may18cepheid, may21cepheid MoreTelescopeImages/VariableStars Each file contains an image of the Cepheid star and a reference star observed on a given night. The Cepheid is the star on the left and the reference star is on the right. 4.26. Use Auto Aperture to measure the brightness in Counts of each Cepheid and reference star. Record the data in a table like the one shown on this page. 4.27. Find the Count ratio, Cc / Cr,, where Cc = the Counts of the Cepheid and Cr = the Counts of the reference star. 4.28. Plot your series of Count ratios and corresponding dates on a graph with axes like the blank graph shown on this page. Be careful to skip nights when dates are missing from the observations. 4.29. What is the period of this Cepheid? le b a le T p m a S le p am S Chapter 4: Fathoming Huge Distances Hands-On Universe h p a r G 39 II. Find the Luminosity of a Cepheid 4 . 3 0 . U s e t h e Pe r i o d Luminosity diagram to estimate Luminosity (V) of the Cepheid measured in Activity I. Note: Both axes are logarithmic scales and luminosity is given in solar units; e.g., 1000 means 1000 times the luminosity of the Sun. Period-Luminosity Diagram for Classical Cepheid Variable Stars 4.31. Use the value for the luminosity of the sun through a V filter to calculate L(V) of your Cepheid in Watts. L(V) of the Sun = 5.7 x 1025 Watts. III. Find the Distance to a Cepheid The apparent magnitude in V of the reference star is 8.0. From the Brightness Conversion Table, this is equivalent to an apparent brightness in V of 2.28 x 10-12 Watts/m2. 4.32. Calculate the apparent brightness of the Cepheid. 4.33. Use the luminosity in V for the Cepheid and the equation for apparent brightness to determine the distance, d, to the Cepheid in meters. (For the equation go to the Cepheid Variable Stars As Distance Indicators Discussion Sheet.) 4.34. Convert the distance to light years. 1 light year = 9.5 x 1015 m. We’ll find out more about uses of Cepheid variable stars in Chapter 9, The Universe Begins ... and Ends? 40 Global Systems Science The observations of the Cepheid were made through a Visible (V) filter. This filter blocks out almost all light except in the yellow-green part of the color spectrum. When you calculate the luminosity and apparent brightness of the Cepheid you must remember that these only refer to the amount of light coming through the V filter. This is fine for your measurements because you can compare them to other measurements taken through the same kind of filter. However, it is not valid to compare these values to the apparent brightness or luminosity of a star over all wavelengths. In this unit, all measurements are through the V filter. A Changing Cosmos Chapter 4: Fathoming Huge Distances Techniques of Distance Finding: the Cosmic Distance Ladder <--- see Chapter 9 Find late breaking news and information about Fathoming Huge Distances at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 4: Fathoming Huge Distances Hands-On Universe 41 Chapter 5 5. Color, Temperature, and Age Filters are used on telescopes to determine the brightness of an object in a specific color. One use of this information is to estimate the color of stars. Astronomers generally use a set of standard filters, meaning that the color of light each filter lets through is very well known. This is so one observer can compare data with another observer. To determine the color of a star, a combination of filters that will show a sharp distinction between stars must be used. The diagram on this page shows plots of brightness versus color for three stars. Vertical boxes are drawn to show the approximate position of red, yellow and blue filters. Astronomers generally use the yellow and blue filters to measure the color of stars because the difference of light through these filters changes significantly for different stars. The naming convention for filters is relatively simple: the blue filter is called B, the red filter is called R, but the yellow filter is called V. This is because yellow is in the center of the visible color spectrum. To determine the color of a star using filters, the B filter is used to measure the amount of blue light coming from the star and the V filter is used to measure the amount of yellow light. These two values are used to get the B–V index of the star: B–V index = (magnitude through B) – (magnitude through V) The B–V index uses magnitudes, which are units astronomers use to quantify brightness. For converting magnitude to brightness use the Brightness Conversion Table In the investigation Measuring the Color of Stars in the next few pages. Quick Tips for Using the Magnitude Scale Magnitude Tip #1: The magnitude scale is an inverse scale, meaning that brighter stars have lower magnitudes than dim stars. One tip to remembering this is to think about replacing the word “magnitude” with “class”. One might expect a first class star to be brighter than a second class star, just as a first magnitude star is brighter than a second magnitude star. Magnitude Tip #2: The magnitude scale is not linear. This means the change in brightness from one magnitude level to the next is not constant. In the magnitude scale, each level is 2.5 times brighter than the adjacent level. A magnitude 1 star is 2.5 times brighter than 42 Global Systems Science a magnitude 2 star and 6.25 (2.5 x 2.5) times brighter than a magnitude 3 star. This leads to some trickier mathematics; see Supplementary Activity 13: Magnitude Calculations in the Measuring Brightness module. Magnitude Tip #3: The magnitude associated with a given brightness depends on which filter is being used. The conversion table for magnitudes to brightness in Watts/meter2 has separate columns for each filter. Be careful to make sure you are looking in the correct column for the data you are seeking. A Changing Cosmos Chapter 5: Color, Temperature, and Age Investigation Observing Color and Temperature A star’s color is a direct effect of the temperature at its surface. To understand this look at an incandescent light controlled by a dimmer or rheostat. As the setting of the dimmer changes, thus changing the current to the light bulb and therefore the temperature of the light bulb filament, note how the color of the bulb is affected. 5.1. List the different colors you see in the light as you change the dimmer. 5.2. What color is the light when the dimmer is on high? 5.3. What color is the light at a middle setting? 5.4. What color is the light at the lowest setting? 5.5. At what setting do you think the light bulb is coolest? 5.6. At what setting do you think the light bulb is hottest? 5.7. What color would you expect a very hot star to appear to be? 5.8. Would a very hot star have a high or low B-V index? (See the Measuring the Color of Stars Discussion Sheet for an explanation of the B-V index.) 5.9. What color would you expect a relatively cool star to appear to be? 5.10. Would a cool star have a high or low B-V index? 5.11. Imagine you could double or even quadruple your distance away from a star. What would happen to the star’s: A. Apparent brightness? B. Luminosity? C. Color? Chapter 5: Color, Temperature, and Age Hands-On Universe 43 Investigation Measuring the Color of Stars In this activity you will determine the color of stars that have been observed with the Leuschner telescope. There are four different stars with two images of each, one using a blue filter (B) and one using a yellow or visible filter (V). These stars will be referred to as your target stars. For each target star there is also a standard star that was observed at nearly the same time so you can assume the observing conditions are the same. Given the known apparent brightness of the standard stars, you can calibrate the target stars to determine their apparent brightness. This procedure is explained in further detail in the Photometry Techniques Unit in the Measuring Brightness module. target star in B btarg1 btarg2 btarg3 btarg4 target star in V vtarg1 vtarg2 vtarg3 vtarg4 standard star standard star in B in V bstan1 vstan1 bstan2 vstan2 bstan3 vstan3 bstan4 vstan4 Perform the following procedure to get the apparent brightness of each target star through each filter. Record all of your data in the table provided. standard star bstan1 vstan1 bstan2 vstan2 bstan3 vstan3 bstan4 vstan4 apparent magnitude 8.0 7.0 9.2 7.2 7.8 7.5 7.0 7.0 5.12. Use Auto-Aperture to get the Counts for each of the stars. (In most cases the target or standard star is the only star in the image; if not, it is clearly the brightest star in the image.) 5.13. Use the Brightness Conversion Table to get the apparent brightness of each standard star. 5.14. Calibrate each target star using this fact: ratio of Counts = ratio of apparent brightness of the target and standard stars These ratios are equal because the two stars were observed at nearly the same time by the same equipment, so presumably under the same observing conditions. Note: There is one exception you must account for. The exposure time for bstan2 is three times longer than the exposure time for btarg2. This means the telescope collected three times more light from the standard star than it would if the exposure time had been the same as the target star’s. You must correct for this in your ratio. You can find the exposure time for any image yourself by selecting Image Info under Data Tools. Scroll down about a page or more and find “exp. time.” The time is given in seconds. 44 Global Systems Science 5.15. Use the Brightness Conversion Table at the end of this Investigation to find the apparent magnitude of each target star. Find the closest magnitude that corresponds to your value for apparent brightness. 5.16. Calculate the B–V index for each target star. 5.17. Use the Table on the next page to approximate the color and temperature of each target star. If your B–V index falls between two values in the table, estimate the answer. A Changing Cosmos Chapter 5: Color, Temperature, and Age le b a le T p m a S Table : B–V index, Temperature and Color Data for Familiar Examples for Main Sequence Stars Chapter 5: Color, Temperature, and Age Hands-On Universe 45 Brightness Conversion Table 46 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age Investigation How Filters Work Based on GEMS Color Analyzers activities and work by Elizabeth E. Roettger [http://www.nthelp.com/eer/ HOAcolorAstron.html], Vivian Hoette, and Kevin McCarron. Use colored filters to decode secret messages, look at rainbows, and learn how astronomers can decode information from the sky. Materials: • Filters - Roscolux: Medium Red #27, Kelly Green #94 or Dark Yellow Green #90, and Primary Blue #80 • Astronomy images: posters, slides, e.g. from ASP Splendors of the Universe slide set, or Kevin McCarron’s HOU Color Astronomy Page - http://faculty.oprfhs.org/kmccarron/ HOU/color/ • White and colored paper, colored objects/ fabric/clothing 5.18. Secret codes. Look at Kevin McCarron’s Visible Spectrum image page [http://faculty. oprfhs.org/kmccarron/HOU/color/spectrum. html] and look through red, green and blue filters to view it. Which filter shows the “secret message that McCarron hid in the words?” Then look at the rainbow/ spectrum at the top of the page through different filters. See if you can figure out why one color filter works best to reveal this secret message. Then, once you think you’ve figured it out, try making your own secret message will colored pens, crayons, or computer tools to see if your theory is correct. 5.19. What is an object’s color? What happens when you look at a colored object through different color filters? Objects reflect certain colors of light, and that’s why they look that color. 5.20. Color Astronomy. Look at images of astronomical objects (posters, slides or Kevin McCarron’s HOU Color Page) through the different filters. What are we seeing? Spectra In the 17th century, Isaac Newton discovered that white light, when passed through a glass prism, can be seen to be made of a spectrum of colors--red, yellow, green, blue, violet. This ultimately led to use of prisms and then grooved glass or plastic (diffraction gratings) to build instruments called spectroscopes, which are used to analyze colors of light from stars. Each element absorbs certain discrete colors of light, so if that element is present, it results in black lines appearing in a spectrum of light, known as a line spectrum. The spectra on this page, hydrogen and helium, the common elements found in stars, illustrate how line spectra can show us what stars are made of. To see spectra of more elements, see http://jersey.uoregon.edu/vlab/elements/Elements.html or http://www.colorado.edu/physics/2000/quantumzone/ Helium Hydrogen Chapter 5: Color, Temperature, and Age Hands-On Universe 47 Age of Stars—Stellar evolution We already spoke of the birth of stars from gravitational contraction of nebulae, or gas clouds. In the next chapter, we’ll speak of the most dramatic and violent possible death of stars. But in between birth and death, stars change slowly, and by examining millions of stars all at different stages in their lifetimes, we can put together a picture of what the stages of a single star’s lifetime must be. Hertsprung-Russell diagram (Using the HR Diagram) Between 1911 and 1913, two astronomers were working independently on the classification of stars and came up with very similar results. A Danish astronomer, Ejnar Hertzsprung, plotted stars according to their absolute magnitudes and spectral classes. An American astronomer, Henry Norris Russell, created a plot of luminosity vs. temperature for many stars. Their investigations were seen as roughly equivalent, and the Hertzsprung-Russell (HR) diagram is a result of their findings. Their goal was to clarify understanding of the life cycle of stars. The HR diagram on the next page is called a general HR diagram because it is based on stars of all different types from many different regions of the sky. The objective is to show the distribution of various types of stars and their relative quantities. To create a general HR diagram, many stars are observed at a given time, their luminosity and temperature are determined and those values are plotted. The HR diagram can be thought of as a snapshot plot of these stars at one time. A star’s position on the HR diagram is determined by its luminosity and temperature at the time of observation. Since HR diagrams of many different stars, in many different regions, observed at many different times all yield similar distributions, it can be assumed that the general HR diagram describes an average distribution of stars. More specific HR diagrams of a single star cluster are used to determine factors about that cluster such as the type of stars in the cluster and the distance or age of the cluster. Ejnar Hertzsprung http://www.phys-astro.sonoma.edu/ BruceMedalists/Hertzsprung/ Henry Norris Russell http://www.phys-astro.sonoma.edu/ BruceMedalists/Russell/ When examining a general HR diagram, notice that the stars are clumped into several groups. The broad line of stars extending from the upper left-hand corner to the lower right is called the main sequence. Most stars on a general HR diagram are on the main sequence because this line represents the luminosity and temperature that exists for most of a star’s life. After its hydrogen fuel is depleted, a star When a star begins to fuse hydrogen in its contracts and begins to fuse helium in its core. core, it assumes its place on the main sequence This can occur rapidly or gradually depending on and stays at that position until its hydrogen fuel the mass of the star, but in either case it causes runs out and it evolves into a later stage of its the star to expand to a greater radius than that of life. The main sequence lifetime of a star is the main sequence star. During the expansion the generally upwards of 90% of its total lifetime. star cools considerably. A low mass star that was The temperature, and accordingly the color, of a a yellow or orange main sequence star evolves star during its main sequence period are primarily to a red giant during this expansion period. It is determined by its mass. High mass stars are very red because it is cool, and it is a giant because hot so they are blue, while low mass stars are it has such a large radius. Similarly, a high mass cool and red. blue or white main sequence star evolves into a yellow or orange supergiant. 