Download Astronomy Laboratory Manual

Hartnell College
Astronomy 1 Laboratory
Manual v 17.0
Revision v 17.0 – 7/2015
P. Moth
Astronomy Laboratory Manual - Hartnell College
AST 1L
Laboratory Content
Lab Module 1: The Observing Project
Lab Module 2: How to Use a Planisphere
Lab Module 3: Navigating the Night Sky
Lab Module 4: The Rotation, Revolution, and Precession of the Earth
Lab Module 5: Angular Size
Lab Module 6: Lenses and Telescopes
Celestia Education Activity 3: The Inner Solar System*
Celestia Education Activity 4: The Outer Solar System*
Lab Module 7: Low Velocity Impact Craters
Lab Module 8: The Spectroscope
Lab Module 9: The Classification of Stellar Spectra
Lab Module 10: Solar Rotation
Lab Module 11: The Classification of Galaxies
Lab Module 12: The Classification of Messier Objects
Lab Module 13: Large Scale Structure of the Universe
* These labs are not included in this manual. They will be handed out to you in class by the
instructor.
Astronomy Laboratory Manual - Hartnell College
AST 1L
Lab Module 1
The Observing Project
The Location and Time of Sunset OR Fremont Peak
Observatory (Worth 15 points)
Due Date: The last lab class before finals
The Location and Time of Sunset
Background
I.
Science depends on observations – particularly careful, well-documented observations.
This exercise requires that you make a series of observations and collect them
systematically in a notebook that will be handed in at the end of the semester.
Equipment
Camera; notebook; pencil; compass (recommended)
Objectives
You will track the seasonal changes in the time and location of the sun over the course of
the semester by observing sunset (or sunrise) at least once every other week for at least
eight consecutive weeks (a total of 4 observations) and photographing your
observations.
Background
At this very moment, you might be nice and relaxed, sitting in a comfortable chair,
reading this lab manual. You are probably completely unaware that you are literally
hurtling through space as you read this sentence. With every beat of your heart, you are
propelled more than 10 miles through our Solar System, more than100 miles through our
galaxy! Indeed, the Earth is not a stationary point in the Universe. Its motion results in
changes in the observed night sky – changes that have been noticed by humans for eons.
City lights and prime-time TV have eliminated our intimacy with the night sky,
especially since the average person no longer relies on this intimacy for survival. We
will try to recover some of this knowledge now by systematically observing the Sun.
The orbital motion of the Earth about the Sun results in some obvious changes in the
night sky. For instance, you can see the constellation of Orion, the hunter, in the January
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Lab Module 1: The Observing Project
Astronomy Laboratory Manual - Hartnell College
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night sky while Sagittarius makes its debut in July when the Earth is on the other side of
the Sun. There are, however, some less obvious changes that occur due to the tilt of the
Earth’s rotational axis relative to the plane traced out by its orbit about the Sun. This
little “accident” of nature results in the seasons experienced (and enjoyed!) north and
south of the equator. More specifically, the tilt causes the Sun to rise and set at different
locations and times depending on the time of year and your location (latitude) on the
Earth. The purpose of this lab is to get you to observe this phenomenon yourself. You
are the scientist. The question you will investigate is: “where and when does the Sun set
(or rise) each day (week)?”
As a precaution, you should not look directly at the Sun (even through a camera lens)
before it sets as it could cause severe eye damage!
•
Choose and describe your location: Choose some observing location with a
reasonably unobstructed view of the western horizon (or eastern if you prefer to
observe sunrise). The view of the horizon should have at least one reference
landmark. The reference landmark that you choose will help you to determine
the direction of motion of the Sun and how far it moves every day. Examples of
landmarks include a tree, building, telephone pole, edge of a cliff. Sketch the
location on your paper. Describe in detail the exact location from which you
made your sketch and indicate on your picture which landmark you chose
as the reference. It is important that every time you make an observation of
the rising or setting Sun, you will need to return to this exact location and
look towards the same direction, so be very specific in your description.
•
Determine time of sunset: Before each observation you need to find out the
time of sunset (or sunrise) by going to the internet site:
www.almanac.com/rise Enter the date, the city, and state of your observing
location. Do NOT photograph the sunset (or sunrise) at the same time every
week as the sunset time will change!
•
Record date and time of sunset from the website: Important: include whether
the time is Pacific Standard Time or Pacific Daylight Time.
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Astronomy Laboratory Manual - Hartnell College
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•
Measure and record the angular distance of the sunset from the reference
landmark: Use the reference landmark on the horizon to determine the Sun’s
location. Use your fist and thumb to determine approximately how many degrees
horizontally in the sky it is away from the reference landmark (that is measure it’s
angular distance from the landmark). One fist represents about ten degrees in
the sky and 1 thumb represents about 2 degrees in the sky. Record the value
of the angular distance in degrees.
•
Take a picture of the Sun when it is starting to touch the horizon: Once every
other week, return to your observing location and watch the sunset (or sunrise).
For each observation, you should make sure to allow yourself plenty of time to get
to the observing location before sunset. Ideally you should get there
approximately 20 minutes before sunset. You should take a picture of the Sun
when it is low in the horizon, before it actually sets. As a precaution, you
should not look directly, or through the camera at the Sun before it sets as it
could cause severe eye damage!
•
Continue to make Sun observations at least once every two weeks (doesn’t have
to be the same day) throughout the semester. Obtain at least 4 cloud free
observations during a minimum of 8 weeks of observations. IT IS
IMPORTANT TO KEEP THE CAMERA ON THE SAME ZOOM EVERY
TIME YOU PHOTOGRAPH IT!
•
Determine and label the direction of North and South: Remember that the Sun
sets in the West and West is always left of North. Turn so that the Sun is directly
to the left of you. Then the direction you are facing is North and the opposite
direction is South. If you are observing the sunrise, remember that the sun rises in
the East and East is always right of North. In this case, turn so that the Sun is
directly to the right of you. Then the direction you are facing is North and the
opposite direction is South. Label North and South on your photos.
•
If it is cloudy that week, do your observations the following week. You should
attempt to get at least 4 good (cloud free) observations of the sunset over a
minimum of 8 weeks.
•
Once your observations are all complete, paste or tape your photographs neatly
onto a sheet of paper. You can also print them out if they are digital photos.
You may either put them all on one piece of paper if they can fit or choose to put
each photo on its own sheet. Above each observation label the date, sunset time,
and the angular distance of the Sun. Label North and South on each photograph.
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Astronomy Laboratory Manual - Hartnell College
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Interpreting Your Results
At the end of the semester, summarize your findings regarding sunset (sunrise) on a page
in your observing notebook. As you describe your findings, answer the following
questions:
1) How many TOTAL degrees did the position of sunset (sunrise) move between your first
and eighth week of observation. Was the position of sunset moving northwards or
southwards during the 8 weeks of observations?
2) How did the time of sunset change over the course of the semester (i.e. was it setting earlier or
later)? How many total hours or minutes did it change from the first observation to the eighth
week? To do this correctly, you must consider whether or not your time measurements were
in STANDARD or DAYLIGHT time and subtract or add an hour to compensate for the time
change if there was a time change during your observations.
3) What do you think is causing the changes in sunset location and time?
4) During the next six months after your last observation, how will the time of the sunset or
sunrise change? Will the location of sunset or sunrise move northwards or southwards?
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Lab Module 1: The Observing Project
Astronomy Laboratory Manual - Hartnell College
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II.
Fremont Peak Observatory Field Trip (Worth 15 points alone or 10
points additional extra credit if the Sunset Project is turned)
Equipment
Flashlight with red cellophane; notebook; pencil
Objectives
You will obtain the opportunity to visit Fremont Peak Observatory and view astronomical
objects through telescopes.
Important Note: If you are in the lecture class, you will automatically receive credit for
one of the observing projects if you choose to go on this field trip. To ensure proper
credit, make sure you indicate on the cover page of your write up that you would like
credit for this in the lecture also.
Introduction
Fremont Peak Observatory is located in the beautiful Fremont Peak State Park in San
Juan Bautista. It is about a 1 hour drive from Salinas. The road up the mountain is
very windy and at times steep. Be very careful when driving at night.
The date of the field trip will be announced several weeks ahead of time in class. The
entire observing experience should last until about 10:00pm. Dress warmly and bring a
flashlight that is covered with red cellophane. You can also bring your planisphere
with you. Once you arrive at the observatory, please be courteous. The staff at Fremont
Peak Observatory are providing us with a service by allowing us to access their
observatory; please respect them and the facilities.
You can find out all the information (including directions) on their website:
www.fpoa.net. Or you can call them: (831) 623-2465. Bring $6.00 in correct change
for the parking fee.
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Astronomy Laboratory Manual - Hartnell College
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Part I: Telescope Observations
1. Once you arrive at the observatory, there should be several telescopes set to view
different objects in the sky. Sketch at least three objects. Take some time to
look through the telescope. Do not move the telescope! Try to capture the image
in your mind. Don’t sketch the object as you are observing it through the
telescope. Draw the object afterwards in order to let others have a chance to
observe the object.
2. Make sure that your drawing is to scale with the eyepiece.
3. Write a sentence describing what the object looked like.
4. Also fill in all the required information. If you don’t know the information, ask
the people who are operating the telescope.
Part II: Instructor’s Signature
This is very important. In order for you to obtain credit for this assignment, you must
ask your instructor or Fremont Peak volunteer to sign your observations sheet and
make sure they record the date.
Part III: Journal Entry
1. Your journal entry should be at least 400 words typed.
2. Describe your thoughts from the time you drove up the mountain until you came
back down.
2. Describe the objects you saw. Which one fascinated you the most and why?
3. What was the weather like?
4. Did you do anything else besides look through the telescope?
5. What did you think about the entire experience?
Note: By choosing to go to Fremont Peak Observatory, you assume all liabilities.
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Lab Module 1: The Observing Project
Astronomy Laboratory Manual - Hartnell College
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Instructor’s or Volunteer’s Signature and Date:
Object 1:
Object Name:
Date/Time :
Telescope Diameter:
Draw what you see through the telescope above.
Describe in words what you see here:
Extra Credit:
Focal Length – Objective:
– Eyepiece:
Magnification=Fobj/Feye:
Object 2:
Object Name:
Date/Time :
Telescope Diameter:
Draw what you see through the telescope above.
Describe in words what you see here:
Extra Credit:
Focal Length – Objective:
– Eyepiece:
Magnification=Fobj/Feye:
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Astronomy Laboratory Manual - Hartnell College
AST 1L
Object 3:
Object Name:
Date/Time :
Telescope Diameter:
Draw what you see through the telescope above.