48 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age A red giant will undergo yet another phase of evolution where it sheds its outer layers leaving a very dense core of carbon. The outer layers drift off to become what is called a planetary nebula, which is a ring of burning hydrogen that looks like a smoke ring. The dense core is called a white dwarf. It is white because it is very hot, but a dwarf because it has a very small radius. In fact, a white dwarf can have the mass of the sun packed into an object about the size of the Earth. A white dwarf does not have enough mass to initiate carbon burning to produce more energy so it will slowly grow cooler and fade away. Facts of life (for stars): Stars have a life cycle: birth through death. Stars consume fuel (initially hydrogen) in their centers. The more massive a star, the faster it consumes its fuel. After all the hydrogen in a star’s core is consumed the star becomes brighter, larger, and redder/cooler. A Typical HR Diagram for a Large Population of Stars. Diagram by Richard Powell http://en.wikipedia.org/wiki/ Image:HRDiagram.png Chapter 5: Color, Temperature, and Age Hands-On Universe 49 Investigation HR Diagrams of Star Clusters [based on activity “Explore the Life Cycle of Stars using data from the Sloan Digital Sky Survey” by Jordan Raddick (Johns Hopkins University), Theresa Moody, and Dr. Wil van der Veen (New Jersey Astronomy Center)] To create a HR diagram with star brightness vs. color, astronomers measure a star’s brightness at two wavelengths, usually in the blue and yellow part of the spectrum. By comparing the amounts of blue and yellow light astronomers determine the stars color. To fairly compare star brightness we need to know how far away they are. However, for stars grouped in clusters, all the stars in the cluster are at about the same distance, so we can make fair brightness comparisons without knowing the actual distance. In this investigation, we’ll make three HR diagrams: one of “Field stars” (stars not in a cluster), one of a nearby “open cluster”, and one of a “globular cluster” above the plane of our galaxy. We will use data from the Sloan Digital Sky Survey, whose main goal is to obtain spectra for millions of galaxies and quasars (and some stars), but in the process, it acquires brightness and color data on everything. It uses a reflector telescope that is 2.5 meters in diameter and has a very wide field of view: about 3 degrees (6 full moon diameters) across. The telescope is actually stationary, and it takes images as Earth rotates so the sky appears to move by the telescope view. All Sloan Digital Sky Survey data is available on the free web site called SkyServer. Materials Computer with spreadsheet software (e.g. MS Excel) and WWW access, specifically to the SkyServer website http://skyserver.sdss.org Part A. Diagramming People [inspired by the activity “Life Cycle of Stars” from the NASA Ceres project, http://btc.montana.edu/ceres/html/EdActivities.html ] Look at the set of images of people on the next page. 1. Can you guess the sequence of ages of each of them? Going by only these pictures, copy the list of names and put a number “1” by the youngest, number “12” by the oldest, and assign 2 though 11 by the others in sequence from youngest to oldest. 50 Global Systems Science 2. What characteristics did you use in order to make your guesses? What physical characteristic data would you like to have in order to make the best attempt for a correct sequencing? A Changing Cosmos Chapter 5: Color, Temperature, and Age Lianna Bernardo Donna Pete Selena Margie Dan Alan Georege Indira Kingsley Reiko Chapter 5: Color, Temperature, and Age Hands-On Universe 51 3. Now look at the “WHA” (weightheight-age) Diagram of people. How would you describe the relationships of weight, height, and age as shown in the diagram? WHA Diagram [Weight-Height-Age] Part B. Getting Data from the Sloan SkyServer 1. Go to the SkyServer web site http://cas.sdss.org/ 2. Click on “Search” in the first column “SkyServer Tools” 52 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age Click on Search 3. Click on “Search form” (third bullet) 4. Click on “Launch the Search Form Tool” Chapter 5: Color, Temperature, and Age Hands-On Universe 53 5. Fill in the following [ra and dec are for Palomar 5 globular cluster]: Show me “stars” in the region “around” ra: 229.022 dec: -0.111 radius (arcmin): 4 Number of objects: click “All” Image Data: check “object IDs,” “RA and DEC,” “Magnitudes” 6. Then click “Generate Query” button 7. Select Output Format: “CSV” 54 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age 8. Then “Submit Query to SkyServer” 9. On “Opening result.csv window,” select “Save to Disk” Repeat steps 1-9 for the other target regions for “Open Cluster” and “Field Stars” Target regions: Name RA Palomar 5 229.02 DEC -0.11 Radius 4’ NGC 2420 21.57 14’ 21.57 4’ 114.59 near NGC 114.875 2420 Chapter 5: Color, Temperature, and Age Type Globular Cluster O p e n cluster Field stars Hands-On Universe 55 Part C. Make HR Diagrams with Spreadsheet Software 1. Open the CSV file with a Spreadsheet program, e.g. Excel 2. Make two new columns, one with formula g - r [example: column J: =E2-F2] and one with simply copy of r [example: column K: =F2] 3. Fill down to last row of data by clicking on upper left cell [J2] and Shift click on lower right cell [K1425 in this example] and filling down. ChartWizard Button 4. Select the two columns of data... 56 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age 5. Click on Chart Wizard 6. Choose XY (Scatter) then “Next” 7. Fill in Chart Title, e.g. “HR Diagram for Palomar 5” Value (X) axis: “Star Color (g-r) [labels the X-axis] Value (Y) axis: “Star brightness (r)” [labels the Y-axis] and click “Next” then “Finish” Chapter 5: Color, Temperature, and Age Hands-On Universe 57 8. Adjust the axes: Reverse the Y-axis, since magnitude scale is reversed (brighter stars have lower numbers). Set appropriate scales. 9. Repeat steps 1-8 for the other target regions (Open Cluster and Field Stars) 58 Global Systems Science A Changing Cosmos Chapter 5: Color, Temperature, and Age Part D. Analyzing the Diagrams What can you tell about the age of each cluster? Hint 1: Why would part of the Main Sequence be missing from one of the clusters? Hint 2: As stars age, their position on the HR diagram changes. They are no longer placed on the Main Sequence. They are now placed in the Giant and Supergiant groups. How would a cluster HR diagram look when the cluster first formed? How would this differ from a much older cluster? Hint 3: What happened to all of the large, bright blue stars on the Main Sequence of Graph 2? Going Further: Get FITS images of the target regions. 1. Go to Sky Server Tools and find the Navigate tool on tools menu. 2. Enter the coordinates for each of the target regions, and use zoom. 3. Click on the quick look tool on the right hand side of the page, and then click “explore”. 5. Sroll down to Corrected frames, and right click on the files next to “g” and “r”. For each file, choose “Save As”, and change the file extension to .fts. 6. For these target regions, the area is always about 10x14 arcmin. 4. Under PhotoObj in the left column, click on FITS. Find late breaking news and information about Color, Temperature, and Age of stars at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 5: Color, Temperature, and Age Hands-On Universe 59 Chapter 6 6. Dramatic Change in Stars We usually think of stars as very stable and constant things. Suppose you were out looking at the sky on a dark, starry night, and suddenly you saw a star that wasn’t there a moment earlier! You might think your eyes were playing tricks on you. You could check by taking a photograph of the region of the sky and comparing it to a photograph taken earlier of the same region. Normally, these photos would be roughly the same. Certain objects, such as planets, may have changed position relative to the background stars, and the brightness or size of the stars may appear different from night to night, but the arrangement of the stars relative to each other generally does not change over a period of nights, years or even centuries. A supernova could be an explanation for seeing a new star. The term comes from the Latin word “nova” meaning new, though ironically a supernova is actually the event associated with the death of a star—the unbelievably violent process that a very massive star undergoes when it dies. Many people think of M1, the Crab Nebula, remains supernovae as explosions, and in some cases this is true, but some stars of a supernova. Image from Ewell implode rather than explode when they die. Astronomers have studied Observatory, Belmot, CA. various types of supernovae and have created possible explanations for the processes that could cause such events. Certain types of supernovae can give important clues to the puzzle of the age, size and fate of our universe, as well as contribute to our evolving Most elements heavier than hydrogen and understanding of the structure of stars. helium are predominantly created inside stars Although the study of supernovae is a or in the process of the supernova explosion very active field in astronomy, theories are itself. These elements are ejected into space by constantly being challenged about the different supernovae and then reused to form new stars types of supernovae and the stars that produce and planets such as the Earth. The atoms that them. Currently more than sixty supernovae are make up almost every substance that you deal discovered each year, but often times they are with everyday, including the chair you are sitting sighted after the maximum peak of the light curve in, the food you eat, and even your body itself, so some of the scientific information is lost. were once inside a star. You are made up of star Astronomers have classified supernovae matter. into two kinds, Type I and Type II, based on the amount of hydrogen observed in the material surrounding the explosion of the star. Type I have Both amateur and professional astronomers no observed hydrogen, leading astronomers to actively search for supernovae, and they are believe the outside layers were already shed. Hydrogen is observed from Type II supernovae, so being discovered more and more frequently. they are generally believed to be explosions of Using the same basic strategy, they look for the higher mass stars. This theory is consistent with appearance of a new star. Supernova SN1994I was the fact that Type II supernovae are only found discovered based on images taken by Hands-On in spiral galaxies, and usually in the arms, where Universe (HOU) students at Oil City High School high-mass star formation is thought to be more in Pennsylvania. Supernova search is an area of prevalent, whereas Type I supernovae are found active research for HOU students. How does it work? in both spiral and elliptical galaxies. Searching for Supernovae 60 Global Systems Science A Changing Cosmos Chapter 6: Dramatic Change in Stars PHOTOMETRY Photometry is the process of measuring the amount of light received from an object. When you display an image using HOU Image Processing software, you can use the cursor to see the amount of light registered by each pixel in the image. This value is given in Counts. With the Auto Aperture and Aperture tools, routines add up all the Counts within a specific area of pixels to give the total Counts for a star. The routines are designed to subtract background light and give only the Counts created by the star itself. Definitions of Photometry words Counts - The measure of light that each pixel of the CCD receives from the star. This measurement is particular to the equipment used and to the atmospheric conditions during the observation. When we display an image, the grayness or color at each pixel is based on the Counts for that pixel. Apparent Brightness - The amount of light reaching Earth per second from a star under ideal conditions (as if there were no atmosphere). This is a standard value that anyone could obtain from their measurements after correcting for observing conditions. Units Watts/meter2. Luminosity - The amount of light emitted per second by a star. It is an inherent property of the star, unlike Apparent Brightness, and is independent of where the observations were made or what telescope is used. Generally the To get ready for the Investigation Finding a Supernova, you’ll need to know something about photometry—the measurement of light. Sometimes a supernova is so bright it can be spotted by eye by just looking at two images taken at different times. In fact, there is an amateur astronomer in Australia, a minister named Bob Evans, who can look at a galaxy and compare it with his memory of this same galaxy at a previous date. Very impressive. For most of us, however, this technique is beyond our capabilities. The best strategy is to compare images of the same object using image processing tools in order to detect the presence of a supernova. However, it’s vitally important that the images must line up and match perfectly in order for this strategy to work. There are 3 reasons images may not match: (A) Alignment. The telescope does not line up on the object the same each night, so images appear offcenter, or shifted with respect to one another. (B) Sky background light can vary significantly from image to image. (C) Exposure time and other observing conditions, such as cloudiness or haze, can change from night to night, so the apparent brightness of all the stars may seem dimmer or brighter. Chapter 6: Dramatic Change in Stars luminosity of a star cannot be measured directly but must be inferred from other characteristics of the star. The units for luminosity are Watts. Reference Star - A star whose apparent brightness and luminosity does not change from one night to the next. The apparent brightness value of the star, however, is typically not known. Standard Star - A steady star is like a reference star but with a known, agreed upon value of apparent brightness. Apparent Magnitude - A measure of apparent brightness commonly used by astronomers. The magnitude scale is inverse, meaning brighter stars have lower magnitudes. Absolute Magnitude - This quantity is analogous to the luminosity but is expressed on the magnitude scale. Light we are receiving from stars has traveled vast distances. Amazingly, the light remains virtually unaffected by the first 99.999999999999% or so of its journey. But the last tiny leg of the trip through the Earth’s atmosphere can reduce the light drastically and star brightness can differ from one observation to the next. Image processing software can correct all three types of mismatch of images through processes called (A) shifting (aligning), (B) Sky background subtraction and (C) Normalization. After the images are properly shifted, sky adjusted, and normalized, we’re ready for step D, comparing the images which can be done one of two ways: i. Subtraction: you can subtract one image from the other to examine the difference. If a significant variation has occurred, such as a supernova, it will be apparent in the subtracted image. ii.Blinking: switching the image display alternately from one image to another can make any object that has change nearly “jump out at you.” But before step D, let’s back up and take a careful look at how to prepare the images with steps A, B, and C. Hands-On Universe: 61 A. Aligning Files by Shifting In order to align two images so they are ready for subtraction you need to use the Axes (Centroid) tool in Data Tools and the Shift option in Manipulation. What happens when you shift a file? At right is data from a small section of an image file with brightness values (Counts) given for the pixel locations to illustrate the result when the image processor shifts a file “to the right by 2” In this case as the image was shifted to the right, the new columns created on the left were filled in with zeroes. There is an option in the software to select a “fill value” so that you can have new columns or rows filled in with a value that matches the background sky. Original File: 107 106 106 Differences in brightness may be due to changes in the background light level, called “sky”, such as the amount of Moon light. 50 60 52 100 90 52 102 100 55 108 108 108 50 60 52 Shift Right by 2: 0 0 0 0 0 0 B. Subtract Sky Background 108 108 108 107 106 106 Original File: 20 23 21 21 108 50 23 180 90 20 100 60 22 22 20 Subtract Sky value 20 from each pixel 0 3 1 1 88 30 C. Normalize Brightness To correct for differences due to change in exposure time, compare the Counts of a reference star (a star that is known to be of constant brightness) in each image. Find the “reference ratio” of Counts for the reference star in one image divided by the Counts for the same reference star in the second image. Then multiply the second image by the reference ratio. Reference ratio is often referred to as normalization ratio. 20 23 21 87 160 70 88 80 40 30 2 0 Reference File: 21 108 50 23 180 90 20 100 60 22 22 20 Multiply each pixel by reference ratio 40 46 42 42 216 100 46 360 180 40 200 120 44 44 40 In this case, normalization (reference) ratio is 2 To summarize the process for finding a supernova: A. Align (shift) the images to correct for differences due to telescope aim. Note: Steps A and B can be reversed, but normalization is best to do last, just before final subtraction/ comparison of the two images. B.Remove (subtract) background skylight due to ground lights and moonlight. Also, both steps B and D are C. Normalize the images to correct for differing observing conditions due to subtractions, but in B, the same count value (sky background) is haze or high thin clouds. subtracted from every image pixel D. Subtract the Reference Image from the new image. and in D, count value of each pixel Finally, identify any new light sources. in a reference image is subtracted from the corresponding pixel in the new image. 62 Global Systems Science A Changing Cosmos Chapter 6: Dramatic Change in Stars Investigation Finding Supernovae Here are a series of exercises on finding supernovae, starting with simple specially prepared images and progressing to real life image analyses. Materials • HOU IP • Images: m51nor, m51fake1, m51fake2, m51fake3, SNW, SNX, SNY, SNZ, m51img1, m51img2, and m51img3, snimg1 through snimg12 I. Comparing Images By Subtracting (Step D) In this first example m51nor is an image of galaxy M51 as it normally appears. m51fake1 includes a supernova that has been pasted into the m51nor image. Since they are nearly the same image, there is no need for Aligning the images (step A), Subtracting Sky Background (step B), or Normalizing Brightness (step C). To find the supernova, you can immediately go to step D: find the difference between these two files by subtracting one from another. Then you can locate the supernova in the Difference File. Fake supernovae are used in these first exercises to make it easier to learn to use the image processor tools. a. Open m51nor and m51fake1 with the contrast (Min/Max) adjusted to show the spirals. b. With m51fake1 highlighted, select Subtract from the Transform menu [Manipulation in old HOU IP]. For what you would like to subtract from it, click on Displayed Image and select m51nor. Click on Display Result in New Window and OK. c. With the new Untitled file window highlighted, click on the supernova and get its position and data about its increase in brightness by clicking on Auto Aperture icon in the Analysis area of the Tools Palette or selecting Auto Aperture the Analyze menu. b. First Subtract m51nor from m51fake2, and click on Display Result in New Window and OK. You will need this image at the end of this activity. c. Select Centroid (Axes in old HOU IP) from the Analysis menu, click on OK and box a reference star in m51nor, (a star that appears in both images). Repeat for m51fake2. 6.1. What is the increase in brightness for the supernova, in Counts? 6.2. Record the center (x,y) coordinates of your reference star in each image. II. Aligning The Images Before Subtracting 6.3. Calculate how much to shift m51nor so it matches m51fake2. Images of a patch of sky may be slightly shifted from one night to the next if the telescope has not been aimed exactly to the same set of coordinates each night. Before using the image processing Subtract tool, one of the images must be shifted so the two “match”. For this you use a second faked image. a. Open images m51nor and m51fake2. Adjust the contrast to show the spirals. Chapter 6: Dramatic Change in Stars right shift = x(fake image) – x(normal image) up shift = y(fake image) – y(normal image). A negative value means shift left or shift down. d.Now shift the normal image, with no supernova, so it is aligned with the fake image that has a supernova candidate. Use Shift in the Transform menu, enter your Offset values, and click on Display Result in New Window and OK. Hands-On Universe: 63 e. Verify that the shifted image lines up with m51fake2 by checking that the coordinates of the reference object are the same in both images. f. Subtract the shifted image from the fake image. 6.4. What is different between the two subtracted images, the one before aligning and the one after aligning? 6.5. Can you find the supernova? Record the position and brightness data. III. Adjusting for Brightness Differences In this section you will learn the two operations you must perform to correct for whole image brightness differences: Sky subtraction and Normalization. a. Open images: m51nor and m51fake3. Adjust the contrast to show the spirals. b. To be able to see how important the brightness adjustment steps are, subtract m51nor from m51fake3, without any brightness adjustments, and click on Display Result in New Window. Keep this image to compare with your result after the brightness adjustments. c. Select Sky to find the brightness of the background sky. e. Subtract sky value from each image. For each image use the ‘Number of Counts’ option and enter the respective sky value; choose “Display Result in New Window,” then OK. Sky is now removed from each image. Adjust brightness (normalization) in the two images. f. Using Auto Aperture, get the brightness value for a reference star that appears in both images. g. Calculate the Normalization factor, N, which is the ratio of brightness of the reference star in the two images: m51nor and m51fake3 (the ones with sky removed). h. Multiply m51nor (with sky removed) by N, Display Result in New Window, OK. i. Subtract this normalized image from the m51fake3 image (with sky removed). 6.6. What is different between the two subtracted images, the one before adjusting for brightness and the one after adjusting for brightness? 6.7. Can you find the supernova? Record the position and brightness data. Image of M51 from Ewell Observatory, Belmot, CA 64 Global Systems Science A Changing Cosmos Chapter 6: Dramatic Change in Stars IV. SN1990H Now look at a series of images of a galaxy to detect the presence of a supernova. The supernova is SN1990H, which was the 8th one discovered in 1990 (H is the 8th letter of the alphabet). The images were taken at two week intervals in the Spring of 1990. IV-1. What can you tell by looking at a single image? Open SNW with the contrast adjusted using Min/Max to bring out the spiral arms of the galaxy. Can you tell if there is a supernova? Supernovae are very bright objects, sometimes brighter than an entire galaxy. In this image, there are five or six very bright objects - are they all supernovae? Not likely. Objects that are also typically very bright include the galaxy core and foreground stars in our own Milky Way galaxy that lie in the same line of sight as the far off galaxy. For most galaxies, we never see single stars within the galaxy from ground-based telescopes — supernovae are the one exception. Galaxy cores and nearby stars tend to keep on being bright. A supernova, on the other hand, changes brightness over time, flaring up and then slowly fading over a period of a couple of weeks to a couple of months. 6.8. Write down the coordinates of objects you think are likely candidates to be SN1990H. IV-2. What can you tell by looking at four images? Open SNW, SNX, SNY and SNZ with the contrast adjusted to bring out the spiral arms in each galaxy. Drag the image windows around until you can see all four images at once. 6.9. Which bright object is the supernova? Write down its coordinates—note which image your coordinates refer to. Is it the one you A. Align the Images: guessed? 6.10. The images are out of order, in terms of • Get the coordinates for a Reference Star using Centroid (Axes) to drag a box around the when each was taken. What do you think is the foreground star you have chosen. Do this for proper order of W, X, Y, Z? (It is ambiguous.) the same star in each image. Explain your answer. IV-3. Subtracting Images To Find a Supernova. You did not need to use more refined tools to discover SN1990H because it stands out when you see all four images. However, that is not always the case. Now try the A, B, C, D process on these images. In order to make comparisons there needs to be both a Reference Image and Reference Star. A Reference Image is one without a supernova. Use SNX as the Reference Image. A Reference Star is a steady star, i.e. one with constant brightness. Choose one of the bright objects outside the galaxy that is presumably a foreground star in our Milky Way galaxy as the Reference Star. 6.11. Which star did you choose as your reference star? Chapter 6: Dramatic Change in Stars • Use Shift in the Transform menu to match all images to the Reference Image, SNX. Enter X and Y Offset values so that your Reference Star’s pixel location will be the same as its location in SNX. Refer to the Results window to get the coordinates of the Reference Star in each image. Enter offsets to two decimal places. B. Remove the background skylight: • Use Sky to get a median background sky Count for the whole image. • Use Subtract in the Transform menu. Enter for ‘Number of Counts’ the ‘Sky’ value listed in the Results window. This value is the mode - the most frequent brightness value in the image. After the subtraction the Sky value should be 0 in each image. Hands-On Universe: 65 C. Normalize the Images (correct for differing observing conditions, high haze, variation in exposure time): • Using the Reference Star, calculate the Normalization Factor for each non-reference image: (brightness of reference star in reference image) (brightness of reference star in new image) 6.12. What normalization factor did you compute for SNY? SNW? SNZ? • With the new image highlighted, go to Multiply in the Manipulation menu. For ‘Number of Counts’ enter the value of your Normalization Factor. This should make the brightness of the Reference Star the same in each image. Other objects should also have roughly equal brightness, except for the supernova, which is new. D. Subtract Images: • With the new image window highlighted, subtract the Reference Image from the new image using Subtract in the Transform menu. Click on Display Result in New Window. Adjust the contrast — you should be able to bring out a “lumpy” detail of black and white spots. Variations within each image account for why the subtracted image is not all blank except for the supernova. Look for a Supernova: Identify any new sources of light using Find in the Analyze menu. 6.13. Record the brightness of the supernova for each image. 6.14. Graph the brightness of SN1990H over time. This plot is called a light curve. Plot these dates along the x-axis: SNW: 5/2/90; SNX: 6/2/90;SNY: 4/19/90; SNZ: 5/17/90 and the brightness values from 6.13 along the y-axis. SNX was taken after the supernova had died out. Give it a brightness value equal to 0, which relative to its supernova brightness is a reasonable value. Sketch a curve to connect the points. V. Light Curve for SN1994i In the spring of 1994 several HOU students were studying M51, the spiral galaxy also known as the Whirlpool Galaxy. In early April, two girls at Oil City High School in Pennsylvania received an important phone call. They had serendipitously obtained the first images of a supernova in M51. The brightness of the supernova increases dramatically and then fades off until it is no longer visible. The rate at which the brightness increases and then fades is an indicator of what type supernova has occurred and what type of star is involved. Use images taken by HOU students to create and study a plot of the brightness of a supernova as it changes over several weeks. 66 Global Systems Science You’ll choose a reference star and use the A, B, C, D steps described earlier. • Open m51img1, m51img2, and m51img3. These are images of M51, the whirlpool galaxy. Scott Miller, an HOU student at Oil City PA requested the first image of M51, m51img1 on February 12, 1994. The core of the galaxy is the bright spot near the bottom of the image. The bright spot near the top is a companion galaxy. Heather Tartara and Melody Spence, Scott’s classmates, requested the second image, m51img2, on March 31, 1994, to further study the galaxy. Heather and Melody received some surprising news soon after obtaining their image. The image m51img3 was requested by Vincent A Changing Cosmos Chapter 6: Dramatic Change in Stars Prosapio, an HOU student at Alan B. Shepard High School in Palos Heights, IL, on April 7, 1994. • Use Log Scaling and adjust the Min/Max on the images to see more detail within the region of the core of M51 and try to find what all the excitement was about. It may be quite tricky. 6.15. Use drawings and words to compare the three images. 6.16. Approximately how many times brighter than the Sun is the supernova? The core of M51 (the bright spot in the center) is about as bright as a million Suns. Use Aperture to compare the brightness of the supernova to the core of the galaxy. Aperture asks you to specify a Star Radius and Sky Radius each time you use it. For this unit, you may use Star Radius = 7 and Sky Radius = 14. For more information on Aperture, Star Radius, and Sky Radius please refer to Supplementary Activity 16: Tools for Measuring Brightness: Auto Aperture & Aperture. 6.17. Use a new image of M51 requested by your class or a recent image of the galaxy from the HOU database. Compare the new image to the images from Spring of 1994. Describe your findings. • Open images snimg1 through snimg12. It is probably easiest to use one image at a time and repeat the procedure below for each one. These twelve images of the supernova were taken in April and early May of 1994. The date of observation and other information are listed under Image Info. To create a light curve you must use only images through the same filter. All these images were taken through the I filter, which lets through infrared light. • Find the night number by looking in Image Info and counting the number of days between the observation date and March 31, 1994. • Use the bright star at approximately 45° to the lower left of the galaxy core as a reference star. You may use Auto Aperture to measure the Counts for the reference star, but you should use Aperture for the supernova since it is so close to the center of the galaxy. The aperture tool allows you to specifically define the region for measuring brightness. • Divide the Counts for the supernova by the Counts of the reference star to get the Count ratio for each night. (See the Photometry Techniques Discussion Sheet for more about the Count ratio, BSN/BR as a measure of brightness changes.) 6.18. Make a light curve for SN1994i by plotting the Count ratio versus night number. 