Describe in words what you see here:
Extra Credit:
Focal Length – Objective:
– Eyepiece:
Magnification=Fobj/Feye:
Object 4:
Object Name:
Date/Time :
Telescope Diameter :
Draw what you see through the telescope above.
Describe in words what you see here:
Extra Credit:
Focal Length – Objective:
– Eyepiece:
Magnification=Fobj/Feye:
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Lab Module 1: The Observing Project
Astronomy Laboratory Manual - Hartnell College
AST 1L
Lab Module 2
How to Use a Planisphere
Equipment
Planisphere, Hartnell Planetarium, flashlight with red cellophane
Objectives
Use the planisphere to locate constellations and identify stars in the night sky. Investigate
other uses of the planisphere in telling time.
Background
Every new stargazer thinks the first thing they need to get started in astronomy is a
telescope, only to discover that they don't know how to find anything with it in the sky.
The problem, of course, is that they don't know the bright stars and major constellations.
Unfortunately, many never find the help they need and give up astronomy and stick their
telescope in the closet. With proper advice and guidance, anyone can turn into a starhopping skymaster.
The first thing you need to learn your way around the sky is a star map, but what kind?
You won't want to get a star atlas like Wil Tirion's "Sky Atlas 2000"; It's way too
detailed. Good places to start are the monthly all-sky star maps that appear in
"Astronomy" or "Sky & Telescope" magazines. You can also download a free monthly
star map from Skymaps.com. Those will help you pick off the most common star patterns
like the Big Dipper, Orion, and the Summer Triangle. Those are set for one time of night
though and that might make it difficult to track down the dim and small constellations.
The best type of star map to start out with is a planisphere. This is a star map that can be
adjusted for the date and time you are observing the heavens. They come in a large and
small size. The larger size costs more of course, but it's easier to read in the dark. There
are many types of planispheres and any should serve you well.
With a planisphere, or star wheel, you turn a disk to set your time against your date. The
edge of the star map then represents the horizon all around you at that time. Some
planispheres come with extra features. The most important aspect of a planisphere,
however, is the clarity and realism of its star map.
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Lab Module 2: How to Use a Planisphere
Astronomy Laboratory Manual - Hartnell College
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Using a Planisphere
In principle nothing could be simpler. You turn a wheel to put your time next to your
date, and presto, there's a custom-made map of the stars that are above your horizon for
that moment. The edge of the oval star map represents the horizon all around you, as you
would see if you were standing in an open field and turned around in a complete circle.
The part of the map at the oval's center represents the sky overhead.
In practice, several complications can throw beginners off. The worst is that a
planisphere's map is necessarily small and distorted. It compresses the entire celestial
hemisphere above and around you into a little thing you hold in your hand. So star
patterns appear much bigger in real life than on the map.
Moving your eyes just a little way across the map corresponds to swinging your gaze
across a huge sweep of sky. The east and west horizons may look close together on a
planisphere, but of course when east is in front of you west is behind your back. Glancing
from the map's edge to center corresponds to craning your gaze from horizontal to
straight up.
There's only one way to get to know a map like this. Hold it out in front of you as you
face the horizon. Twist it around so the map edge labeled with the direction you're facing
is down. The correct horizon on the map will now appear horizontal and match the
horizon in front of you. Now you can compare stars above the horizon on the map with
those you're facing in the sky, and you're all set!
Once you understand the workings of a planisphere, you can "dial in" any constellation
visible from your hemisphere and then look at the edge to see when that constellation is
visible. Constellations that are visible all-year are known as Circum-Polar, because they
seem to spin around the north star Polaris, and never set completely below the horizon.
Most other constellations are prominent during a particular season of the year. For
example, Orion the Hunter is very easily seen in Winter, but in Summer, it is hidden in
the sun's glare and is up during the day.
The most obvious parts of the chart are all the little dots that represent the stars. You'll
notice that the dots are different in size, big dots are bright stars and smaller ones denote
faint stars. Most of the stars on the map are connected by lines. These are the imaginary
lines that show us the general structure of the constellations and asterisms. The brightest
stars and most of the constellations and asterisms are labeled, so you know what they're
called.
The large circle around the stars represents the lowest point in the sky, which we call the
horizon. It's where we see the Sun, Moon, and stars appear to rise and set in the sky.
Outside the circle you'll see the letters N, S, E, W at 90° angles to one another. These are
the cardinal directions north, south, east, and west. Hopefully you've heard of these by
now because it's vital to know your directions to find star patterns and deep sky objects.
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Lab Module 2: How to Use a Planisphere
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The planisphere also provides additional information. Your chart may be marked with the
ecliptic (the sun’s path in the sky) and the coordinates of stars: right ascension and
declination. Right ascension is given in terms of hours and minutes. Declination is in
degrees.
Questions/Activities
Using just the planisphere, answer the following questions:
1) List three constellations that will be visible tonight at 9pm.
2) Name a constellation that is rising at 9pm tonight.
3) Name a constellation that is setting at 9pm tonight.
4) At what time will Orion have just fully set on March 20th?
5) Turn the planisphere to February 14th at 8pm and list three constellations that will
be visible
6) At what time will Leo have just fully risen on February 14th?
7) Name two constellations that are visible at 10pm tonight, but not at 2am tomorrow
morning?
8) What does the ecliptic represent?
9) Name four constellations on the ecliptic that are visible tonight at 7pm.
10) What is special about the constellations that you’ve listed that are located on the
ecliptic?
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11) Record your birthday:
List three constellations that are visible at 11pm on your birthday:
12) The central hole “punches” through what star?
13) Why is this star used as the center?
14) This star is part of what constellation?
Now we’ll visit the planetarium.
1) Locate the following on the planisphere and see if you can find them in the
planetarium:
a. Constellation Ursa Major (includes the Big Dipper)
b. Polaris (star)
c. Constellation Ursa Minor (includes the Little Dipper)
d. Constellation Cassiopeia
e. Constellation Cepheus
f. Milky Way Spiral Arm
2) The planetarium will now be set to some time tonight. What time is displayed?
1.
2.
3) The planetarium will now be set to a different day at midnight. What day is it?
1.
2.
4) The planetarium will now rotate, simulating the rotation of the Earth:
a) In which direction do the stars rise? (i.e. north, south, east, west)
b) In which direction do the stars set? (i.e. north, south, east, west)
c) Name three constellations that are always above the horizon (never rise or set).
These are called circum-polar constellations.
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7) Find the ecliptic. List three constellations that are located on the ecliptic tonight.
8) Find the region representing the Milky Way, our home galaxy. Name three
constellations visible tonight along the plane of the Milky Way. Try to see if you
can find them in the planetarium.
9) The constellation Sagitarrius (which resembles a teapot) represents the direction of
the center of the Milky Way Galaxy. On this evening, are you able to see towards
the center of the Milky Way?
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Lab Module 2: How to Use a Planisphere
Astronomy Laboratory Manual - Hartnell College
AST 1L
Lab Module 3
Navigating the Night Sky
Equipment
Hartnell Planetarium, flashlight with red cellophane
Objectives
Use the planetarium to learn how to identify constellations. Learn how to use the
constellations as a map in the sky to identify stars in the night sky. Learn the difference
between altitude and azimuth.
Background
When you gaze upon the sky at night and observe the stars, you will be able to notice that
the different groupings of stars can be formed to make up patterns in the sky. These
recognizable patterns in the sky are called constellations. In this lab, you will learn the
names of several of these constellations and how to recognize the patterns that they form
in the sky.
In the past, constellations were very useful as navigational aids and were associated with
mythology. Today the constellations represent mainly beautiful formations in the night
sky that are fun to observe and learn. Astronomers use constellations mainly as a map of
the sky to help locate fainter stars and celestial objects. In this lab, you will also use the
constellations as a map to help you locate a mystery star.
The location of the stars and constellations in the night sky may also be locally identified
by two positional coordinates. The coordinate that describes the angular height of the
object from the horizon is called the altitude. The coordinate that describes the angular
position with respect to North is called the azimuth. The altitude and azimuth of the
object changes during the course of the night as the sky appears to move due to the
Earth’s rotation. In this lab, you will practice determining the altitude and azimuth of the
celestial object or constellation.
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Lab Module 3: Navigating the Night Sky
Astronomy Laboratory Manual - Hartnell College
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I. Identifying constellations:
1. The meridian is the line that runs from North to South and divides the sky into two
hemispheres. The meridian is represented as the dashed vertical line in the following
box. The zenith represents the point that is straight up above you. The top of the box
represents the zenith. The horizon represents the boundary between the surface of the
Earth and the sky. The bottom of the box represents the horizon (in the planetarium the
horizon is the bottom edge of the planetarium dome.
2. You will learn to identify the constellations both in the North and the South.
3. As the instructor points out the constellations and stars in the planetarium sky, draw
and label them carefully in the following box using the meridian as a reference. Be sure
to draw them in the same configuration as you see them on the planetarium sky.
Date:
Time:
Zenith
South
Horizon
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AST 1L
Zenith
North
Horizon
II. Circumpolar Constellations
1. For this part, you should face towards the North. The center of the circle represents the
position of Polaris (The North Star). The vertical dashed line represents the observer’s
meridian in the north. The radius of the circle is about 36 degrees. The constellations
within the circle are the north circumpolar constellations. They never set.
3. Choose one circumpolar constellation to sketch. You will be making three
observations and three sketches for that one circumpolar constellation during different
times of the night.
4. Accurately sketch the stars of the circumpolar constellation on the same circular
diagram for the three different observations. Record the date and times for the three
observations. Remember to label each observation with its appropriate number.
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Date:
Times: 1)
2)
3)
5. What are circumpolar constellations? What causes them to appear to move?
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III. Locating a mystery star:
1. For this part, you should work with a partner. Each of you should pick a star in the
planetarium sky that is located in one of the constellations. Don’t tell your partner which
star you picked.
2. Draw the constellation with that star in it. Also draw several (at least 10) stars around
the star in question. Make these stars larger in your picture if they are brighter and try to
get the separations right. Draw an arrow that points to your chosen star.
3. Exchange the maps with your partner. Examine their map carefully and try to see if
you can locate their star
Can you find your partner’s star from their constellation map (yes or no)?
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IV. Altitude and Azimuth:
1. The altitude represents the height above the horizon expressed in degrees. The
horizon represents 0° and zenith is 90° altitude. Azimuth represents the angular degress
from North. An object due north has an azimuth of 0°, one due east 90°, south 180° and
west 270°. Using this definition of altitude and azimuth, find the altitude and azimuth for
both stars.