6.19. Compare your light curve with those on this page and infer the type supernova for SN1994i. Chapter 6: Dramatic Change in Stars Hands-On Universe: 67 Science of Supernovae Type I Supernovae Most stars in the Universe are found in multiple star systems, meaning that two or more stars are in a gravitational orbit around a common center point. When these stars are very close together the material from one star can spill over onto another star, greatly effecting the evolutionary process of each star. Current theories suggest that Type I supernovae occur in binary systems containing a white dwarf and a massive star. A white dwarf is the very compact remnant of a low mass star that has burned up all the hydrogen and helium in its core leaving a very dense remnant of mostly carbon. The outer layers of unburned hydrogen were blown off during a burst of helium fusion that created a planetary nebula around the white dwarf. A white dwarf is always less than 1.4 times the mass of the Sun. Any additional mass will cause the white dwarf to collapse and create a different type of remnant called a neutron star. When a white dwarf is part of a binary, mass can be exchanged between the white dwarf and its companion. Each star has an imaginary shell around it within which all matter is gravitationally bound to that star. Astronomers refer to these regions as the Roche lobes for the binary system (see figure 1). As the companion star evolves, its radius will expand due to thermal pressure. This may cause some of its outer material to overflow its Roche lobe and fall onto the white dwarf. The white dwarf gains more and more mass by this method until it reaches the critical threshold of 1.4 times the mass of the Sun, where it can no longer support itself. In a violent implosion, called a Type Figure 1 a) A star and its companion white dwarf within their Roche lobes. b) The star bloats into a red giant and its outer layers overflow the Roche lobes. The overflowing matter falls onto the surface of the white dwarf. c) The white dwarf implodes and ignites fusion causing a bright flash called a Type I supernova. Ia supernova, the white dwarf succumbs to the increased pressure and, in turn, heats up to the point where it can burn fuel again. This time the fuel is carbon. The ignition of the fuel results in a tremendously bright flash, which then fades over a period of days or weeks. Discoveries of these supernova have been made out to the edge of the visible universe. The critical threshold of 1.4 times the mass of the Sun is the same for all white dwarfs. This means that no matter what the mass or temperature was for the original star, it will implode with the same amount of fuel left to burn. Since the mechanism for ignition is the same and the amount of fuel is the same, it follows that the luminosity resulting from the rapid ignition is the same for all white dwarfs undergoing a Type Ia supernova. Astronomers call such an object a “standard candle”, meaning that its luminosity is known so we can use it as a point of reference from which to compare other objects. We can observe the apparent brightness of the supernova 68 Global Systems Science as seen from earth, and knowing its absolute brightness as a standard candle, we can then determine its distance away from us. Type I supernovae are often categorized as Type Ia, Type Ib, or Type Ic supernovae. The different letters refer to differences in the specific elements detected after the explosion and the rate at which its brightness fades. Theories that attempt to explain the differences among the various categories of Type I supernovae focus on the specific mass of the original star. It is thought that a Type Ib or Ic supernova may be caused by the remnant of a very high mass star, such as a neutron star that is part of a binary system. A Changing Cosmos Chapter 6: Dramatic Change in Stars Type II Supernovae High mass stars undergo even more violent explosions called Type II supernovae (see figure 2). High mass stars achieve much higher temperatures inside so they are able to burn heavier elements than low mass stars. A very dense core of iron builds up within the center of the star as a result of the burning, with the lighter elements in the surrounding layers. This configuration is sometimes referred to as an onionskin model because of the spherical shells of various elements. Through energy-producing nuclear fusion, only elements as heavy as iron can be produced. Any nuclear reactions producing heavier elements require an input of surplus energy. Therefore the star only continues to burn fuel until iron is produced in the core and then fusion stops. After the fuel runs out, the core cools to the point where the gravitational pressure causes the star to come crashing in on itself. The implosion is so strong that the outer layers of the star crash into the hard iron core and bounce back out with tremendous energy. This is called a shock wave. The shock wave ignites the material in the outer layers of the star and the result is a sudden explosion that can be one billion times as bright as the original star. The remnant of the core of a Type II supernova will either be a neutron star or a black hole, depending on the original mass of the star. Figure 2: a) In a Type II supernova the outer layers of a high mass star come crashing in and b) bounce off the dense core sending a shock wave outward. The intense brightness of a Type II supernova is caused by the burning of the lighter elements that are in the outer layers of the star. This material is thrust outward by the explosion, creating an expanding bright nebula or halo that can remain visible for thousands of years. The explosion releases such tremendous amounts of energy that the surplus energy required for nuclear fusion of elements heavier than iron is available. In fact, it is believed that supernova explosions may be responsible for the creation of all material heavier than iron or at least for providing “seed” iron elements that are the fuel for further nuclear and chemical evolution. This includes elements such as lead, zinc, gold, and silver. Chapter 6: Dramatic Change in Stars Hands-On Universe: 69 Variable Stars 6.20. The six graphs below are graphs of data (light curves) from four different stars. What is happening at each of these stars that is causing its brightness to change? A B C D E F What would happen with two stars orbiting each other (binary star)? What would cause brightness to change? What factors would affect the shape of the curve? 70 Global Systems Science A Changing Cosmos Chapter 6: Dramatic Change in Stars Investigation Eclipsing Binary Stars Many stars in the Universe are multiple star systems. If a binary star system (two stars orbiting each other) is oriented in space in a way so that the orbit plane is in line with us on Earth, then the stars alternately pass in front of and behind one another. If a star goes behind another star, it is said to be eclipsed (similar to how the Sun is eclipse by the Moon during a solar eclipse). Such a binary star system is called an eclipsing binary star. The American Association of Variable Star Observers (AAVSO) maintains a database of observations from many observers over many years. It is a rich source of information. Their Eclipsing Binary Observing Program is described at http://www.aavso.org/observing/programs/ eclipser/ 6.21. Find the longest and shortest period binary system. The most obvious thing that is different about such eclipsing binary stars other than brightness and type of star, is the time it takes for the stars to orbit one another: the period. Mine the data in the AAVSO database to see if you can find the shortest period binary system and the longest period binary system. It’s OK to coordinate your efforts with others to make things go faster. a. Go to the AAVSO website and pick subject star from the database. To use the database, you need to know the star name of the eclipsing binary star. A list of eclipsing binary names is at http://www. aavso.org/observing/programs/eclipser/ tom/starlist.html b. A useful gateway is the Published Times of Minimum Database at http://www.aavso. org/observing/programs/eclipser/ebtom. shtml which lists the times of all the eclipses that have been observed by AAVSO observers. When you enter a star name and click the “Get Data” button, a graph appears, but you might find it easier to use the text file (.txt) list that is available there also. c. The date/time used may seem odd to you— it’s Julian date, which is the time recorded in days and decimal fractions of days after a particular time in history: January 1, 4713 BCE. If you want to know the “normal” calendar date corresponding to any Julian date, us the Naval Observatory Julian Date Converter at http://aa.usno.navy.mil/data/ docs/JulianDate.php 6.22. Use information in the database to predict when there will be an upcoming eclipse of an eclipsing binary system and then request a series of images from a HOU telescope to record the event. Measure the brightness of the binary compared with reference stars nearby and then graph the data. If you do this for successive eclipses, you might see if one of the stars in the system is brighter or bigger than the other star by looking at the difference in drops in brightness and the shapes of the light curves that you graph. Light curves on the previous page will give you a sense of that. Finally, you may wish to analyze a series of images of a binary star that you can find in the folder MoreTelescopeImages/VariableStars/CepheidBDCas_ARO_AndEclipsingBinary. Find late breaking news and information about Dramatic Change in Stars, supernovae, neutron stars and black holes at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 6: Dramatic Change in Stars Hands-On Universe: 71 Chapter 7 7. Planet-Star Systems We wonder “Where did we come from, in the big scheme of things?” That leads to questions of how our planet began, which in turn leads to the question, “Where did our Solar System come from?” and “Where did the Universe come from?” That last question will be a focus of the last chapter in this book, but the first question is one that some people have been struggling with for a long time. Evolution of Solar System Models People in ancient civilizations observed the heavens with care and came to a number of conclusions that were excellent in explaining what they saw in terms of movement of the Sun, Moon, planets and stars. Babylonian astronomer-astrologers (Chaldeans) kept thorough clay-tablet records of eclipse observations covering many centuries, as long ago as 26 February 747 BC. They also knew that the lengths of the seasons are not equal. All early models of the Universe, based on obvious movements of things in the sky appearing to move around Earth, placed Earth at the very center of the Universe. Hipparchus Hipparchus, a Greek astronomer, geographer, and mathematician that lived between 147 BC and 127 BC used Chaldean records to develop good models for the motion of the Sun, Moon, and planets that predicted positions used by sailors for navigation. He was the first to compile a trigonometric table, which he used in devising solar and lunar theories that could reliably predict solar eclipses. He measured the differences in the length of the seasons through equinox and solstice observations, finding that spring lasted 94.5 days (spring equinox to summer solstice), and summer lasted 92.5 days (from summer solstice to autumn equinox). That was an unexpected result since the prevailing idea was that the Sun moves around the Earth in a circle at a constant speed. Hipparchus’ solution was to place the Earth not at the center of the Sun’s motion, but at some distance from the center— about 1/24 of the radius of the orbit. That model described the apparent motion of the Sun fairly well. Hipparchus Hipparchus created a star chart with about 850 stars and is perhaps most famous for the discovery of precession, the slow change in direction of the axis of rotation of the earth. He also made estimations of the distance from the Earth to the moon. 72 Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems Ptolemy Claudius Ptolemy, Roman astronomer, mathematician and geographer living in Alexandria, Egypt from approx. 87–150 AD established a model of the Universe based on the Greek model that would explain the motions of heavenly bodies well enough to be the standard for many centuries. Ptolemy’s model still assumed that the Earth was the center of not only the solar system, but the entire Universe—a geocentric theory. In Ptolemy’s system, everything orbits the Earth in the order Mercury, Venus, Sun, Mars, Jupiter, Saturn. For accuracy in predicting naked eye positions, it requires at least 80 epicycles, which are smaller orbit paths superimposed on the main orbits. The stars move on a celestial sphere around the planetary spheres. Claudius Ptolemy Nicolas Copernicus Christian Church doctrine based on Greek and Roman philosophers required a solid belief in an Earth-centered Universe. The idea of a sun-centered system had been proposed by Aristarchus of Samos around 200 B.C., but arguments of Greek philosopher Aristotle prevailed, when he refuted the Sun-centered system with three questions: (1) If the Earth spun on an axis, why didn’t objects fly off?; (2) If the Earth was moving (around the sun), why didn’t it leave behind the birds flying in the air?; (3) If the Earth was orbiting the sun, why didn’t the stars appear to change their position since they were being viewed from a different perspective (the 7.1 What’s wrong with Aristotle’s questions as reasons phenomenon of parallax)? This last phenomena, to believe in an Earth-centered universe? parallax, does occur, but is much too small to be seen without a telescope due to the extreme distance to stars. [See chapter 4.] Statue of Nicolas Copernicus. From “Copernicus and the Planet position predictions of Ptolemaic Church” http://filer.case.edu/sjr16/pre20th_europe_church.html model were getting worse and worse over the centuries. Polish astronomer Nicholas Copernicus (1473-1543 A.D.), actually a church official, favored a Sun-centered view of the Universe, yet he never publicly announced his views until he was old so as not to be branded a heretic by the Church, risking prison or even death. Copernicus’ fears were well founded, as witnessed by later notable proponents of Sun-centered systems, such as Giordano Bruno (1548–1600 A.D.) who was burnt at the stake as a heretic by the Roman Inquisition. Copernicus recognized that a Sun-centered— heliocentric—model could easily explain certain planet movements that were serious problems for the geocentric system. He organized the five planets that were known at that time in the order that we know they are in today: Mercury, Venus, Chapter 7: Planet-Star Systems Hands-On Universe: 73 Earth, Mars, Jupiter, Saturn. The moon orbits around the Earth, he stated, but the stars are distant and don’t revolve around the sun. Since the Earth rotates around its own axis, the stars appear to revolve around the Earth in the opposite direction. Earth moving around the Sun also explained retrograde motions of the planets much more easily than the epicycles of the Ptolemaic model. Alas, Copernicus still thought that the planets move around the Sun in perfect circles, which is not actually the case, so his model still needed to have epicycles—quite a lot of them—to make accurate predictions for the motions of the planets. http://www.library.usyd.edu.au/libraries/rare/ modernity/copernicus.html Copernicus’ work, On the Revolutions of the Celestial Orbs (published in Latin: De revolutionibus orbium coelestium), was not published until the year of his death and about 73 years later (1616) the Church placed it on its Index of Prohibited Books. Johannes Kepler’s Laws of Planetary Motion The problems and messiness associated with epicycles would not be overcome until Johannes Kepler (1571–1630 A.D.) came to the rescue. Kepler worked with renowned Danish astronomer, Tycho Brahe in Prague. Kepler was assigned the task by Tycho Brahe to analyze the observations that Tycho had made of Mars. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho’s data were the best available before the invention of the telescope and the accuracy was good enough for Kepler to show that Mars’ orbit would precisely fit an ellipse. Kepler inherited Tycho’s post as Imperial Mathematician when Tycho died in 1601. In 1605 he announced his first law of planetary motion. “In the center of everything the sun must reside; . . . there is the place which awaits him where he can give light to all the planets.” -Copernicus Kepler’s First Law: 1. Planets move in ellipses with the Sun at one focus. For a circle the motion is uniform as shown above, but in order for an object along an elliptical orbit to sweep out the area at a uniform rate, the object moves quickly when the radius vector is short and the object moves slowly when the radius vector is long. In work starting in 1602, Kepler calculated the position of the Earth in its orbit and after several years discovered that an imaginary line connecting the Sun and Earth sweeps out greater areas when the Earth is closer to the Sun, indicating Earth is moving faster in its orbit when it is closer to the Sun. Kepler stated his finding more precisely in his second law. http://kepler.nasa.gov/johannes/ Kepler’s Second Law: 2. The planet’s radius line describes [sweeps] equal areas in equal times. 74 Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems Kepler published his first two laws in 1609 in his book Astronomia Nova. It wasn’t until May 15, 1618 that he arrived at his third law. Circular and Elliptical Orbits Having the Same Period and Focus Kepler’s 2nd Law: The planet’s radius line sweeps equal areas in equal times. Kepler’s Third Law: 3. The squares of the periodic times are to each other as the cubes of the mean distances. This law he published in 1619 in his Harmonices Mundi. It can be stated mathematically as follows for any two planets labelled “1” and “2”: 2 T1 2 T2 = 3 R1 3 R2 where T1 = period of planet 1 T2 = period of planet 2 R1 = orbit radius of planet 1 R2 = orbit radius of planet 2 7.2 Assuming Earth’s period is 1 year and its orbit radius is about 150,000,000 km, using Kepler’s 3rd law, (a) what is Mars’ orbit radius if it takes 687 days to orbit the Sun and (b) how long is Jupiter’s year if it’s distance from the Sun is about 780,000,000 km? For elliptical orbit, speed decreases with distance from the Sun. For circular orbit, speed remains constant Illustration of Kepler’s Second Law of planetary motion. Here we see two orbits with the same focus point (“center”) semimajor axis (“diameter”), and orbital period: one a circle with an eccentricity of 0.0; the other an ellipse with an eccentricity of 0.8. Eccentricity is a measure of how “skinny” an ellipse is, with a circle having an eccentricity of “0” being the “fattest” kind of ellipse, and the very “skinniest” of ellipses having eccentricities approaching “1.” An animated version of this diagram is on this web page http://kepler.nasa.gov/johannes/ Galileo Galilei Italian mathematician, physicist, and astronomer, Galileo Galilei (1564–1642 A.D.) was a contemporary of Johannes Kepler and a kindred spirit, to boot. Using the newly invented telescope, Galileo discovered moons of Jupiter, mountains and craters on the Moon, phases of Venus, and sunspots. Some of these observations supported the Copernican heliocentric theory. In 1610, Kepler heard of Galileo’s discoveries, and though they did not have any rapid means of communication, like Internet, telephones, or e-mail, Kepler published a letter of support for Galileo: Dissertatio cum Nuncio Sidereo (“Conversation with the Sidereal Messenger”). He also obtained a telescope and published his observations of Jupiter’s satellites: Narratio de Observatis Quatuor Jovis Satellitibus (“Narration about Four Satellites of Jupiter observed”). These were enormous support to Galileo, whose discoveries were doubted or denied by many. Kepler encouraged Galileo to publish his discoveries and conclusions (see excerpts of letters on the following page), but when Galileo published papers that said that the Universe is Chapter 7: Planet-Star Systems Galileo Galilei Original portrait by Justus Sustermans painted in 1636. heliocentric, he was brought before the Inquisition and accused of being a heretic (1616) for opposing the Church’s teachings. He was cleared of the charges but told to keep quiet. When Galileo published a book in 1632 that indirectly supported the heliocentric theory, he was again called before the Inquisition and found guilty of heresy, forced to recant what he had said, and sentenced to life imprisonment. Because of his age, he was placed under house arrest and continued working and experimenting until his death on January 8, 1642. Hands-On Universe: 75 [Galileo to Kepler, 1597] ....Like you, I accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many of my reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured immortal fame among a few but stepped down among the great crowd (for the foolish are numerous), only to be derided and dishonored. I would dare publish my thoughts if there were many like you; but, since there are not, I shall forebear.... [Kepler to Galileo, 1597] .... You advise us, by your personal example, and in discreetly veiled fashion, to retreat before the general ignorance and not to expose ourselves or heedlessly to oppose the violent attacks of the mob of scholars.... But after a tremendous task has been begun in our time, first by Copernicus and then by many very learned mathematicians, and when the assertion that the Earth moves can no longer be considered something new, would it not be much better to pull the wagon to its goal by our joint efforts, now that we have got it under way, and gradually, with powerful voices, to shout down the common herd, which really does not weigh the arguments very carefully? Thus perhaps by cleverness we may bring it to a knowledge of the truth. With your arguments you would at the same time help your comrades who endure so many unjust judgments, for they would obtain either comfort from your agreement or protection from your influential position. It is not only your Italians who cannot believe that they move if they do not feel it, but we in Germany also do not by any means endear ourselves with this idea.... Be of good cheer, Galileo, and come out publicly. If I judge correctly, there are only a few of the distinguished mathematicians of Europe who would part company with us, so great is the power of truth. If Italy seems a less favorable place for your publication, and if you look for difficulties there, perhaps Germany will allow us this freedom. Source: Giorgio de Santillana, The Crime of Galileo (1955). Isaac Newton If Kepler provided the most accurate descriptions of planet orbits, it was not until the work of Sir Isaac Newton (1643 -1727 A.D.) that the orbit motions would be explained in his theory of universal gravity. Newton made many other discoveries and inventions including: • white light, when passed through a glass prism, can be seen to be made of a spectrum of colors--red, yellow, green, blue, violet • the first reflecting telescope • three Laws of Motion (see next page for complete description) In 1666, Newton made the breakthrough of imagining that the Earth’s gravity extended to the Moon. Using Kepler’s third law of planetary motion, Newton deduced that there is a force (known as centripetal force) holding the Moon (or any planet) in orbit, and that force depends on distance in a certain way. If the distance is doubled, the force becomes one-fourth as much; if distance is tripled, the force becomes one-ninth as much. In general, if distance increases by a factor of “n,” the force decreases by a factor of 1/n2, a relationship known as the inverse square law. Newton also showed that Kepler’s second law (that the line joining a planet to the sun sweeps out equal areas in equal times) can be explained by the fact that a body moving in an elliptical path and attracted to one focus must indeed be drawn by a force that varies as the inverse square of the distance. 76 Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems Newton ultimately concluded that this applies to all objects, and it became the Newton’s Laws of Motion Law of Universal Gravitation: Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects. The mathematical relation is: Newton’s First Law of Motion: I. Every object in a state of rest or in uniform motion tends to remain in that state unless an external force is applied to it. Fg = G (m1m2)/r2 Newton’s exact words were “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.” This is often called the “Law of Inertia” and is a concept that Galileo first elucidated. where: Fg is the magnitude of the gravitational force between the two objects, To understand Newton’s second law of motion, it’s helpful to know that • G is the gravitational constant, (a) a force is a push or pull on an object, • m1 is the mass of the first object, (b) an object’s speed in a particular direction is known as the object’s velocity (in other words, velocity is both speed and direction of motion), and • m2 is the mass of the second object, • r is the distance between the objects. The constant of proportionality G is known as the universal gravitational constant. It is termed a “universal constant” because it is thought to be the same at all places and all times and thus universally characterizes the intrinsic strength of the gravitational force. Given the law of gravitation and the laws of motion, Newton could explain a wide range of seemingly unrelated phenomena such as • apples falling from trees, • cannon balls falling to the ground at some distance after being fired, • the orbit of the Moon, planets, and the eccentric orbits of comets, • the causes of the tides and their major variations, • the precession of the Earth’s axis, • the subtle change in motion of the Moon caused by Sun’s gravity. Newton’s one system of laws of nature gave order to most of the known problems of astronomy and terrestrial physics. The work of Galileo, Copernicus, and Kepler was united and transformed into one coherent scientific theory. The new Copernican world-picture finally had a firm physical basis. Chapter 7: Planet-Star Systems (c) a change in an object’s velocity is known as acceleration. For example, if you are in a car that goes from a speed of zero to 50 mph in 5 seconds, you and the car have experienced an acceleration of 10 mph/sec. Newton’s Second Law of Motion: II. The acceleration of an object is proportional to the force on it and is in the direction of that force. Newton’s exact words were “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” Mathematically, Newton’s Second Law is often stated as follows: If a force (F) is exerted on an object of mass (m), then the object undergoes an acceleration (a) in direct proportion to the force: F = ma Newton’s Third Law of Motion: III. For every action there is an equal and opposite reaction. This law is exemplified by what happens in the recoil of a gun that people so often see in TV shows and movies. When the bullet fires off in one direction, the gun recoils in the opposite direction: “an equal and opposite reaction.” Hands-On Universe: 77 Investigation Tracking Jupiter’s Moons Galileo discovered the four largest moons of Jupiter in 1610, and they are often referred to as the Galilean Moons. He was using a simple telescope and a keen mind. It is a testimony to his observational prowess that out of all the stars and bright objects he could see in the sky, he noticed that Jupiter and these four dimmer lights, which he assumed were stars, were stretched out along a straight line. When he looked again he saw that the positions had changed from one night to the next, which is not what stars do. After repeated observations he determined that they were moons orbiting around Jupiter. Materials: • HOU IP • Images: jup20020122_0000.fts and jup20020122a through i I. Find the Moons • Open jup20020122a and jup20020122b with the contrast adjusted using Min/Max so the moons are visible. To help keep track of the moons, refer to them as # 1, 2, 3, & 4, starting from the bottom of the window. 7.3. Record your image settings. 7.4. Which Direction is Each Moon Moving? Make a sketch of the jup20020122a image, or use the Print option in the File menu, then draw an arrow at each moon showing whether it appears to be moving closer to or further away from Jupiter. You can tell by eye which direction the two moons shown closest to Jupiter are moving. A way to answer this question for the other two moons is to compare position coordinates. Use Find in the Data Tools menu with the default setting. Do this for both images. Adding two images together to make a double exposure is another way to compare the positions of the moons in two images taken an hour apart. • Starting with jup20020122a as the active window, use Add in the Transform menu (or + in the Tool Palette). Click on Displayed image and scroll down to select jup20020122b for what to add. Click on Display result in new window. • If you want to save this double image, select Save As from the File menu and enter a new file name including your initials, such as “jupab-jd”. • Use Find to get the brightness Counts for the Sky and the moons in all three images. 7.5. Adding the two images made the Sky about twice the value in either image. The moons, however, are not twice as bright. Why? 7.6. Which image did each moon come from? Compare moon coordinates in the double image with moon coordinates in one of the single images. Make a sketch, or Print out a copy, of the double image and draw in arrows from the jup5 position to the jup6 position of each moon. 78 II. Making a Double Exposure Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems III. What Happens to the Moons During 6 Hours? You need to collect data on the positions of each of the moons in each of the 10 Jupiter images, jup20020122a through i taken at 1 hour intervals. 7.7. For each image check the Image Info (under Data Tools) and record the date and time that the image was taken. Date is day/month/year and time is Universal Time, UT. Make a quick sketch of the image. Universal Time is the time in Greenwich England. • In order to see how each moon moves during the time sequence represented by the six images, combine all six images into one composite image. This may be done in several ways: by adding all of them together at one time; by adding them together one at a time and checking after each addition; by subtracting some and adding some. You may think of some other ways. Try whatever you like. Once again keep a careful record of all that you do, including the names of the files you create and how you create them. Remember, your goal here is to create an image or images that will allow you to see as clearly as possible how these Moons are moving. Here are ways to collect moon position data; you may think of more. 4Use the cursor to get the coordinates for the positions of each moon. 4Use Slice in the Analyze Tools menu to get the number of pixels between each moon and the center of Jupiter or between moon positions. (It helps to make the Slice window larger.) Drag the cursor on the Slice graph to display values for distance along the Slice in pixels and brightness in Counts. Corresponding pixel (x,y) coordinates and Counts are shown in the Status Bar - be sure you understand the differences between the (x,y) values for the Image window and the values shown on the Slice graph. 7.9. Identify on your sketch the orbits in which each moon is traveling by putting the number of the moon at its initial position in jup20020122a and in its last position in jup20020122i. 4Use Find to get cursor coordinates for all six positions of each moon, and use the Pythagorean Theorem to compute distances and speed. A hand calculator helps here. 7.11. Record the direction and speed of each moon. Your units of speed will be either pixels/ hr or mm/hr, depending on your method of collecting the data. 7.8. Make a sketch (or printout, if possible) of your composite image. If you sketch it, please take enough time so that it’s clear to someone else who looks at it. Share your results with other groups around you and see what approach they used that might be different from yours. This is particularly valuable as you begin to answer the questions below. Chapter 7: Planet-Star Systems 7.10. Which moon(s) appear to be traveling the fastest? Slowest? Does this depend on the portion of the orbit you are examining? Explain your reasoning. 7.12. How do you explain the apparent paradox that, despite the fact that the moons all move at roughly constant speeds around Jupiter in almost circular orbits, your data shows that the speed seemed to change? 7.13. Draw a top view of Jupiter and each moon in its 10 successive positions. Hands-On Universe: 79 IV. Interpreting Your Data The four moons Galileo discovered in 1610 are named Io, Europa, Ganymede, and Callisto. This table shows the period and orbit radius for each moon. The period is the time for one complete revolution. Moon One more piece of information: the further the orbit from Jupiter, the slower the speed of the moon. This is Io because Jupiter’s gravity weakens with distance. Europa 7.14. Who Is Io? For each moon, see if you can match the Ganymede name with its number. Use a process of elimination, Callisto crossing out numbers that are not candidates. Period (days) 1.8 3.5 7.2 16.7 Orbit Radius (km) 421,600 670,900 1,070,000 1,883,000 7.15. Explain how you decided on the name for each moon. The moon Io. The moon Europa. The moon Ganymede The moon Callisto 80 Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems V. The Mass of Jupiter By analyzing images of Jupiter and its moons, you can determine values for the variables D and T in the equation below and solve for the mass of Jupiter, MJ. MJ = 2 4π D G T2 Information Box 3 1 degree = 60 arc minutes: 1° = 60’ 1 arc minute = 60 arc sec: In this equation, D is the radius of orbit of one of 1’ = 60” Jupiter’s moons and T is the time it takes the moon to complete one orbit (the orbital period). G, the constant 1 pixel = 0.63 arcsecs (Plate scale for of universal gravitation, has a currently accepted value of telescope that took this image) G = 6.67 x 10-11 m3/kg-sec2. Note that this equation looks 1 radian = 57.3 degrees exactly like Kepler’s Third Law, as modified to incorporate = 206,265 arcsec Newton’s universal gravitation constant—it applies to any Distance from Jupiter to Earth in central body that is being orbited by a much less massive object; e.g., The Hubble Space Telescope orbiting the Earth, jup5-jup10 images: 6.63(108)km a moon around a planet, one of the planets around the sun, 1 km = 1000 m or the sun around the center of our Milky Way galaxy. In all these cases the mass of the orbiting body is insignificant compared to the mass of the central body, and as you can see, its mass is not even included in the equation. If the mass of the orbiting body were significant, it would be orbiting around a common center, and a different equation would be needed. 