1. Your star: Altitude
Azimuth
2. Your partner’s star: Altitude
3. Determine the Altitude
Azimuth
and Azimuth
of Polaris, the North Star.
V. Zenith
Astronomers refer to the position in the sky that is straight up above the observer as the
zenith.
1. Draw and label the constellation that is approximately located at the zenith here:
2. What altitude does the zenith represent?:
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Lab Module 3: Navigating the Night Sky
Astronomy Laboratory Manual - Hartnell College
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Lab Module 4
The Rotation, Revolution,
and Precession of the Earth
Equipment
Hartnell Planetarium, flashlight with red filter
Objectives
In everyday life, we observe the effects of several different types of motions in the sky,
which occur under different timescales. There is the rotation of the Earth which causes
the apparent daily motion of the Moon, Sun, planets, and stars, the revolution, the
motion of the Earth around the Sun which is partially responsible for the seasons, and
precession, the wobbling of the Earth’s axis which causes the north polar axis to change
direction. With the aid of the planetarium, you will learn about the diurnal motion of
stars, the seasons, and the precession of the Earth.
Part I: Rotation of the Earth- The Diurnal Motion of Stars
Background
If you track the position of a star at night, you will notice that it will change over the
course of several hours. The reason for this is that the Earth is rotating. It takes
approximately 24 hours for the Earth to complete one full rotation. Because the Earth is
rotating, the star appears to move over the course of the night. The movement of the
stars due to the Earth’s rotation is called diurnal motion or daily motion. Due to the 24hour counterclockwise rotation of the Earth, all the stars in the sky will follow a
predictable path. The paths that they follow depend upon the latitude on Earth that you
are observing the stars from and the position of the North Star in the sky. The reason for
this is because the altitude (angular distance from the horizon to the star) of
the North Star changes depending upon where the observer is located. The altitude of the
North Star is, however, always equal to the observer’s latitude. For example, if you lived
at 36 deg latitude, the North Star would be located at an altitude of 36 deg. The other
stars will appear to revolve around the North Star due to the rotation of the Earth. If you
live at the North Pole, the North Star would be located at 90 deg altitude, or at the zenith
which is the point in the sky directly above you.
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
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If you have a sensitive enough camera, you can take photos of the night sky using long
exposure times. When you observe the photograph, the stars do not appear as points of
light but rather as long streaks of light. The planetarium can simulate the star trails that
you would typically observe in such a photograph. In this part of the lab, you will
observe and sketch the star trails, and in doing so, you will obtain a better understanding
of the diurnal motion of stars at different latitudes on the Earth.
Planetarium Activity
Star trails will be shown at different latitudes. The zenith is located at the center of the
top of the box (represents 90 deg altitude) and the horizon is located at the bottom of the
box (represents 0 deg altitude). The vertical dashed line represents the meridian.
A. Record the observer’s latitude and altitude of Polaris.
B. Draw Polaris with a large dot on the meridian using the zenith and horizon as a
guide to pinpoint the position of the star. (e.g., if the North Star is at 45 deg
altitude, you should draw it at the center of the box)
C. Draw the star trails from the horizon to the zenith. Make sure to use the horizon,
the position of the North Star, and the zenith as a reference. (e.g. if stars are
moving parallel with respect to the horizon, draw them as parallel lines).
D. Indicate with an arrow on one of the trails, the direction that the star is moving.
Observer’s Latitude:
Altitude of Polaris:
West
Observer’s Latitude:
Altitude of Polaris:
East
West
East
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
Astronomy Laboratory Manual - Hartnell College
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Observer’s Latitude:
Altitude of Polaris:
West
Observer’s Latitude:
Altitude of Polaris:
East
West
East
Questions
1. In which direction do stars rise? (i.e.,North, East, South, or West?)
2. In which direction do stars set? (i.e., North, East, South, or West?)
3. At what latitude would you be if all the stars are circumpolar?
4. Would Polaris be located at the zenith or the horizon at this latitude (refers to Question
3)?
5. At what latitude would you be if no stars are circumpolar?
6. Would Polaris be located at the zenith or horizon at this latitude (refers to Question 5)?
7. How long does it take the Earth to complete one full rotation on its axis?
Part II: Revolution of the Earth- The Analemma
Background
Contrary to popular belief, the seasons are not caused by the changing distance of the
Earth to the Sun as it moves in its orbit around the Sun. According to this scenario, the
Earth would be warmest (summertime) when it is closest to the Sun and coolest
(wintertime) when it is farthest away from the Sun. Furthermore, the Earth would exhibit
the same seasons in both the northern hemisphere and the southern hemisphere.
However, as we are all well aware, this is not the case. When it is wintertime in the
northern hemisphere, it is summertime in the southern hemisphere and vice versa.
In fact, in the northern hemisphere, the Earth is actually closest to the Sun during winter
time and farthest away from the Sun during summertime.
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
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The actual explanation for the seasons results from the combined effects of the Earth’s
revolution and the 23.5 degree tilt of the Earth’s axis of rotation relative to the plane of
our orbit around the Sun. It takes the Earth one year to complete one full revolution
around the Sun. During that year, the Earth experiences four seasons. For one half of the
year, the northern hemisphere is tilted towards the Sun, whereas for the other half of the
year, the northern hemisphere is tilted away from the Sun. During the months when the
northern hemisphere is tilted towards the Sun, we experience summer in the northern
hemisphere and winter in the southern hemisphere. During the months when the northern
hemisphere is tilted away from the Sun, we experience winter in the northern hemisphere
and summer in the southern hemisphere. As the Earth revolves around the Sun, the
maximum height that the Sun reaches in the sky changes, and thus the total amount of
daylight hours also changes. This is the reason why we have seasons and why there are
temperature changes through the course of a year.
Have you ever observed a globe and seen a figure which looks like an 8 on the globe and
wondered what it meant? In this lab, you will come to understand that figure 8 shape,
which we call the analemma. The analemma is a shape that represents the height of the
Sun, which is measured at the same time of day during different times of the year. The
shape of the analemma is caused by two factors. The height of the analemma is due to
the Earth’s tilted axis of rotation, whereas the width is caused by the eccentricity of the
Earth’s orbit around the Sun. In this lab, you will track the apparent motion of the Sun in
the sky during different days of the year at the same clock time, and in doing so, you will
generate your own analemma.
Planetarium Activity
An image of the Sun will be shone on the planetarium sky during different days of the
years. Each image will be a representation of the Sun at the same time of the day. The
central dashed line represents the meridian (the line that extends from North to South).
As an aid, the grid is labeled with the altitude on the vertical axis. To accurately
reproduce the analemma, it is critical to accurately plot the position of the Sun (e.g., if
the Sun is located to the left meridian, draw it to the left, if it is located on the meridian,
draw it on the line that represents the meridian).
A. Using the angular measurements you learned in class, approximate the altitude of
the Sun in the planetarium sky.
B. On the following grid, plot the altitude of the Sun on the meridian with a dot and
label it with the date that the Sun is at that position.
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
Astronomy Laboratory Manual - Hartnell College
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90 degrees
80 degrees
70 degrees
60 degrees
50 degrees
40 degrees
30 degrees
20 degrees
10 degrees
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
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Questions
1) On which date was the Sun highest in the sky?
2) What season does this correspond to?
3) On that date, what altitude did it reach?
4) On which date was the Sun lowest in the sky?
5) What season does this correspond to?
6) On that date, what altitude did the Sun reach?
7) On which dates did the Sun reach the same position in the sky?
a)
b)
8) Which seasons do these dates correspond to?
9) On these dates, what altitude did the Sun reach?
10) How long does it take the Earth to complete one full revolution around the
Sun?
11) During which season will we have the longest days? Why?
Part III: Precession of the Earth
Background
When you spin a top, you might notice that, as the top loses energy, the top will start to
wobble; that is its axis of rotation will start to trace a circle. The Earth also exhibits this
wobbling as it spins upon its axis. However, since the timescales of the wobbling are
rather huge, we don’t feel this effect in our day to day life. It takes about 26,000 years
for the Earth’s spin axis to trace a complete circle! The circular motion of the Earth’s
spin axis is called precession. The Earth’s speedy 24-hour rotation rate causes the
Earth’s shape to deviate from spherical. Instead, the Earth is slightly thicker across the
equators than it is across the poles. The gravitational “tugs” of the Sun and the moon on
the Earth’s equatorial bulge causes the Earth’s axis of rotation to precess with a period of
26,000 years.
Because of the precession of the Earth, the north polar axis will not always point toward
the direction of Polaris; thus, Polaris will not always remain the “North Star”. Depending
on which direction the north polar axis points to, the North Star will change. There will
also be times when the north polar axis will not line up with any bright stars in the sky.
During these times, there will be no North Star. Indeed the North Star used by Greek
sailors for navigation was a different one than we use today.
Because of the tilt of the Earth’s axis of rotation, the ecliptic and celestial equator are
inclined to each other by 23.5 degrees. These two circles intersect at two points called
the equinoxes (“equal nights” in Latin). Since the rotation axis is precessing, the celestial
equator also precesses with time which means that the position of the equinoxes will also
change with time. Thus, the precession of the Earth may also be referred to as the
precession of the equinoxes.
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
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Furthermore, the precession of the Earth may be responsible for extreme temperature
conditions exhibited on Earth over a long period of time. According to the Milankovich
theory, the precession of the Earth could partially explain the occurrence of ice ages! In
this part of the lab, we will observe the precession of the Earth’s axis of rotation and
determine which star (if any) is closest to being the North Star at different epochs.
Planetarium Activity
In the planetarium, you will observe a great circle in the sky. This circle represents the
path of the north polar axis projected onto the sky. The intersection of the meridian with
the circle represents the location of the north polar axis projected into the sky. The
planetarium director will simulate the passage of time. As time passes, you will notice
that the north polar axis will travel along the circle.
A. When the planetarium director stops the motion of the north polar axis, mark on
the circle provided, the location of the north polar axis with an X and record the
date.
B. If there is a constellation that coincides with the axis, draw it in, making sure that
it is in the right location on the circle. Then circle and label the star which could
be used as the North Star. This star would be located on or near the intersection
of the meridian with the great precession circle.
13,000 years
19,500 years
6,500 years
0 years
Lab Module 4: The Rotation, Revolution, and Precession of the Earth
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Questions
1) In 5,000 years which star will be the North Star (if any)?