7.16. As a practice problem, use the equation above to find the mass of the Earth in kilograms given the following observational data. The period of the Moon around the Earth is 27.3 days and the mean radius of its orbit is 384,000 km. Use meters for the units of D and seconds for T. Determining the mass of Jupiter a) You need the distance data you determined in the Tracking Jupiter’s Moons Unit for the images jup5 through jup10. Distances need to be in pixels; go back to the Tracking Jupiter’s Moons Unit and redo this if your original measurements were in millimeters. b) For each image you also need to know the time of day of the exposure. Use Image Info in the Data Tools menu. Time is given as Universal Time, UT, which is the time at Greenwich, England. Universal Time is based on a 24-hour clock rather than our familiar 12 hour ones. 7.18. For all four moons in all the images, plot the pixel distance from the center of Jupiter versus the time the image was taken. 7.19. What does the plot you made above represent? 7.20. Use your plot to estimate the maximum distance for the moon that reaches its turnaround point; i.e., the moon that seems to stop getting further away from Jupiter. Your pixel distance from question 7.7 can actually be thought of as the angle subtended by imaginary lines connecting Jupiter and its moon. Line D is the radius of the moon’s orbit. We can use this “pixel angle” to find the radius, D, in km once we convert the pixel value of Angle A to units of radians. 7.17. Organize your distance and time data in a neat table before you proceed. Call the distances for the moons to the left and below Jupiter in the image negative (-) and the distances to the right and above Jupiter positive (+). Chapter 7: Planet-Star Systems Hands-On Universe: 81 7.21. Convert the pixel value you found above to radians using the Information Box on the previous page. 7.22. Use the Small Angle Approximation (pp. 26–29) to determine the radius of the moon’s orbit in kilometers. D= dxA where D is the radius of the moon’s orbit, d is the distance from Earth to Jupiter at the time the images were taken, and A is the angular distance of the moon from Jupiter in radians. This is the value for one of the two variables you need in order to solve for the mass of Jupiter. To determine the period of the moon, which is the other variable, T, you need to extrapolate from your data by sketching what you think the graph would look like with data for more hours. Use your extrapolation to estimate the time for one quarter of an orbit and for one half an orbit. 7.23. Use your estimates of time for 1/4 and 1/2 an orbit to determine the period of the moon. 7.24. Estimate how much possible error there is in your value for the period and explain how you made your error estimate. 7.25. You now have the period and radius for one of the moons. Use this information to determine the mass of Jupiter from the equation for MJ. Use meters for the units of D and seconds for T. 7.26. Find a data table and look up the currently accepted value for the mass of Jupiter. Determine the percent difference between the accepted value and your calculated (experimental) value using the following equation: % Difference = accepted value - experimental value accepted value x 100% Wrap Up: 7.27. Design an experiment that would allow you to obtain a more accurate value for the mass of Jupiter. Be specific. 82 Global Systems Science A Changing Cosmos Chapter 7: Planet-Star Systems How Do Star-Planet Systems Form? M42, the Great Nebula, star forming region in Orion To finish the story that was begun at the beginning of Chapter 3, a nebula — a huge cloud of gas and dust in space — starts to collapse, with gravity pulling the gas and dust together. The explosion of a nearby star (a supernova), may generate shock waves in space which squeeze the cloud and trigger the collapse. Just like a dancer that spins faster as she pulls in her arms, the cloud spins faster and faster as it collapses. Space Telescope Science Institute http://hubblesite.org/gallery/album/ At the same time, the cloud gets hotter and denser in the center and forms into a disk that gets thinner and thinner. When the center of the cloud gets hot enough, nuclear reactions start occurring and a star, like the Sun, is born. The star not only radiates heat and light but blows its own particles outwards, pushing out remaining gas and dust of the new star system with sort of wind called a stellar wind. Chapter 7: Planet-Star Systems Image of NGC 281 taken with NASA’s Hubble Space Telescope in October 2005 shows an example of dense knots of dust and gas in our Milky Way Galaxy. This is part of an emission nebula and star-forming region located nearly 9,500 light-years away in the direction of Cassiopeia. Image is a region about 6 LY across. The dark, opaque knot of gas and dust is an example of a “Bok globule,” cosmic dust and a concentration of elements responsible for the formation of stars. Hands-On Universe: 83 Giant planets, rocky planets, asteroids, comets, meteoroids. Meanwhile, particles have been colliding and sometimes sticking together in clumps, eventually forming planets and moons. Two main types of planets form: smaller planets of mostly rocky material (e.g. Earth, Venus, Mercury and Mars), and large planets made of icy material and gas (e.g. Jupiter, Saturn, Uranus, and Neptune). Other icy material settles in the outer regions of the disk along with rocky material, where they form a myriad of smaller bodies. We often refer to two types of planets, rocky planets and giant planets, but there is really a whole range of size of objects, all the way from dust grains to the giant planets. The smaller bodies are mixtures of different kinds of rock and ice—not just water ice, but other types as well, such as ammonia ice. Historically, small rocky bodies have been referred to as asteroids, while the icy bodies, that partly vaporize and form long beautiful tails when they travel to the inner parts of the solar system, are referred to as comets. [Not to scale] Giant planet Rocky planet Giant planets in our solar system are Jupiter, Saturn, Uranus, and Neptune. The rocky planets are Mercury, Venus, Earth and Mars. Very small bodies, either icy or rocky are called meteoroids. When a meteoroid falls into Earth’s atmosphere, it interacts with the atmosphere, heats up and leaves a streak of light in the sky that is called a meteor. If it makes it all the way to the ground, the rocky visitor from space is called a meteorite. Studying meteorites, which are thought to be left over from this early phase of the solar system, scientists have found that the solar system is about 4.6 billion years old. A Galileo spaceraft image of Jupiter’s moon Callisto, showing evidence of a chain of craters that may have resulted from a fragmented comet similar to Comet Shoemaker Levy 9. 84 Global Systems Science Hubble space Telescope image of Comet Shoemaker-Levy 9 fragments before they collided with Jupiter. A Changing Cosmos Chapter 7: Planet-Star Systems Image of asteroid Eros. Courtesy NASA, Near Earth Asteroid Rendezvous (NEARShoemaker) mission. Asteroids are solar system bodies that are smaller than planets— anywhere from the size of a boulder to a few hundred miles in diameter. Investigation Asteroid Searches In Chapter 1, we saw how asteroids can be major threats to the well being of life on Earth. You can find out more about the NASA efforts concerning near Earth asteroids at the NASA Ames Research Center’s Asteroid and Comet Impact Hazards page http://impact.arc.nasa.gov/ You can join the Hands-On Universe Asteroid Search, which began as a research project started by high school teachers Hughes Pack and Tim Spuck in 1996. In October of 1998 students at Northfield Mount Hermon School in western Massachusetts, USA, discovered a faint and distant Kuiper Belt object, now known as 1998 FS144. The project has used images from large telescopes, observatory archives, and small telescopes for asteroid tracking, searching, and discovery. The web site currently has four main options. Current status of the Hands-On Universe research projects can be found through the “Staying Up to Date” pages for A Changing Cosmos chapter 7 http://lhs.berkeley.edu/gss/uptodate/10acc The worlds come into being as follows: many bodies of all sorts and shapes move from the infinite into a great void; they come together there and produce a single whirl, in which, colliding with one another and revolving in all manner of ways, they begin to separate like to like. —Greek philosopher (atomist), Leucippus (~480-420 B.C.) Chapter 7: Planet-Star Systems For example, the International Astronomical Search Collaboration (http://iasc.hsutx.edu/) is an educational outreach program for high schools and colleges, provided at no cost to the participating schools. IASC (“Isaac”) a collaboration of • Hardin-Simmons University (Abilene, TX), • Hands-On Universe, (HOU - Lawrence Hall of Science, University of California, Berkeley), • Astronomical Research Institute (http://ari.home. mchsi.com in Charleston, IL), and • Astrometrica (H. Raab, Austria). Most recently, HOU collaborates the NASA WISE mission (Wide-field Infrared Survey Explorer) http://wise.ssl.berkeley.edu/mission.html WISE will survey the whole sky in infrared light, producing an all-sky image atlas and catalogue of over 300 million infrared sources. In addition to asteroid research, WISE scientists will study the coldest and nearest stars, regions of new star and planet formation, the structure of the Milky Way Galaxy, Ultra-luminous infrared galaxies, and the large scale structure of the Universe. Find late breaking news and information about PlanetStar Systems at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Hands-On Universe: 85 8. Search for Habitable Planets We know of one habitable planet in the Universe, habitable meaning suitable for supporting life such as that we are familiar with. That one habitable planet is our own: Earth. For centuries, some people have speculated that there may be many many such planets in other planet-star systems. Until the latter part of the 20th century, there was no evidence that planets of any sort around other stars even existed, much less habitable planets like Earth. That’s not surprising. It’s nearly impossible to see exoplanets because they are very distant, very faint and lost in the overwhelming glare of the stars they orbit. As of July 2007, only four exoplanets were observed with direct imaging methods—planets that were very large and orbiting very faint stars with very large orbit radii. But although we cannot easily observe exoplanets directly, we have detected lots of them by certain effects they have on the stars they orbit. Here are the main methods that have been thought of: Chapter 8 Planets orbiting other stars are called exoplanets, or extrasolar planets. Planets in any way similar to Earth are called terrestrial planets. 8.1 What factors make a planet habitable? The first detection of extrasolar planets was made by Alexander Wolszczan in 1994 by measuring the periodic change in arrival time of radio pulses from a pulsar—an incredibly dense neutron star, which is the remains of a supernova, that normally emits very regular pulses of radio waves. Geoffrey Marcy (right) and Paul Butler Most exoplanet discoveries have been the result of looking for at Lick Observatory, where they made movement of the “parent” star. In Kepler’s Laws, the Sun is fixed at a their first exoplanet discovery in 1987: point in space and the planet revolves around it. But why should the 70 Virginis b in the constellation Virgo Sun be thus privileged? Kepler had rather mystical and 47 Ursae Majoris b in the Big ideas about the Sun that justified its special place. Dipper. (photo: Mickey Pfleger) However Newton, in connection with his 3rd Law, showed that the Sun does not occupy a privileged For up-to-date accounting of all exoplanet position. As a planet orbits its star, its gravity discoveries, see The Extrasolar Planets Encyaffects the star so that the two bodies actually orbit clopaedia at http://exoplanet.eu/ each other. Of course the larger body dominates and the smaller body moves a lot more. But the small movement of the star as the orbiting planet tugs on it can in theory be detected in two ways: (1) If the star alternately moves towards us and The other practical way to discover away from us, its spectrum should shift slightly back and forth, alternately towards the blue end exoplanets is to watch the periodic dimming of then towards the red end—a spectroscopic shift. the star caused by a planet passing in front of (2) We should be able to see the position of the the star—an event known as a transit. Measuring star shift as well. Accurate measurement of position brightness is known as photometry. This method is known as astrometry. Spectroscopes have in theory, with four years of observing, could been used to detect star spectrum shifts caused detect planets about half the mass of Earth in a by orbiting giant planets. From ground-based 1 AU radius orbit about a sun-like star or a Mars observatories, spectroscopists can measure shifts mass planet in a Mercury-like orbits. Planets due to velocity changes as small as 3 m/sec. This with orbital periods greater than two years are corresponds to a planet at least 33 times the mass of not readily detectable, since their chance of Earth orbiting a Sun-like star. No exoplanet being properly aligned along the line of sight detections have been confirmed using astrometry, to the star is very small. Photometry is the only but there have been many exoplanet discoveries practical method for finding Earth-size planets in the habitable zone. with the spectroscopic method. 86 Global Systems Science A Changing Cosmos Chapter 8: Search for Habitable Planets Investigation Exoplanet Transits Plot and analyze a light curve for a planet transit. Then, from transit data, find out critical properties of a planet that could make the planet habitable or not. This is a rather idealized light curve—most are quite a bit more rough or difficult to discern the brightness drop. Materials • HOU IP software and computer • 19 Images of star SAO_107623 * These are 19 observations of a star named HD209458 during a transit. This was the very first star for which planet transits were observed. The planet had already been discovered by the spectroscopic method. The planet is known as HD209458b. Planets around a star are designated by a letter of the alphabet, with the star taking the letter “a” and each orbiting body taking a letter in the order of their discovery. Thus, HD209458b is the first planet discovered around star HD209458. Each image is really 20 or so images “stacked” on one another so that “noise” in the resulting image is kept to a minimum. First let’s have another look at graph E of the light curves near the end of chapter 6. 8.2. What would determine how much dimming occurs during a transit of a planet in front of a star? Check the “Staying Up To Date” web pages for A Changing Cosmos chapter 8 http://lhs.berkeley.edu/gss/ uptodate/10acc for possible new sets of images for Exoplanet Transits. 8.3. What would affect how long the transit lasts? 8.4. What would determine how often a transit occurs? 