2) In 10,000 years, which star will be the North Star (if any)?
3) In 12,000 years, which star will be the North Star (if any)?
4) In 21,000 years, which star will be the North Star (if any)?
5) In 26,000 years, which star will be the North Star (if any)?
6) What is precession and why does it to occur?
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Lab Module 4: The Rotation, Revolution, and Precession of the Earth
Astronomy Laboratory Manual - Hartnell College
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Lab Module 5
Angular Size
The Reason for Total Solar Eclipses
Equipment
Meter stick; ruler with mount; cookie; CD; calculator
Objectives
In this laboratory, you will measure the angular size of several objects using a cross-staff,
use angular size to determine the diameter of objects, and compare the calculated value of
diameter with the measured value. You will also learn how Astronomers determine the
true sizes of objects in space, how two objects of different physical size can appear to be
the same size, and why total solar eclipses happen.
Background
On chance occasions when the Moon, Sun, and Earth is directly aligned with each other,
the Moon blocks out the light from the disc of the Sun. If you are lucky enough to be
located in the path of the Moon’s shadow on Earth, you will see a rare and spectacular
event, a total solar eclipse! Although the Sun’s true size is much larger than the Moon, a
total solar eclipse is possible because the Sun has the same angular size as the Moon.
Whereas the true size of an object never changes, its angular size (the angle that it
appears to subtend in the sky) depends upon the distance between the observer and the
object. Thus, it is possible for two objects with different sizes to possess the same
angular size. In this lab, you will use a simple device called a cross-staff to measure an
object’s angular size, and in doing so, you will learn how Astronomers determine the true
sizes of objects in space. You will also demonstrate why total solar eclipses are possible
even though the Sun is much larger than the Moon.
Part I: Measuring Angular Size
In this laboratory activity, we'll practice using one the most important astronomical
distance measuring techniques, but in terrestrial context. You will construct a version of a
cross-staff, a basic tool for measuring angles. Then, you'll use it for measuring angular
sizes of objects.
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Step 1: How to construct a cross-staff
Equipment: meter stick, ruler and mount for the ruler.
Ruler
57.3 cm
Sliding mount
Look from
here
Meter Stick
Procedures:
1. Attach your ruler to the sliding part of your cross-staff.
2. Slide the mount, with ruler attached, so that the ruler is 57.3 cm away from the
end of the meter stick that you will hold up next to your eye, see sketch above.
This distance is chosen because one degree subtends an arc length of 1 cm at 57.3
cm distance, see sketch below.
a
L=1 cm
a = L/D =1/57.3
radians = 1
degree
D=57.3
Step 2: How to use your cross-staff
Hold the end of the meter stick marked with "0" close to your eye; then, the ruler should
be at 57.3 cm away from your eye.
Step 3: Measuring angular size of an object
Aim your cross-staff in the direction of the object whose angular size you wish to
measure. Align one of the centimeter marks with the left-hand edge of the object. Now,
find the mark closest to the right-hand edge of the object. The angular size of the object
in degrees is just the distance along the ruler in centimeters between the left and
right edges of the object.
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Example: If you aligned one of the cm marks with the left-hand edge of your object, and
the right-hand edge is near the fourth mark to the right, then the angular size of the object
is 3 divisions (cm) = 3 degrees. See drawing.
object
ruler
cm marks
Direction of
viewing
Step 4: Measure the angular size of the 3 circles on the blackboard and record these
values in Table 1.
Part II: Determining the true size (diameter) of objects.
Now that you know how to determine the angular size of objects, you can determine the
true size of objects.
Step 1: Use the measuring tape to measure the distance from you to the circle in inches.
Then convert the distance to cm by using: 1 inch = 2.54 cm. Record these values in
Table 1.
Step 2: If you know the angular size of the object and the distance to the object, you
can calculate the true size (diameter) of that object by using Equation 1:
Angular size
Distance
Diameter
Equation 1: Diameter=(Angular size)X(Distance)/57.3
Step 3: Calculate the true sizes (diameters) of the circles by using Equation 1.
Record these values in Table 1.
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Lab Module 5: Angular Size
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Step 4: : Use a ruler to measure the diameter of the 3 circles in cm. Record the values in
Table 1.
Step 5: Use Equation 2 to calculate the % difference between the measured value of
the diameter and the calculated value of the diameter of your object. This gives you
an idea of the accuracy of your calculations. Record the values in the Table 1.
Equation 2: % diff=
measured value − calculated value × 100%
measured value
Table 1
Object
observed
Measured^
angular size
of object
(degrees)
Measured+
distance of
object from
you (cm)
Calculated*
diameter of
the object
(cm)
Measured
diameter of
object (cm)
%
Difference~
Circle 1
Circle 2
Circle 3
^ Measure the angular size of your object using the cross staff.
+ Remember to convert from inches to cm by multiplying your distance by 2.54.
* You can calculate the diameter of the object using equation 1.
~ You can calculate the % difference by using equation 2.
Step 7: Repeat Steps 1-5 using two objects of your choice. Fill in the values in Table
2.
Table 2
Object
observed
Measured^
angular size
of object
(degrees)
Measured+
distance of
object from
you (cm)
Calculated*
diameter of
object (cm)
Measured
diameter
of object
(cm)
%
Difference~
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Question 1: What happens to the angular size of the circle as you move farther away from it? Try
to do angular size measurements at different distances for the same circle.
Question 2: In order to determine the true sizes (diameters) of objects in space (please be
specific), what two pieces of information does the astronomer need to know or measure?
Question 3: Determining the true size of the Moon.
If the Moon’s angular size is 0.5 degrees and it is located at an average distance of
385,000 km. What is the true size (diameter) of the Moon? Record the information here and also fill
in this information in Table 4.
Diameter of the Moon: _____________
Part III: The reason for solar eclipses.
Equipment: cookie, CD, measuring tape, ruler
Step 1: One person in the group should hold the cookie at eye level with the arm fully extended
away from the eye.
Step 2: Another person should take the CD, start out holding it just in back of the cookie, then slowly
move it away from the person holding the cookie. It is important that the person holding the CD
continues to hold it at the eye level of the person holding the cookie.
Step 3: Once the person holding the cookie sees that the CD is approximately the same angular size as
the cookie (in this situation, the cookie should be fully blocking the CD), the person holding the CD
should stop. A third member of the group should then take the measuring tape and first measure and
record the distance from the person’s eye to the cookie and then measure and record the distance from
the person’s eye to the CD. Here you do not need to convert the distance to cm.
Step 4: Calculate the ratio of the distance to CD and the distance to the cookie and fill in
Table 3.
Step 5: Measure the diameter of the cookie and the CD in cms with a ruler.
Step 6: Calculate the ratio of the diameter of the CD to the diameter of the cookie
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Table 3
Distance to CD
(inches)
Distance to cookie
(inches)
Diameter of CD
(cm)
Diameter of cookie
(cm)
Ratio of distances =
Distance to the CD ÷Distance to the cookie
Ratio of diameters =
Diameter of the CD ÷ Diameter of the cookie
Question 4: How many times larger is the CD compared to the cookie (ratio of the
diameters)?
Question 5: How many times farther away from the observer (the person holding the
cookie is the observer) is the CD compared to the cookie (ratio of the distances)?
Question 6: In order for two objects of different sizes to be the same angular size, what
condition must be met?
Step 9: Record the distance to the Sun and the diameter of the Sun in kilometers. From
Question 3, find out the distance to the Moon and the diameter of the Moon in
kilometers. Record these values in the Table 4.
Step 10: Calculate the ratio of the distance to the Sun and the distance to the Moon.
Record in Table 4.
Step 11: Calculate the ratio of the diameter of the Sun and the diameter of the Moon.
Record in Table 4.
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Table 4
Distance to Sun
(km)
Distance to Moon
(km)
Diameter of Sun
(km)
Diameter of Moon
(km)
Ratio of distances =
Distance to the Sun ÷ Distance to the Moon
Ratio of diameters =
Diameter of the Sun ÷ Diameter of the Moon
Question 7:
How many times larger is the Sun compared to the Moon (ratio of the diameters)?
Question 8:
How many times farther away from the Earth is the Sun compared to the Moon (ratio of
the distances)?
Question 9:
If the true size of the Sun is much larger than the moon, why is it still possible for the
moon to completely block out all the light of the Sun during a total solar eclipse?
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Lab Module 5: Angular Size
Astronomy Laboratory Manual - Hartnell College
AST 1L
Lab Module 6
Lenses and Telescopes
Equipment
Two lenses, light bulb, paper towel tubes, telescope tubes, lenses, lens holders,
screen, meter stick, and calculator.
Objectives
To determine the focal lengths of lenses by different methods. To investigate the images
formed by the converging lens. To investigate the properties of a telescope.
Background
A telescopic system is designed to produce parallel rays of light. An astronomical
telescope amplifies light with a system of lenses and/or mirrors Astronomical telescopes
gather light over a broad area (the objective) and redirect it to an eyepiece. The light rays
exiting from the eyepiece replicate the angles at which they entered the objective, but
over a smaller area. The result is an image that contains all the light gathered by the
objective, reduced to a size that matches the size of an eye or camera. This results in a
brighter and more detailed image than can be gathered directly by the eye or camera.
There are many arrangements of lenses and mirrors that will redirect light in this manner.
Telescopes that use lenses as their objective, or light-gathering element, are called
refractive telescopes. The refractive telescope that Galileo constructed, for instance, uses
two converging lenses in series. Telescopes that use mirrors as their objective are called
reflective telescopes. Sir Issac Newton was the first to figure out that mirrors could be
used to focus light instead of lenses. Over the years, reflective telescopes have come to
dominate the field of astronomy, resulting in many improvements.
The lenses and mirrors that make up telescopic systems have two key characteristics. The
first is the focal length (f ) of a lens. Focal length may be loosely defined as the distance
from a lens at which a distant object will produce an image. Object Distance (do) is the
distance from an object to the lens. An image is the likeness of an object produced at a
point in space by a lens or system of lenses, again, a lens, a telescope, a pair of binoculars
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Lab Module 6: Lenses and Telescopes
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AST 1L
or your eye. Image Distance (di) is the distance from a lens or other optical element to
an image.
Focal length (f) is related to the object distance (do) and the image distance (di) by the
following thin lens equation:
1
1
1
+
=
di do f
Rewriting we get and alternate form of the thin lens equation:
Equation 1:
f = (di*do)/(di + do)
Procedure
1. Determining the focal length of a lens by using the thin lens equation:
1. Place the light bulb at one end of the meter stick.
2. Place the lens without the red dot in a lens holder 35 cm from the light bulb.
3. Adjust the position of the screen to obtain a sharply focused image of the light
bulb.