8.5. What properties of a planet could we tell from observations of transits? I. Plot a Transit Light Curve In order for a planet transit to be observed: • The planet’s orbital plane must be in line with our view of the star (as with eclipsing binary stars). • The planet must be large enough for us to detect a drop in brightness. Earth based observations C. Find reference star(s). The bright star about 45° to the upper right of HD209458 (x = 564, y = 266) can detect a drop of 1% from a transit of a can be a reference star. Even better reference Jupiter sized planet. stars are at (x = 185, y = 181) or (x = 311, y = With each of the nineteen images of HD209458, 276). use the following procedure (like the Finding 8.6. Using Aperture, measure and record the Counts Supernova investigation—Chapter 6) of HD209458 and the reference star. Then divide A. Find the time of each image from the Image the Counts for HD209458 by the Counts of the Header Info. Find the difference, in minutes, reference star to get the Count Ratio for each between the observation time and the time of image. Make a light curve for HD209458 by the first image (i.e. 10/20/2001, 3:06 UT). plotting the Count Ratio versus time (in min). B. Identify the correct star on the image. Use your Before graphing, look at the range of Count judgment (or a finder map if available). For the Ratios and optimize the range of y-axis values image set of star SAO_107623, the star that is (maximum value just above the highest Count the brightest is HD209458, so take some Counts Ratio and the minimum value just below the measurements using the Aperture tool. lowest Count Ratio on the axis). Chapter 8: Search for Habitable Planets Hands-On Universe 87 II. Examine the Light Curve DURATION 8.7 If you do not have data for a full transit, is there any way you could still determine the transit duration? 8.8 What was the duration of the transit you plotted in Part I? 8.9 Would the duration be the same for all transits of a given star-planet combination? TRANSIT DEPTH Transit Depth is the dip in the light curve. This is the drop in brightness of the star as a planet passes in front of it. 8.10 What is the Transit Depth (TD)—the maximum dip in brightness— of the transit you plotted in Part I, expressed as the ratio between the brightness before the transit and the brightness at the deepest point in the curve? TD = fraction decrease in brightness of the star due to the transit = (B1- B2)/B1 or (C1- C2)/C1 [B = brightness; C = Counts] 8.11 What makes it difficult to find the Transit Depth for this planet? III. Find the Planet’s Size The transit depth (TD) is related to the size of the planet in a very simple way: the area of light blocked when the planet transits is exactly the area of the apparent disk of the planet. So, the ratio of area of planet disk to star disk should directly determine the drop in brightness. TD = (area planet)/(area star) Since area = πr TD = (πrplanet 2)/(πrstar 2 ) TD = (rplanet /rstar )2 2 , 8.12. What is the radius of planet HD209458b? First find the radius of star HD209458a (from Internet or clues from teacher or colleagues), and then use the transit depth equations in both II and III to find the radius of the planet] Size Matters The size of the planet gives us crucial information about its possible habitability. It’s a little like the Goldilocks story. If the planet is too small (like Mercury or Mars), it will not have enough gravity to hold on to an atmosphere—gas molecules will escape the planet over a time-span of not many years in the lifetime of the planet-star system. If the planet is too large, it will retain a huge amount of atmosphere and have crushing atmospheric pressure, like the giant planets Jupiter and Saturn. PERIOD 8.13. What does Kepler’s Third Law tell us about how the period of a planet is related to its distance from a star? One light curve cannot show the period of the planet. The star must be observed for many days, weeks or months in order to establish that the transits occur in a regular period. IV. Find the Distance of the Planet from its Star 8.15 Using Kepler’s Third Law, what is the orbit radius of planet HD209458b in Astronomical Units? 8.14. What is the period of planet HD209458b? (Use library or Internet search.) 88 Global Systems Science A Changing Cosmos Chapter 8: Search for Habitable Planets Distance Matters The distance of the planet from its star gives us crucial information about its possible habitability. Again, it’s like the Goldilocks story, but an even closer analogy, since the “soup” will be either too hot or too cold for life. More precisely, the temperature must be in the range to allow for liquid water, which is an essential ingredient for nearly all life forms that we know of. If the planet is too close to its star, all water vaporizes, and if the planet is too far from its star, water is all frozen. To find out about the NASA mission to find Earth-size exoplanets, see the Kepler mission website - http://kepler.nasa.gov b-v Surface magnitude Temperature (Kelvin -0.31 34,000 -0.24 23,000 -0.20 18,500 -0.12 13,000 0.00 9,500 0.15 8,500 0.29 7,300 0.42 6,600 0.58 5,900 0.69 5,600 0.85 5,100 1.16 4,200 1.42 3,700 1.61 3,000 V. Conclusion—Is the Planet Habitable? 8.16. What factors besides distance from star might impact the temperature of a planet? 8.17 Is planet HD209458b habitable? Justify your answer with results from parts I through IV of this investigation. More advanced exoplanet investigation Visit the TransitSearch website - http://www. transitsearch.org - to find and download data on exoplanets with observed transits. Find the time between consecutive transit observations to find period. Find the transit depth. If possible, get information about the parent star to determine the size of the planet and its orbit radius. Visit the Sloan Digital Sky Survey (SDSS) web page on Calculating the radius of a star - http://cas.sdss.org/dr6/en/proj/advanced/hr/radius1.asp. See the meaning and derivation of a formula that can be used to compute a star’s radius in relation to our Sun’s radius: R/Rs = (Ts/T)2(2.51) (ms-M)/2 Where R = star radius T = Temperature of the star Rs = Sun’s radius Ts = Temperature of the Sun M = absolute magnitude of the star ms = absolute magnitude of the Sun = 4.83 Relationship of b-v magnitude and temperature is in chart at left. Absolute magnitude is M = m - 5 log d + 5 Where d = distance to the star in parsecs. Use the Hipparchos skyplot to find parallax, distance to star, and compute absolute magnitude - http://www.rssd.esa. int/?project=HIPPARCOS&page=Sky_plot Finally, visit the AAVSO website (http://www.aavso. org) and look for any exoplanet “campaigns” that are there (e.g on http://www.aavso.org/ news/campaigns.shtml) Also, try getting names of stars known to have transiting exoplanets from http://exoplanet.eu/ catalog-transit.php (52 as of July 2008) and then do a search on the AAVSO website for any light curves they have for any of those stars. Find late breaking news and information about the Search for Habitable Planets at the Staying Up To Date pages for A Changing Cosmos: http://lhs.berkeley.edu/gss/uptodate/10acc Chapter 8: Search for Habitable Planets Hands-On Universe 89 9. Cosmos Begins...and Ends? Viewing the largest realms of the Universe requires really good telescopes, since the farther away objects are, the dimmer they appear. In chapter four, we found out about distance finding by observation of brightness of Cepheid variable stars. Distances to nearby galaxies can be found by observing Cepheid variable stars and other types of variable stars in those galaxies. The Cepheid variables that Henrietta Leavitt studied were all about the same distance away, in a nearby galaxy—the Small Magellanic Cloud—about 160,000 light-years away from us. Though the Magellanic Clouds are nearby in relation to other galaxies, they are extremely far away compared to the stars in our immediate neighborhood. To say that all the stars in one of the Magellanic Clouds are roughly the same distance away from us is somewhat like saying that all the people in New York are about the same distance away from Los Angeles. To find distances to the most distant galaxies, Cepheid variable stars are of no use, since we cannot see individual stars in galaxies that far away. For great distances we use “standard galaxies.” Studies of Cepheid variables in nearby galaxies have shown that certain types of galaxies have fairly predictable absolute brightnesses. We assume that those same types of galaxies have the same absolute brightness no matter how far away we find them. Then, just as we did with the Cepheid variable technique, we can figure out how far away the galaxy is by measuring its apparent brightness. 90 Global Systems Science Zoomable version of this “Goth Strip” is at Where did the Universe come from? How did it start? What were things like way back when? Will the Universe end and if so, how? Contemplating such questions is a realm of study called cosmology. Getting at answers can take us to the very largest realms of the Universe—galaxies and arrangements of galaxies—and to the very smallest realms of the Universe—subatomic particles. http://hubblesite.org/newscenter/archive/releases/cosmology/2007/06/image/ Chapter 9 Mosaic of more than 500 images near the handle of the Big Dipper taken with NASA’s Hubble Space Telescope reveal at least 50,000 galaxies yielding clues about the Universe’s youth, from its “preteen” years to young adulthood. This is part of a larger project to study galaxies: the All-wavelength Extended Groth Strip International Survey (AEGIS), observing the same small region of sky in the radio, infrared, visible, ultraviolet, and X-ray regions of the electromagnetic spectrum. Team co-leader Marc Davis, professor of astronomy at the University of California at Berkeley said, “The goal was to study the Universe as it was when it was about half as old as it is at present, or about 8 billion years ago, a time when youthful galaxies undergoing active formation were becoming quieter mature adults.” From News Release Number: STScI-2007-06. NASA, ESA, and M. Davis (UC Berkeley) A Changing Cosmos Chapter 9: The Universe Begins ... and Ends? Doppler effect and Red shift Yet another way to tell what’s happening at great distances from us is to look carefully at the spectra of distant objects. It’s helpful first to recall what happens when you hear a train or fast moving car first come towards you and then go away after it passes by. You hear a distinct change of pitch—higher pitch as the train or car approaches you, and lower pitch as the train or car is going away. The sound waves are vibrations of air molecules. The pitch of the sound is related to basic properties of the sound waves: wavelength (length of each sound wave) and frequency (how “frequently” the sound is vibrating). The higher pitch waves are higher frequency and shorter wavelength than the lower pitch waves. Hearing the Doppler Effect with Sound Waves Aside from seeking out a train, fast moving car or motorcycle, it’s possible to create a Doppler shift sound effect using a loud sound generator, like a beeper, alarm clock, watch alarm, or buzzer. You’ll need to figure out how to very securely attached the buzzer, beeper, or alarm to a rope, heavy-duty fishing line, or very heavy duty string about one meter long. Once secured, start the sound generator whirling around so that it alternately goes towards and away from friends nearby. For safety, it is best to whirl the sound generator in a vertical circle, so if the device accidentally slips away, it’s less likely anyone will be struck. However, using a longer string can get a more noticeable Doppler shift, but you will probably have to whirl it horizontally rather than a vertically. How does the sound frequency change when the sound source is coming towards you?” [Should get higher.] How does it change when the sound source is going away from you? [Should get lower.] Light waves can exhibit Doppler effect as well, only higher frequency (shorter) waves are not higher pitch sound but instead colors towards the bluer end of the spectrum, and lower frequency (longer) waves are towards the red end of the spectrum. Light also can be described as particles called photons, each with a set amount of energy. Photons of red light are lower energy, corresponding to lower frequency waves, while photons of blue light are higher energy. Chapter 9: The Universe Begins ... and Ends? Model Waves With a partner, you can model sound waves with a slinky, long skinny spring, or even a long rope. Each of you holds one end of the spring and stretch it out. As a model, the spring represents air molecules (or air pressure, be more exact). Real sound waves travel through air much faster than spring waves—about 1/3 km/sec. One partner holds their end still as the other shakes their end of the spring. See if you can produce single wavelength (with two crests going up and down alternately), a half wave (a single crest going up and down, like a jump rope, two, three, and four waves. What is the relationship between a wave’s frequency and its wavelength? You’ll probably find that higher frequencies correspond to shorter wavelengths. You’ll also find that it takes more energy—more “oomph”—to make the higher frequency waves. A common unit of frequency is “cycles/sec” also known as “hertz.” One full wave Two waves Three waves Hands-On Universe: 91 Investigation Hubble’s Law What’s the evidence that our Universe is expanding, contracting, or staying the same? Materials • Worksheet “Spectra of Fast-Moving Galaxies” • Worksheet “Hubble’s Law” The line spectrum of hydrogen, the most common element in the Universe, has characteristic lines (wavelengths or frequencies) in the regions red, turquoise, blue, and violet. The boldest line in the hydrogen spectrum is in the red region. That is if the star or galaxy is not moving towards you or away from you. If it is moving towards you or away from you, each spectrum line will be shifted either toward the red or toward the violet end of the spectrum because of the Doppler effect. 9.1. If a star is coming towards us, which end of the spectrum will its spectrum lines be shifted towards? If a star is going away from us, which end of the spectrum will its spectrum lines be shifted towards? On the “Spectra of Fast-Moving Galaxies” data sheet there are spectra of a number of galaxies. The darkest line indicated in each the spectrum is the one that is normally in the red region of the spectrum. With extreme Doppler shifts, that bold line can appear in radically different parts of the spectrum. The scales at the top and bottom of the sheet relate Doppler shifts of the galaxies’ spectra with velocities of the galaxies. Positive velocity means the galaxy is moving away from us and negative velocity indicates the galaxy is moving towards us. 9.2. If a galaxy’s spectrum is shifted towards the red end of the spectrum, is the galaxy moving towards us or away from us? Find out how fast each galaxy is moving. Plot the speed on the “Hubble’s Law” worksheet to create a graph of distance vs velocity. 9.3. What does the graph tell you? The relationship between galaxy distance and velocity that you determined is called the Hubble Law because it was first discovered by astronomer Edwin Hubble. 9.4. What does Hubble’s Law imply about how our Universe is behaving? 