4. Measure and record the value of the image distance (di) and record it in Table
Remember that the image distance is the distance from the lens to the focused
image on the screen and the object distance is the distance from the light bulb
to the lens.
5. Determine the focal length, f, using Equation 1.
6. Decrease the distance of the light bulb to the screen by 5 cm at a time and
repeat steps 1 through 5.
7. Record all information in the Table 1.
8. Calculate and record the average value for the focal length of your lens by
using Equation 2:
To calculate the average of five measurements, add the five values and divide the
result by five.
Equation 2: favg =
f 1+ f 2 + f 3 + f 4 + f 5
5
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Lab Module 6: Lenses and Telescopes
Astronomy Laboratory Manual - Hartnell College
AST 1L
Table 1
Object distance
(do)
35cm
30cm
25cm
20cm
Image Distance
(di)
Focal Length
(f)
Average Focal Length:
Question 1:
a) Examine the two lenses that your instructor has given you. What property of the lens
affects its focal length?
Guess:
Actual:
b) Which of the two lenses has a shorter focal length? The one with the red dot or the one
without the red dot? How can you tell?
Question 2: The actual value of your lens is 10 cm, how does your average calculated
focal length determined from the measurements you made in the lab compare with the
actual value? Answer this question by using Equation 3 to calculate the
% difference from your calculated value with the actual value.
Equation 3: % diff=
calculated value − actual value
× 100%
actual value
2. Focal length determined by observing a distant object:
A second, much easier technique to determine the focal length of the lens is to observe a
very distant object. In the case of a distant object, the object distance is much greater
than the image distance di (do>>di), when this occurs, f ≈ di since 1/do goes to zero.
When focusing on an object that is very far away, the focal length of the lens is
approximately equal to the image distance:
Equation 4: f=di
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Lab Module 6: Lenses and Telescopes
Astronomy Laboratory Manual - Hartnell College
AST 1L
For the purposes of this experiment, a building or other object 30 meters or more away
may be considered a distant object.
1. Set up one of the lenses in front of your viewing screen
2. Focus the image of your distant object upon the screen.
3. Measure the distance from the lens to the viewing screen when the best focus has
been obtained. This is the image distance (di). Record the value of di.
4. Use Equation 4 to determine and record the focal length of the lens.
5. Repeat this method for the other lens.
Image Distance (di) for the lens without the
red dot :
Image Distance (di) for the lens with the red
dot:
Use Equation 4 to determine:
Focal Length (f) for the lens without the red
dot:
Focal Length (f) for the lens with the red
dot:
3. Building a Telescope: A simple refracting telescope is very easy to create. All that is
needed are two converging lenses and two cardboard tubes. Knowing the focal length of
lenses is important for building a telescope because once you know the focal length of the
two lenses (eyepiece + objective) of a refracting telescope, you can easily determine how
far apart to place the two lenses from each other (and thus determine how long to make
the tube to hold the lenses).
A refracting telescope is a simple optical system composed of elements that you have
already studied. A refracting telescope consists of an objective lens and an eyepiece. The
objective lens is a converging lens in the leading end of the telescope (the end you point
at whatever you are looking at). The eyepiece is another converging lens that is used by
the eye to examine the image produced by the objective.
A diagram of a simple refracting telescope like the one that you are to construct is shown
below. The object is to the left of the diagram. Notice that the distance between the two
lenses is equal to the sum of their individual focal lengths.
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Lab Module 6: Converging Lens
Astronomy Laboratory Manual - Hartnell College
AST 1L
Finding the Focus of the Lenses
In order to construct a telescope, you must first find the focal length of your two lenses.
Since you did this in parts 1 and 2 of the lab, you should now be an expert at this!
Now you need to examine your two lenses and determine which lens to use as the
eyepiece (this is the one you will look through) and which is the objective lens.
Question 3: By definition, the eyepiece lens should be the lens with the smaller focal
length. Which of your two lenses should you use as the eyepiece? The one with the red dot
or the one without the red dot? _______________
Record the value of the focal length for the two lenses:
Remember by definition, the eyepiece lens should be the lens with the smaller focal
length.
Focal Length (f1) for the objective lens:
Focal Length (f2) for the eyepiece lens:
Question 4: If you focus the telescope on an object that is infinitely far away, the
ideal distance from the eyepiece lens to the objective lens (the length of the telescope
tube) can be calculated:
Equation 5: D= f1+ f2
Use Equation 5 to calculate, D, the ideal distance from the eyepiece lens to the objective
lens and record:
Making a Simple Refracting Telescope
•
•
•
Place the lenses inside the plastic rings of the telescope tubes. Make sure
you know which lens is the eyepiece lens. This is the lens that you will look
through.
Place the cardboard tube inside the two telescope tubes.
Look through the eyepiece lens at a distant object and slide tube with the
objective lens back and forth until you see a focused image. Voila, you
have just made a simple (cheap) telescope!
Question 5: Using the telescope, look through the eyepiece at a distant object and move
the inner tube until you can get a focused image. Measure the distance, D, the distance
from the eyepiece lens to the objective lens (length of the telescope tube) and record:
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Lab Module 6: Lenses and Telescopes
Astronomy Laboratory Manual - Hartnell College
AST 1L
Question 6: How did the calculated telescope tube length in Question 4 compare to your
measured telescope tube length in Question 5? Use Equation 3 to calculate the %
difference of this value from the calculated value.
For a system with two lenses such as a telescope, the Magnification of the telescope
can be calculated with:
Equation 6: M= f1 / f2
Question 7: Use Equation 6 to calculate the magnification of your telescope:
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Lab Module 6: Lenses and Telescopes
Astronomy Laboratory Manual - Hartnell College
AST 1L
Lab Module 7
Low Velocity Impact Craters
Equipment
Sand, metal tray, 5 steel balls with different diameters, vernier caliper, meter stick, ruler,
lamp
Objectives
This exercise is designed to familiarize you with a process whereby the surfaces of nearly
every solid planet and satellite in the Solar System became pock-marked with myriad
craters. The process even has implications for the demise of the dinosaurs! We also hope
to give you a little more experience with the techniques of experimental science.
Background
Everyone has seen photographs of the Moon
with its surface riddled with large and small
craters, looking like a battlefield. An
example is shown on the following page.
What caused these craters? Are they
remnants of past volcanoes?
Until relatively recent times, the
volcanic theory was generally accepted.
However, during the 20th Century evidence
accumulated that pointed to impacts as the
source of lunar cratering. It is now
generally accepted that virtually all of the
craters resulted from the impacts of asteroids
and meteorites very early in the history of
the Solar System. Further, recent spacecraft
exploration of the planets has shown that
nearly every solid surface in the Solar
System is similarly pock-marked with
craters of many sizes. We believe most of
this cratering occurred during an "era of
heavy bombardment" about four billion
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Lab Module 7: Low Velocity Impact Craters
Astronomy Laboratory Manual - Hartnell College
AST 1L
years ago, when the Solar System was filled with fragments of material that had failed to
condense into planets or satellites. Whizzing about in space, these fragments bombarded
and cratered the surfaces of the planets and satellites.
What about the Earth itself? Once we asked, "Why is the Moon cratered?" Now
we must ask, "Why is the Earth not cratered?" Actually, there are dozen of remnants of
impact craters on the Earth, but most are so badly eroded as to be nearly invisible. One
presumes that 4 billion years ago the Earth was heavily cratered, much like the Moon, but
weathering, glaciers, the rise and fall of oceans, and crustal movements have effaced the
terrestrial craters. On less active bodies like the Moon, the fossil craters are almost
perfectly preserved.
Interest in impacts has blossomed since the recent discovery that an asteroid
impact in the Gulf of Mexico 63 million years ago was the likely cause of the sudden
disappearance of the dinosaurs. Material flung aloft spread over the Earth and darkened
the skies for years, creating a global cooling that made the dinosaurs' habitat unlivable.
Could such an event occur now and threaten our own environment? The answer,
unfortunately, is "Yes." Hundreds of asteroids are in orbits that cross the orbit of the
Earth. Another collision is probably inevitable. Serious government-funded programs are
detecting and tracking these “Earth-crossing asteroids.” What to do if one is found to be
on a collision course is unclear!
Part I: Effect of the Size of the
Impactor.
The purpose is to determine how the
size of the impacting body (or
impactor) affects the size of the crater
that is created. Your “target” is a tray
of loose, dry sand. Before each trial,
carefully smooth the surface of the
sand with the edge of your ruler. You
are also provided with a graduated set
of metal spheres; these represent the
impactors. A meter-stick will be used
to measure the height from which the
spheres are dropped.
To obtain neat, symmetrical craters, try
to drop the spheres so that they strike
near the center of the tray; also try to
drop without imparting spin or
horizontal motion. If one of your
drops produces a distorted crater, it is probably best to repeat the drop to obtain a nice,
symmetrical crater that can be measured accurately.
You will find it easier to determine the locations of the peaks if the tray is illuminated
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very obliquely by a portable lamp so that the shadows are pronounced. (Does this suggest
to you why the lunar craters and mountains are much better seen when they are near the
sunrise line? Full Moon, when the illumination is vertical, is the very worst time to try to
see the Moon’s surface features!).
Step 1: Measure the diameters of your spheres with a vernier caliper in centimeter (cm).
Step 2: To more easily see the craters, shine a light at an angle onto the sand.
Step 3: Drop the sphere into the sand from a height of 1 meter. Use a centimeter scale to
measure the crater diameter from the peak of one wall to the peak of the opposite wall.
Record the data in your Table 1.
Step 4: Repeat drops and measurements two more times for the given sphere. Record the
data and calculate the average crater size of the three times you dropped the sphere.
Step 5: Using the Graphical Analysis plotting program on the computer, plot the results
of the average crater diameter (y-axis) vs. diameter of impactor (x-axis). Make sure to
label the x and y axes accordingly.
Step 6: Perform a Power Law fit to the profile (e.g., choose the function y=A*x^B)
Step 7: Record the value of the power index, B. This value is related to the overall shape
of the curve, i.e., if the curve falls off steeply, it has a higher power index. It also
determines how much of an influence the x-axis (size for this part) has on the y-axis
(crater diameter for this part). If the power index is higher, the curve is steeper and
changing the value of the x-axis (size for this part) will have a larger effect on the
y-axis (crater diameter for this part).
Part II: Effect of Velocity of the Impactor.
How does the velocity of the impactor affect the size of the crater? You will vary the
impact velocity by dropping a sphere from various heights.
In elementary physics we learn that your impact velocity v is given by:
Equation 1: v
2gh
where h is the drop height and g is the acceleration due to the Earth's gravity
(980 cm/s2). Thus, once you have a measurement for the height at which you dropped
the impactor, you can calculate the impact velocity (the velocity at which the sphere
strikes the sand).
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Step 1: Select one of the medium-size spheres. Start at a height of 1 meter.
Step 2: Drop the metal sphere three times, recording the height (in cm), the crater
diameter (in cm) associated with each trial, and the average crater diameter (in cm) from
the three trials. You should record these values in a Table 2.
Step 3: Repeat steps 1 and 2 for the SAME metal sphere, but decreasing the height 20 cm
at a time until you reach 20 cm.
Step 4: Calculate the value of the velocity associated with each height using Equation 1.
Record the velocity associated with each height in the table.
Step 5: Using the Graphical Analysis plotting program on the computer, plot the results
of the average crater diameter (y-axis) vs. the velocity (x-axis). Make sure to label the
x and y axes accordingly.
Step 6: Perform a Power Law fit to the profile (e.g., choose the function y=A*x^B)
Step 7: Record the value of the power index, B.
Questions
1. What happens to the velocity of the impactor if you increase the height?
2. What happens to the crater diameter as you increase the impactor size?
3. What happens to the crater diameter as you increase the velocity of impact?
4. Compare the power index (B) from part 1 (effect of the size of the impactor) with the
power index (B) from part 2 (effect of the velocity of the impactor). Which one affects
the size of the crater more, the velocity of the impactor or the size of the impactor (i.e.,
which one has the higher power index value)? Were the results what you expected?
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Hypothesis: What affects the crater size more, size or velocity of the asteroid? Why?
DATA TABLE 1: EFFECT OF IMPACTOR SIZE
Power Index (B):
Size of Impactor
(cm)
Diameter of Crater
(cm)
Average Crater Diameter
(cm)
DATA TABLE 2: EFFECT OF VELOCITY
Power Index (B):
Height Dropped
(cm)
100
Impact Velocity
(cm/s)
Diameter of Crater
(cm)
Average Crater
Diameter (cm)
80
60
40
20
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Lab Module 8
The Spectroscope
Identifying Elements with Emission Line Spectra
Equipment
Incandescent light bulb and power supply; gas discharge tubes and their power supplies;
spectroscope; color pencils.
Objectives
We will learn about the tools astronomers use to separate a light source into its
constituent colors. We will learn how to quantify color by measuring the wavelength of
light. We will observe the difference between a continuous spectrum and an emission
line spectrum. Finally, we will see how astronomers identify elements by observing the
patterns of emission lines found in a spectrum.
Background
Chances are, you have seen a rainbow after a soft spring shower. Or perhaps you’ve seen
the rainbow of color that comes from light shining through a crystal or triangular prism.
The colorful light you see – the familiar red, orange, yellow, green, blue pattern – is
called a spectrum. Where do all of those colors come from? Many people before you
have wondered the same thing. For a very long time, most people imagined that the
raindrops, crystal, or prism glass somehow contaminated the white light shining through
them. That seems like a very logical conclusion. In fact, the more glass you use (the
bigger the prism), the broader the spectrum and the more colors you can see!
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But things aren’t always as they appear. In the 1660’s, a British scientist by the name of
Isaac Newton (later knighted “Sir” Isaac Newton by Queen Anne) performed a very
simple experiment. He passed white light through not one, but two prisms. By turning
the second prism upside down, Newton observed that the emerging light was just like the
simple white light he shined on the first prism. The first prism made a spectrum, and the
second prism got rid of the spectrum. This contradicted the idea that the glass added
color. Newton concluded that white light is a mixture of all of the colors of the rainbow.
He described the prism as a tool that could spread the colors out enabling our eyes to see
each of them separately. The upside-down prism in Newton’s experiment still spread out
each of the colors. But it did so in exactly the opposite direction of the first prism.
A spectroscope is exactly like a prism in that it is a tool for spreading out the colors
contained in a light source. You will observe various light sources with a spectroscope
and discover which colors they are actually comprised of. Perhaps you will also find
that things aren’t always as they seem!
Fill in data in the Data Tables provided.
Part I: The Continuous Spectrum
The spectroscope spreads light out into its constituent colors just like the prism. Try it
and see! Look at a light bulb through the spectroscope. You should see a rainbow of
colors. This is called a continuous spectrum. Light from a normal incandescent bulb
contains all of the colors perceivable by the human eye. Scientists have devised a way to
quantify the colors that you see using wavelength.
It is often handy to think of light as a wave – like the wave you make by dropping a stone
in a pond – because light has many wave-like properties. When you drop a stone in a
pond, you create ripples, and you could actually measure the distance between the
ripples. This distance is called the wavelength. Each color of light has a unique
wavelength. It is handy to be able to describe the color of light with a number. Scientists
like that a lot because it allows them to make un-biased observations. You can imagine
the confusion one would make by describing an object as being muddy-greenish-yellow!
Step 1: Your spectroscope has a scale inside of it to help you determine the wavelength
of the light that falls on a certain position. Observe the continuous spectrum that the light
bulb produces through the spectroscope.
Step 2: In the first column of the data table, list each color that you see and the
wavelength associated for each color in the data table. If the color is located at a range of
wavelengths, list the range of wavelength associated with each color.
Step 3: In the last column, estimate the brightness of each color you observe. You can
give verbal descriptions like “very bright”, “weak”, etc. You can also describe any other
observations that seem noteworthy. For example, one color is very sharp while another is
rather “fuzzy”. Or perhaps you observe unusual spacing patterns between colors.
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Step 4: Using the information from steps 2 and 3 and using colored pencils, sketch the
spectrum that you observe through the spectroscope in the empty rectangle below the
table. Be sure to label the wavelength and make the sketch to scale (i.e., if a color is
wider than another color, be sure that your sketch reflects this).
Part II: The Study of Individual Elements
In the laboratory, you will find several glass tubes, called discharge tubes. Each tube
contains a gas comprised of a different element. For example, one tube contains pure
hydrogen gas. When you add energy to this gas (by applying a voltage), the gas will
become luminous. Each element shines with its own characteristic colors. The pattern of
colors emitted by each element is a fingerprint of sorts. No two elements emit exactly the
same colors of light. These bright colors in the spectrum are called emission lines.
Repeat steps 1-4 for the Hydrogen gas tube. Be very careful when handling the gas
tubes as they can get hot!
Part III: Mystery Spectra!
As you can see, every element has its own unique pattern of colors. Now that you have
practiced using the spectroscope, it is time to put your skills to use. Two of the gas
discharge tubes have lost their labels. Fortunately, scientists have been studying spectra
for many decades and can provide us with information on the spectra of nearly every
element. We know that the remaining two tubes must be filled with one of the following
elements: Helium, Krypton, Neon, and Nitrogen.
Repeat steps 1-4 for the mystery gas tubes. Once you are finished, ask your instructor
to give you a comparison spectra sheet. Compare your observations with the comparison
spectra and try to guess what the mystery gas is. Write down your guess. Afterwards,
look at the gas tube and write down the name of the actual gas. You will not be penalized
for a wrong guess!
Part IV: Drawing Conclusions
Even the closest of stars are so far away that we can only dream of visiting them. That’s
very unfortunate. Many astronomers would like to scoop up a handful of “star stuff” to
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see just what their made of. Surprisingly, though, we know a great deal about what stars
are made of without ever having to visit them. We learn by collecting the light they emit
– the light that actually reaches Earth and falls into our telescopes. It can tell us a lot!
Questions
1. What are the units of wavelength? How do they relate to the meter?
2. Observing your sketches of a continuous (light bulb) and emission line spectrum (gas
lamps), describe the similarities and differences of the two types of spectrum.
3. Were you able to guess the identity of the two mystery gases? If not, describe the
difficulties you faced when making the guesses.
4. How do you think astronomers can determine what stars are made of?
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Color
400nm
550nm
Color
400nm
Continuous Spectrum (Light Bulb)
Brightness Comments
Wavelength
Hydrogen Spectrum (H)
Wavelength
550nm
700nm
Brightness Comments
700nm
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Mystery Gas #1
Color
Guess:
Brightness Comments
Wavelength
400nm
Mystery Gas #2
Color
Actual:
550nm
Guess:
700nm
Actual:
Wavelength
Brightness Comments
400nm
550nm
700nm
400nm
550nm
700nm
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Lab Module 9
The Classification of Stellar
Spectra
Equipment
This experiment uses a Windows computer, the CLEA program Spectral Classification, and a scientific
calculator. (Note that the computer mentioned above may provide such a calculator.)
Objective
In this exercise you will:
Take spectra using a simulated telescope and spectrometer.
Obtain spectra of good signal to noise levels and store them for further study.
Compare these spectra with standard spectra of known spectral type.
Assign spectral classifications to main sequence stars with a precision of one or two
tenths of a spectral type.
Recognize prominent absorption lines in both graphical and photographic displays of the
spectra.
Obtain spectra of unknown stars from a simulated field of stars.
Background
The History And Nature Of Spectral Classification
Patterns of absorption lines were first observed in the spectrum of the sun by the German physicist
Joseph von Fraunhofer early in the 1800’s, but it was not until late in the century that astronomers were
able to routinely examine the spectra of stars in large numbers. Astronomers Angelo Secchi and E.C.
Pickering were among the first to note that the stellar spectra could be divided into groups by the general
appearance of their spectra.
In the various classification schemes they proposed, stars were grouped together by the
prominence of certain spectral lines. In Secchi’s scheme, for instance, stars with very strong hydrogen lines
were called type I, stars with strong lines from metallic ions like iron and calcium were called type II, stars
with wide bands of absorption that got darker toward the blue were called type III, and so on.
Building upon this early work, astronomers at the Harvard Observatory refined the spectral types
and renamed them with letters, A, B, C, etc. They also embarked on a massive project to classify spectra,
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carried out by a trio of astronomers, Williamina Fleming, Annie Jump Cannon, and Antonia Maury. The
results of that work, the Henry Draper Catalog (named after the benefactor who financed the study), was
published between 1918 and 1924, and provided classifications of 225, 300 stars. Even this study, however,
represents only a tiny fraction of the stars in the sky.