92 Global Systems Science Measuring red shift turns out to be yet another powerful way to find the distances to the most far away galaxies. Assuming Hubble’s Law applies for most galaxies, astronomers estimate distances to the most remote galaxies by measuring red shifts, finding velocities, and calculating distances from Hubble’s Law. 9.5. How distant is a galaxy that is found to be receding from us at 120,000 km/sec? A Changing Cosmos Chapter 9: The Universe Begins ... and Ends? Spectra of Fast-Moving Galaxies Chapter 9: The Universe Begins ... and Ends? Hands-On Universe: 93 Hubble’s Law 94 Global Systems Science A Changing Cosmos Chapter 9: The Universe Begins ... and Ends? Age of the Universe When we talk about how big the Universe is, we start speaking in light-years, which, though not a measurement of time, certainly reminds us of time. When we look at a galaxy a hundred million lightyears away from us, we must realize that the light that reaches us from that galaxy has been traveling for a hundred million years. We are looking out into space and back in time as well. It makes you wonder about the age of our Universe. One of the main objectives of the Hubble Space Telescope is to see farther into the Universe than ever before. The farthest galaxies detected are several billion lightyears away. That’s extremely old light. The overall movement of distant galaxies leads us to the idea that if we imagine backtracking in time, the Universe may have started as a sort of fireball of unimaginably dense energy. Such an event is often called the Big Bang. The age of the Universe can be estimated by backtracking in a cosmological model based on the Hubble constant. As of 2007, the best estimate of age is 13.7 billion years (+/- 0.2 Gyr). There are other independent ways of estimating the age of the Universe, for example the age of the chemical elements, the age of the oldest star clusters, and the age of the oldest white dwarf stars. Mysteries of the Universe There are many mysteries in modern cosmology. Dark Energy A discovery that the rate of expansion of the Universe is increasing led to problems with previous cosmology models and is leading to the idea that there is some sort of unknown form of energy causing the “anti-gravity” force that is pushing everything in the Universe away from every other part of the Universe. That unknown form of energy is referred to as dark energy. Dark Matter Way before the discovery of increasing rate of expansion of the Universe, odd behavior in the spinning of galaxies led observers to conclude that there must be some additional matter in those galaxies that would explain the odd behavior. In fact, we were shocked to realize that there must be way more unseen matter in the Universe than matter that we can see. Considering matter and energy together, and referring to both as energy, only about 4% of the total energy in the Universe can be seen directly. About 22% is very likely of dark matter. and the remaining 74% is likely dark energy. Global Systems Science We do not know much about either dark matter or dark energy. But we see their effects. The myriad of galaxies in the Hubble panorama images at the beginning of this chapter does not appear evenly spread out. Some galaxies seem to be grouped together. Others are scattered through space. This uneven distribution of galaxies traces the concentration of dark matter, in an apparently invisible web-like structure stretching throughout space. Galaxies form in areas rich in dark matter. And students of astronomy form in areas rich in cosmic mysteries. You can get the whole book, A Changing Cosmos, for HOU high school courses at: http://www.handsonuniverse.org/hs/ Contact Alan Gould <[email protected]> if you want a print-enabled version, or would like to get the Image Processing software. Also, feel free to send him any comments or suggestions. A Changing Cosmos 95 List of Investigations Using Star Maps.............................................................................. 10 CCD Image Color Coding................................................................ 14 Browsing the Universe.................................................................... 15 Size and Scale of the Sun............................................................... 25 Parallax........................................................................................... 32 A Law of Brightness......................................................................... 34 Star Magnitudes.............................................................................. 36 A Cepheid Variable Star.................................................................. 39 Observing Color and Temperature.................................................. 43 Measuring the Color of Stars........................................................... 44 How Filters Work............................................................................. 47 HR Diagrams of Star Clusters......................................................... 50 Finding Supernovae....................................................................... 63 Eclipsing Binary Stars..................................................................... 71 Tracking Jupiter’s Moons................................................................. 78 Asteroid Searches........................................................................... 85 Exoplanet Transits........................................................................... 87 Hubble’s Law................................................................................... 92 96 Global Systems Science A Changing Cosmos Chapter 8: Search for Habitable Planets References Alvarez, Walter, Alvarez, Luis Michel, Helen, and Asaro, Frank, Science, June 6, 1980. Alvarez, Walter and Asaro, Frank, and Courtillot, Vincent E., “What Caused the Mass Extinction?” Scientific American, Vol. 263, No. 4, page 7692, October, 1990. Dobb, Edwin, “Hot Times in the Cretaceous,” Discover, February, pages 11-13, 1992. Gribbin, John, Blinded by the Light: The Secret Life of the Sun, New York: Harmony Books, 191991. Milne, Lorus J., and Milne, Margery, Understanding Radioactivity, New York: Atheneum, 1989. Monastersky, Richard, “Closing in on the Killer,” Science News, Vol. 141, No. 4, pages 56-58, January 25, 1992. Morrison, David, Wolff, Sidney, and Fraknoi, Andrew, Abell's Exploration of the Universe, Seventh Edition, Philadelphia: Harcourt Brace Jovanovich College Publishers, 1995. Smithsonian Exposition Books, The Fire of Life, New York: W.W. Norton & Company, 1981. Wentzel, Donat G., “The Solar Chimes: Searching for Oscillations Inside the Sun,” Mercury, May/ June, 1991, pages 77-84. Global Systems Science A Changing Cosmos 97 Acknowledgments Staff of the Global Systems Science Project Director: Alan Gould Series Authors: Richard Golden Eloise Farmer John Pickle John Michael Seltzer Alan Gould Karen Hoffman Ted Robertson Joe Snider Cary Sneider John Erickson Brian Rogan Sylvia Velasquez TERC Authors: Jodi Asbel-Clarke, Tim Barclay (Hands-On Universe Project) Editors: Kay Fairwell Librarian: Marian Drabkin Assistants: Harriette Searle Precious Perry Andrys Basten Design: Jim Hurd Design Illustrations: Audre Newman Cary Sneider Carl Babcock Miho Rahm Jennifer Yim Hemma Mistry Alan Gould Liz Unger Peggy Storrs Neeraja Venkateswaran Reviewers: The following individuals reviewed all or part A Changing Cosmos and provided feedback and suggestions: Carleton Pennypacker, Lawrence Berkeley National Laboratory Tom Morin, Belmont High School, New Hampshire. Michael Kran, Amateur Astronomer Kristin Nagy-Katz, Evaluator, Lawrence Hall of Science, University of California, Berkeley GSS Advisers Hans Anderson, president, National Science Teachers Association, Washington, D.C. Roger Bybee, executive director, Center for Science, Mathematics, and Engineering Education, National Research Council, Washington, D.C. Victor J. Mayer, Earth Systems Education Program, The Ohio State University, Columbus, Ohio. Senta Raizen, director, National Center for Improving Science, Education, Washington, D.C. 98 F. James Rutherford, director, Project 2061, American Association for the Advancement of Science, Washington, D.C. Steven Schneider, professor, Department of Biological Sciences and Institute for International Studies, Stanford University, Stanford, California Herbert Thier, director, Science Education for Public Understanding of Science (SEPUP) Project, Lawrence Hall of Science, University of California at Berkeley, Berkeley, California Global Systems Science A Changing Cosmos Thanks! Development of the Global Systems Science course would not have been possible without the creative input of the more than 150 teachers, listed below, who suggested improvements in the printed materials, and developed new laboratory activities. We are indebted to them and to their students, who helped to test the course materials. Tracey Ackerman Mother of Mercy H.S. Cincinnati, Ohio Terry Anderson NRHEG High School New Richland, Minn. Martha Andreski North Springs H.S. Atlanta, Georgia Jay Atkins Director of Education Winston-Salem, North Carolina Valerie Ayala Valley High School Sacramento, California Janet Baker Tucson High Magnet Tucson, Arizona Linda Baker Davis High School Davis, California Bob Banõs Lowell High School San Francisco, California Gary Barrigar Elizabethton H.S. Elizabethton, Tennessee James Beaber Fort Lupton H.S. Fort Lupton, Colorado Richard Beadle Spokane School Dist. Spokane, Washington Arnold Beckerman Jamaica High School Jamaica, New York Larry Beeson North High School Sioux, Iowa Doug Bell Centennial H.S. Gresham, Oregon. Deborah Bennett Hamilton County H.S. Jasper, Florida Joan Bennett Baton Rouge Magnet H.S. Baton Rouge, Louisana Dianne Bernaciak Hudson High School Hudson, Ohio Charles Berry Eastwood H.S. El Paso, Texas Daphne Blyden Boschulte J.H.S. St. Thomas, U.S. Virgin Islands Global Systems Science Burt Blumkin New Rochelle H.S. New Rochelle, New York Susan Boone Elk Grove H.S. Elk Grove, California Daniel Borick Norcum High School Portsmouth, Virginia Evelyn Bradshaw Cleveland Hts. H.S. Cleveland Hts., Ohio Gayle Brickert-Albrecht Tucson Magnet H.S. Tucson, Arizona Patricia Brown Brownell-Talbot H.S. Omaha, Nebraska Sarah E. R. Brown Phelps Career H.S. Washington, D.C. Lori Bryner-Goldstein Northglenn H.S. Northglenn, Colorado Gro Buer BEST Alternative H.S. Kirkland, Washington Keith Camburn West Mecklenburg H.S. Charlotte, North Carolina Joycelin Cayetano Polytechnic H.S. Sun Valley, California Alan Chan Glencoe High School Hillsboro, Oregon. Jayson Chang Concord High School Concord, California John G. Clarke Tewksbury H.S. Tewksbury, Massachusetts Dora J. Coleman Provine H.S. Jackson, Mississippi Gerard Collins Wakefield H.S. Arlington, Virginia Paul Conway Glendale Jr/Sr H.S. Flinton, Pennsylvania Gary Courts Miamisburg H.S. Miamisburg, Ohio Deborah Crough Saddleback H.S. Santa Ana, California Linda Culp Thorndale H.S. Thorndale, Texas Bonita Deiter Jefferson W. H.S. Meriden, Kansas Don Deresz Ctr. Environmental Ed. Miami, Florida Christine Donovan Sunnyside H.S. Tucson, Arizona Jimmy Early Van Horn Eng./Tech Independence, Missouri Tom Estill Lyme School Lyme, New Hampshire Christine Falta Englewood H.S. Englewood, Colorado Eloise Farmer Torrington High Torrington, Conneticut William Feddeler Macomb MSTC Warren, Michigan Aaron Feik Northshore Schools Bothell, Washington Neil Fetter Drew College Prep San Francisco. California Kathleen Field Haverhill H.S. Haverhill, Massachusetts Sharon Fisher North High School Des Moines, Iowa H.L. Flisser Scarsdale M.S Scarsdale, New York Adele Gomez St. John’s School San Juan, Puerto Rico Kathleen Green Hillsboro High School Beloit, Wisconsin Susan R. Green Miami Beach Sr H.S. Miami Beach, Florida Joni Grisham Pittsburg High School Pittsburg, California William Hanneken Turpin High School Cincinnati, Ohio Manisha Hariani Roanoke Valley School Roanoke, Virginia A Changing Cosmos Thomas Havel Stadium High School Tacoma, Washington Elizabeth Hedgepeth Mt. Ararat School Topsham, Maine Sharon Heineman Sabinal High School Sabinal, Texas Charlsa Henderson Wellington High Wellington, Florida Dean Heyenga Oceanside High Leucadia, California Lynn Higgins Proviso Twnship H.S. Maywood, Illinois Linda Hill Bothel High School Bothell, Washington Steve Hilton L.H. Watkins H.S. St. Louis, Missouri Phyllis Hoar G H Braddock Sr. H.S. Miami, Florida Glenda Holmes Wilson Senior H.S. Washington, D.C. Jennifer Huntsperger Gadsden H.S. Anthony, New Mexico Chad Husting Bishop Fenwick H.S. Middletown, Ohio Matt Huston Flint Hill School Oakton, Virginia Craig Huff University High Irvine, California James Ingram San Andreas H.S. Holister, California Teresa Jimarez Coronado H.S. El Paso, Texas Elizabeth Jones Springbrook H.S. Silver Springs, Maryland Connie Jones Enka High School Enka, North Carolina Dean Karagianes Mira Loma H.S. Sacramento, California Carl Katsu Fairfields Area School District Fairfield, Pennsylvania Arnold Kaufman Jefferson High School Brooklyn, New York 99 LaToy Kennedy GAMSEC-MC A&T State Greendboro, North Carolina Hellon Key Oakland Technical High Oakland, California Rick Kincaid Glenelg High School Glenelg, Maryland Wesley Knapp Scotia-Glenville Schools Scotia, New York Marjory Knights MacArthur Sr. N. H.S. Hialeah, Florida Frank Kowalczyk State College High State College, Pennsylvania Al Krulock Mission High School Mission, Texas Joseph Krupens Bell J. High School San Diego, California R. James Kurtz Univ. Detroit Jesuit H.S. Detroit, Michigan Victoria Lamkey Wichita N. High School Wichita, Kansas Peter Leddy Norton High School Norton, Massachusetts Steve Lege Davis Senior H.S. Davis, California Angela Lewis Stoneman High School Parkland, Florida Jim Lockard Shawnee Mission E. H.S. Prarie Village, Kansas Janice Lord-Walker Skyline High School Oakland, California Kerry Lohr Highline High School Seattle, Washington James Lucey Wilton High School Wilton, Conneticut Melissa Marchino Heritage High School Littleton, Colorado Michael Martin Iowa City Schools Iowa City, Iowa Carl Max Los Alamos H.S. Los Alamos, New Mexico Megan McCarthy Kingston Junior High Kingston, Washington 100 Elizabeth McCullough Thomas Johnson H.S. Frederocl, Maryland Jake McDermott Brattleboro Union H.S. Brattleboro, Vermont Robin McGlohn Burton Academy San Francisco, California Nancy McIntyre Chaminade College Prep West Hills, California Donna Millett Attleboro High School Attleboro, Massachusetts Hector Montano Canutillo High School Canutillo, Texas Catalina Moreno Boston Public Schools Boston, Massachusetts Donna Morey Fair High School Little Rock, Arkansas Isabella Morrison Shorewood H.S. Seattle, Washington Sandra Morrow Hot Springs H.S. Truth or Consquences, New Mexico Cindy Y. H. Moss Cicero-N. Syracuse H.S. Cicero, New York Irene Munoz North CarolinaaliforniaR Boulder, Colorado Stephen Nakano Waipahu High School Waipahu, Hawaii Patricia Owens Homewood H.S. Birmingham, Alabama Shelly Pelham Garrison Forest School Owings Mills, Maryland Glenda Pepin Dorsey H.S. Los Angeles, California Kenneth Pitman Heritage High School Littleton, Colorado David Podd Rio Tierra J.H.S. Sacramento, California Gilbert Richardson Shabazz High School Madison, Wisconsin Amy Ryken Berkeley High School Berkeley, California Faimon Roberts LSU Lab School Baton Rouge, Louisiana Robena Robinett North Caroline H.S. Ridgely, Maryland Brian Rogan Dublin School Dublin, New Hampshire Lina Russ Alice Deal H.S. Washington, D.C. Thomas Russell San Pedro High School San Pedro, California Fernando Salvador City as School H.S. New York, New York Sallie Sanders North Atlanta H.S. Atlanta, Georgia Erin Servillo-Gross AIM Center Trenton, New Jersey Alan Sills West Essex Reg. H.S. North Caldwell, New Jersey L. Trevor Smith Troy High School Troy, Michigan Doug Squire Union H.S. Union, Oregon Joseph Stanislaus Samoa High School Pago Pago, American Samoa John Stegmaier Gunnison High School Gunnison, Colorado Thelma Stepan Holy Cross H.S. Waterbury, Conneticut Michelle Stern Terra Linda H.S. San Rafael, California Elizabeth Stewart Westside High School Memphis, Tennessee Ellen Strother-Pitts Western Sr. H.S. Baltimore, Maryland Richard Sturgeon Glastonbury High Glastonbury, Conneticut Cindy Suchanek Mira Loma H.S. Sacramento, California Christopher Sullivan E. Longmeadow H.S. E. Longmeadow, Massachusetts Irene Swanson Northridge High Northridge, California Teresa Thompson Grapevine H.S. Grapevine, Texas Jane Ann Toth East High School Kansas City, Missouri Global Systems Science Louis Tremblay Avon High School Avon, Conneticut Jon Valasek School for Math/Sci. Columbus, Mississippi Larry Walker Academy of Sci/Tech Conroe, Texas Charles Walsh Vianney High School St. Louis, Missouri Margery Weitkamp Chaminade College Prep. West Hills, California Tom Wellington Wilton High School Wilton, Conneticut Tom Wellnitz Shore Country School Beverly, Massachusetts Fred Wetzel Science Hill H.S. Johnson City, Tennessee Jane Whitaker Lenoir City H.S. Lenoir, Tennessee Rich White Cholla High School Tucson, Arizona Patrick Wildermuth Lowell High School San Francisco, California Belinda Wight John T. Hoggard H.S. Wilmington, North Carolina Peter Wilding San Rafael H.S. San Rafael, California Bill Williams Williamsburg Scools Williamsburg, Virginia Rocky Wolf Sonora High School Sonora, California Agnes Wu Greyhills High School Tuba City, Arizona Ron Yob Native American Learning Center Grand Rapids, Michigan Jonathan Yoder North Salem High School Salem, Oregon. Paul Zastrow Hood River Valley High Hood River, Oregon. Anne Zellinger Kahuku High School Kahuku, Hawaii Glenn Zwanzig DuPont Manual H.S. Louisville, Kentucky A Changing Cosmos M51, courtesy Ewell Observatory, Belmont, CA Global Systems Science A Changing Cosmos 101 Solar System Science 2009 Edition1 By Alan Gould and Vivian Hoette SOLAR SYSTEM SCIENCE Global Systems Science http://lawrencehallofscience.org/gss Lawrence Hall of Science University of California, Berkeley Global Systems Science http://lawrencehallofscience.org/gss 102 Global Systems Science A Changing Cosmos