In the course of the Harvard classification study, some of the old spectral types were consolidated
together, and the types were rearranged to reflect a steady change in the strengths of representative spectral
lines. The order of the spectral classes became O, B, A, F, G, K, and M, and though the letter designations
have no meaning other than that imposed on them by history, the names have stuck to this day. Each spectral
class is divided into tenths, so that a B0 star follows an O9, and an A0, a B9. In this scheme the sun is
designated a type G2 (see Appendix I).
The early spectral classification system was based on the appearance of the spectra, but the
physical reason for these differences in spectra were not understood until the 1930’s and 1940’s. Then it
was realized that, while there were some chemical differences among stars, the main thing that determined
the spectral type of a star was its surface temperature. Stars with strong lines of ionized helium (HeII),
which were called O stars in the Harvard system, were the hottest, around 40,000 o K, because only at high
temperatures would these ions be present in the atmosphere of the star in large enough numbers to produce
absorption. The M stars with dark absorption bands, which were produced by molecules, were the coolest,
around 3000 o K, since molecules are broken apart (dissociated) at high temperatures. Stars with strong
hydrogen lines, the A stars, had intermediate temperatures (around 10,000 o K). The decimal divisions of
spectral types followed the same pattern. Thus a B5 star is cooler than a B0 star but hotter than a B9 star.
The spectral type of a star is so fundamental that an astronomer beginning the study of any star
will first try to find out its spectral type. If it hasn’t already been catalogued (by the Harvard astronomers or
the many who followed in their footsteps), or if there is some doubt about the listed classification, then the
classification must be done by taking a spectrum of a star and comparing it with an Atlas of well-studied
spectra of bright stars. Until recently, spectra were classified by taking photographs of the spectra of stars,
but modern spectrographs produce digital traces of intensity versus wavelength which are often more
convenient to study. FIGURE 1 shows some sample digital spectra from the principal MK spectral types; the
range of wavelength (the x axis) is 3900 Å to 4500 Å. The intensity (the y axis) of each spectrum is
normalized, which means that it has been multiplied by a constant so that the spectrum fits into the picture,
with a value of 1.0 for the maximum intensity, and 0 for no light at all.
The spectral type of a star allows the astronomer to know not only the temperature of the star, but
also its luminosity (expressed often as the absolute magnitude of the star) and its color. These properties, in
turn, can help in determining the distance, mass, and many other physical quantities associated with the
star, its surrounding environment, and its past history. Thus knowledge of spectral classification is
fundamental to understanding how we put together a description of the nature and evolution of the stars.
Looked at on an even broader scale, the classification of stellar spectra is important, as is any classification
system, because it enables us to reduce a large sample of diverse individuals to a manageable number of
natural groups with similar characteristics. Thus spectral classification is, in many ways, as fundamental to
astronomy as is the Linnean system of classifying plants and animals by genus and species. Since the group
members presumably have similar physical characteristics, we can study them
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as groups, not isolated individuals. By the same
token, unusual individuals may readily be
identified because of their obvious differences
from the natural groups. These peculiar objects
then be subjected to intensive study in order to
attempt to understand the reason for their unusual
nature. These exceptions to the rule often help us
to understand broad features of the natural
groups. They may even provide evolutionary
links between the groups.
The appendices to this manual give the basic
characteristics of the spectral types and
luminosity classes. But the best way to learn about
spectral classification is to do it, which is what
this exercise is about.
Figure 1
Digital Spectra of Main Sequence Stars
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Part I. Spectral Classification of Main-Sequence Stars
THE SPECTRAL CLASSIFICATION TOOL
The Spectral Classification tool provides for the display of stored files of stellar spectra from the
VIREO single-object or multi-channel spectrograph. These files can be compared with several stored
standard-star atlases to facilitate the classification of the star’s spectral class and luminosity class. Access this
tool from the Tools Spectral Classification option on the Virtual Observatory Control Screen.
Figure 11: The Spectral Classification Tool
Controls on The Spectral Classification Tool:
•
Controls on the Menu Bar:
o File Unknown Spectra: selects the unknown spectrum to be displayed. It can be displayed from a
stored data file taken with the VIREO telescope (or any other telescope—as long as the spectra are
text files of wavelength vs relative intensity), or from a list of stored data files used for the CLEA
Classification of Stellar Spectra activity. This file is displayed in the center of the three screens
below the menu bar.
o File Atlas of Standard Spectra: Loads an atlas of standard spectra, which is displayed in pairs of
spectra, one above, and one below the unknown, to make it easier to see where the unknown fits into
the sequence. Currently, VIREO has a main-sequence spectral atlas and spectral atlases as a function
of luminosity classes for several regions of spectral class.
o FileSpectral Line Table: Loads a descriptive list of diagnostic spectral lines with descriptions of
how they can be used to classify spectra. Users can click on a spectral line as they move around a
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spectrum, and the table will display the source of the line. When a line table entry is double-clicked,
a description of some of the characteristics of that line is displayed.
Part II. Taking Spectra Using A Simulated Telescope And Digital
Spectrometer
THE VIRTUAL OBSERVATORY CONTROL SCREEN
Choosing the Virtual Observatory option brings up the Virtual Observatory Control Screen (figure 1), which
is the base of control for the various functions of VIREO.
Figure 1: The Virtual Observatory Control Screen
1.
2.
3.
4.
Select a telescope: From the Virtual Observatory Control screen, select one of the three available
telescopes. The larger the telescope, the brighter the images and the shorter the exposure times. You
can always return to this screen to choose a larger telescope if you find that the objects you are
studying are too faint for the telescope you are using. Once you have selected the telescope, a status
message at the bottom of the window will say “Accessing telescope”. Wait until the message “You
now have control of the telescope” appears. Select “OK” and the dome shutters will appear on the
screen. You are now ready to observe.
Open the dome shutters: so that the telescope can see the sky by clicking on the Dome open/close
switch at the upper right. The dome shutters will slide open, revealing the night sky. The bright stars
you see are those crossing your meridian at the present time for your location, as you would see them
if you were standing in the dome.
Access the Telescope Control Panel: Click on the optical telescope control panel button at the
lower right of the Observatory control screen. The telescope Control Panel Screen will open. You
can now use the telescope.
General description of the Telescope Control Panel. Controls on the telescope control panel allow
you to move the telescope to different parts of the sky, switch the view between the wide-field finder
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and the narrow-field telescope view, and access optical instruments such as the photometer,
spectrometers, and cameras. Large digital displays show Universal Time, Sidereal Time, as well as
the Right Ascension and Declination the telescope is pointed at. Smaller displays show the Julian
Day to six decimal places (essentially a fraction of a second), and a display at the upper right shows
local standard time. A central window shows, in a “TV-camera” view, what the sky the telescope
sees through the finder or narrow-field telescope, depending on which is selected. In the TV view,
north is to the top, and east is to the left, which is the standard orientation in most telescopes and
astronomical images.
Figure 2: The Optical Telescope Control Screen
5.
Controls on the Telescope Control Panel
• Tracking Control: Must be turned on to access other controls. Without it, the telescope does
not track the stars. Without the tracking on, you will be able to see stars drift across the field of
the TV monitor from east to west at the rate of 360° per day.
• Telescope Motion: The four N-E-S-W buttons move the telescope to the north, east, south, or
west. The Slew Rate slider controls the speed of the motion. The telescope can also be moved
to specific spots in the sky using the Slew… option, by typing in coordinates, or by selecting
objects from a hot list.
• View: The slider selects between a wide-field finder view, and a narrow field telescope view. A
display under the slider shows the width of the field of view. Default for the wide-field finder
view is 2.5 degrees, and the default for the narrow-field telescope view is 15 arc minutes (0.25
degree). The telescope view must be used to access the instruments. In the narrow field view, a
red mark around the center of the screen indicates the position of measuring apertures or fields
of view of the camera.
• Instrument: The slider selects the available instruments for the telescope, including the
Aperture Photometer, single-slit Spectrometer, multi-aperture Spectrometer, CCD camera, and
IR camera. Clicking the Access button under the slider will bring up a control screen for the
instrument chosen.
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USING THE SPECTROMETER
Make sure you are in the Telescope Control screen, that the telescope is tracking, that you are pointed at the
approximate coordinates of the object of interest, and that the telescope is set for the narrow-field
(“Telescope”) view. Access the spectrometer by setting the Instrument slider to Spectrometer, and click the
Access button. The Spectrometer Control window should appear.
Figure 4: The Spectrometer Control Window
Controls on the Spectrometer Control Screen:
•
•
•
•
•
•
Spectrum Display: Displays the spectrum being obtained. The spectrometer is a photon-counting
spectrometer, so when the spectrum is actually accumulating counts this display shows the individual
counts in each channel as dots. When the spectrum is complete (or paused) the points are connected, and
the overall pattern of the spectrum can be seen. The display axes are wavelength in Ångstroms, along the
y axis, and relative intensity, on the y axis---which is the number of counts in a channel normalized to the
maximum counts in all the channels. To alter the spectral range displayed on the x axis, choose File
Preferences Spectral Range from the menu bar on the Spectrometer Control Screen.
Photon Count: Displays the total number of photons recorded by the spectrometer.
Photons Per Channel (avg): Displays the total number of photons divided by the number of channels in
the spectrum.
Integration Seconds: Displays the total length of time the spectrum has been accumulating
Signal to Noise Ratio:
Go/Stop buttons: Start and stop the observations. The stop button pauses the accumulation of photons,
but the start button can be pressed again if more counts are desired (e.g. to achieve a higher signal to
noise ratio.)
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Taking Spectra:
1.
2.
Using the NESW buttons on the Telescope Control screen, position the object of interest directly
in the center of the slit marked by two red lines on the TV display window. Note that the
spectrometer is only sensitive to light that enters through the slit. If you point it at the blank sky,
you will get background noise. If you are observing an extended object like a galaxy, you will
get the strongest signal if you center on the brightest part of the object. When you have the
telescope in the desired position, simply press Go, and watch the spectrum accumulate. You can
press Stop at any time to examine the spectrum, and take a longer exposure if you wish to
increase the signal to noise ratio.
To save it for further measurement for redshift, line strength, or spectral classification, choose
the options on the File Data drop-down menu. The spectrum can be saved under a name
determined by the user or under a default name by the software.
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Sketches of Stellar Spectrum
Continuous Spectrum
Guess
Actual
Emission Line Spectrum
Guess
Actual
Absorption Line Spectrum
Guess
Actual
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Data Table 1
Star Name
Spectral
Type
Temperature
Range
Absorption Lines
(Wavelength, Element)
HD124320
HD 37767
HD 35619
HD 23733
O1015
HD 24189
HD 107399
HD 240344
HD 17647
BD +63 137
Data Table 2
Star #
1
2
3
4
5
Star Name
Spectral Type
Temperature Range
Questions
1.
Look at your data from Tables 1 and 2.
a) List the names of the star or stars that is\are the coolest?
b) What spectral type is this associated with?
c) What is the range of surface temperatures associated with this spectral
type?
2.
Look at your data from Tables 1 and 2.
a) List the names of the star or stars that is\are the hottest?
b) What spectral type is this associated with?
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c) What is the range of surface temperatures associated with this spectral
type?
3.
a) What spectral type is our Sun?
b) What is the range of surface temperatures associate with our Sun?
c) Which star or stars is/are most like our Sun?
4. What three elements exist inside a star?
EXTRA CREDIT
Having both the spectral classification and the apparent magnitude, m, of a star enables one to determine its
distance, since there is a relation between the spectral type of a star and its absolute magnitude. Once the
absolute magnitude, M is known, we know the so-called “Distance Modulus”, m-M of the object, and we
can apply the relationship:
logD = m – M + 5
5
and
D = 10logD
to determine the distance to the object in parsecs.
Appendix II contains a table of absolute magnitudes for stars of various spectral types. Using this
information, determine the absolute magnitudes and distances of the two stars you classified in the previous
part of this exercise. Present your results on the following table.
Sta r
Spectral Ty pe
Absolute
Magnitude, M
Appa rent
Magnitude, m
Distance in
pa rsecs
Question: Are these stars members of the Milky Way Galaxy of which our Sun is a part? (The
Diameter of the Milky Way is about 30, 000 parsecs)_
.
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Appendix I
Distinguishing Features Of Main Sequence Spectra
SPECTRAL TYPE
SURFACE TEMP
(° K)
Distinguishing Features
(absorption lines unless noted otherwise)
O
28-40,000
He II lines
B
10-28,000
He I lines; H I Balmer lin es in cooler
types
A
8-10,000
Strongest H I Balmer at A0; CaII
increasing at cooler types; some other
ion ized metals
F
6000-8000
Ca II stronger; H weaker; Ionized metal
lines appearing
G
4900-6000
CaI II stron g; Fe and other Metals strong,
with neutral metal lines appearing; H
weakening
K
3500-4900
Neutral metal lines strong; CH and CN
bands developing
M
2000-3500
Very many lines; TiO and other molecular
bands; Neutral Calcium prominent. S
stars show ZrO and N stars C2 lines as
well.
WR (Wolf-Rayet)
40,000+
Broad emission of He II; WC stars show
CIII and CIV emission, while WN stars
show NII prominently
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Appendix II
Absolute Magnitude Versus Spectral Type
(from C.W. Allen, Astrophysical Quantities, The Athlone Press, London, 1973)
Main Sequence Stars, Luminosity Class V
Spectral Type
Absolute Magnitude
O5
-5.8
B0
-4.1
B5
-1.1
A0
+0.7
A5
+2.0
F0
+2.6
F5
+3.4
G0
+4.4
G5
+5.1
K0
+5.9
K5
+7.3
M0
+9.0
M5
+11.8
M8
+16.0
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Lab Module 10
Solar Rotation
Tracking Magnetic Active Regions Across the Face of the Sun
Equipment
High resolution images of the Sun taken in the optical and ultra-violet by the SOHO
spacecraft; latitude/longitude grid transparency overlay; transparency markers; calculator.
Objectives
Using modern images of the solar surface taken with instruments aboard the SOHO
spacecraft, we will track the position of sunspots as the Sun rotates. Our tracking data
will allow us to compute the period of the Sun’s rotation. We will compare the results
obtained using spots at different latitudes.
Background
Modern astronomy has deep roots in ancient Greek tradition. While virtually every
culture has contemplated the cosmos, only Hellenistic Greece is recorded as having
performed detailed quantitative observations of the heavens on which to base their
cosmology. Greek thought placed the Earth at center stage. Moreover, Greek
philosophers distinguished the Earth from other celestial bodies as described by Thomas
Kuhn in The Copernican Revolution:
“The earth is not part of the heavens; it is the platform from which we
view them. And the platform shares few or no apparent characteristics
with the celestial bodies seen from it. The heavenly bodies seem bright
points of light, the earth an immense nonluminous sphere of mud and rock.
Little change is observed in the heavens: the stars are the same night after
night… In contrast the earth is the home of birth and change and
destruction. Vegetation and animals alter from week to week; civilizations
rise and fall from century to century; legends attest the slower
topographical changes produced on earth by flood and storm. It seems
absurd to make the earth like celestial bodies whose most prominent
characteristic is that immutable regularity never to be achieved on the
corruptible earth.”
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Indeed, the heavenly realm was considered to encompass the celestial bodies beginning
with the Moon and extending past the Sun and planets to the stars and beyond. All
objects in the realm were thought to be perfect in form, divine, immutable.
This view changed forever during the Renaissance. In 1610, the Italian astronomer,
Galileo Galilei, pointed a telescope to the sky. On the surface of the Sun – the giver of
life itself – he saw blemishes that looked like dark spots. With consistent observations,
he was able to conclude that the “blemishes” were, indeed, features on the surface of the
Sun. Moreover, with time, he saw that these features changed. The dark spots (now
called sunspots) crossed the solar disk with great regularity. Galileo correctly concluded
that the Sun is rotation – or spinning – on one axis. He could even determine the time it
takes for the Sun to spin around once – its rotational period. His observations
completely changed the perception of the Sun as perfect and immutable.
The spots appear dark because they represent regions of the photosphere that are cooler
than the rest of the Sun. The average number and location of sunspots have been known
to go through an average cycle of 11 years. Within the 11-year cycle, the most sunspots
appear at sunspot maxima and the least number of sunspots appear during sunspot
minima. Although it may look small in the telescope, the typical sunspot is 10,000 km
across (slightly smaller than the diameter of the Earth).
In 1908, the American astronomer George Ellery Hale discovered that sunspots occurred
as a result of the intense magnetic field of the Sun. Sunspots are connected in pairs, one
where the magnetic field leaves the sun and one where the magnetic field enters the Sun.
The immense magnetic field of the Sun is also responsible for other solar atmospheric
phenomenon . Plages appear just before nearby sunspots appear and are believed to be
created by magnetic fields that crowd upward just under the photosphere. As these fields
push upward, the gas just above is compressed and becomes hotter. For this reason,
plages appear as bright regions in the Sun’s atmosphere. Dark streaks in the corona are
called filaments. Filaments are huge ejections of gas that are lifted by the magnetic field
above the photosphere. When viewed from the side, they form gigantic arches and are
called prominences.
In this lab, we will repeat Galileo’s observations and measurements of the rotational
period of sunspots using data taken by the SOHO spacecraft. We will also observe
through a telescope to determine the number of sunspots the sun currently posses and
sketch the appearance of filaments and prominences on the Sun’s surface.
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Lab Module 10: Solar Rotation
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Part I: Taking Data
The instructor will provide you with:
1. Two sets of Solar images
2. Two latitude/longitude grids printed out on acetates.
3. Colored acetate markers.
The Solar images were taken at two different epochs (times) with two different
instruments: the EIT images were taken in 1996 (at a time of minimum solar activity),
and the MDI images were taken in 2002 (during maximum solar activity). The
latitude/longitude grids will be used to track the motion of spots from one image to
another as explained below.
First, spread out the images in front of you. Lay them out in order of when they were
taken. The date and time is listed at the top of each image. Examine the images to
become familiar with the features. Can you track with your eye how the motion of a
sunspot progresses from image to image? Can you do the same for the bright features on
the EIT images?
You have marked spot locations from successive images onto your spherical grid. The
spots are actually moving along the surface of a sphere. The vertical lines on your grid
tell you how many degrees the spot moved (measured from the center of the Sun). The
space between one longitude line and the next corresponds to 10 degrees.
Now, select three spots that can be seen in five or more successive images. Look for
spots that begin on the edge of the image and travel all the way across the solar disk.
Select your spots so that :
1. they are located at different latitudes (north/south).
2. at least one is from the EIT set and at least one is from the MDI set.
Carry out the following steps, repeating the sequence for each spot you have chosen.
You will track your spots all on the same grid, so be neat.
Step 1: Lay the transparency grid over the image containing the first appearance of the
first spot you are analyzing.
Step 2: Carefully align the transparency grid with the image. Up/down (north/south)
alignment is very important here.
Step 3: With a colored marker, mark the location of the center of the spot directly onto
the grid. Keep your mark as small as possible, and label your mark A1. Record the
longitude, date, and time for the spot on the Sunspot Data Table.
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Step 4: Go to the next image in the sequence. The spot will have moved slightly in
longitude, but should be located at approximately the same latitude. Using the same
transparency grid, mark the new position, labeling the mark A2. Record the date, time,
and longitude for the spot on the Sunspot Data Table. Repeat this for all of the images
containing this particular spot, numbering them A3, A4, etc.
Step 5: Repeat Steps 1-4 for two other spots, giving each a different letter label (B, C).
Part II: Computing the Rotational Period
You will now use the information that you recorded on the Sunspot Data Table to
estimate how many degrees each spot moved and how long it took to move that distance.
From this information, you will be able to compute the rotational period as described
below. Record the following information in the Rotational Period Table.
1. Determine how much each spot moved
Determine the number of degrees that the spot has moved for each configuration listed in
the Rotational Data Table. Each line of the data table tells you which spot positions to
consider. For example, the first line says “1 to 3”. In this case, you will determine the
number of degrees the spot moved by subtracting its longitude at the third position from
its longitude at the first position. Record this information in the second column
(Degrees) of Data Table 2.
2. Determine the time the spot took to move
For each configuration, determine the time it took for the spot to move the given distance.
Enter this value in the third column (time) of the Data Table 2. Do this for every spot.
Express your values in units of hours. For example, if it took 2 days, 3 hours, and 45
minutes for the spot to move from position one to position three, you would change this
to hours using the following calculation:
Number of hours = ( N days × 24 hours/day) + (N hours ) + ( N minutes ÷ 60 minutes/hour)
= (2 × 24) + (3) + (45 ÷ 60)
= 51.75 hours
NOTE: Be very careful that you account for the correct number of days the spot
moved by noting the dates for each position.
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3. Compute the Rotational Period
For each line in your data table, you will compute a rotational period and enter it in
column four. To do this, we set up the following ratio:
Time
P
=
Degrees 360 
In the ratio, “Time” is the value in column two of your data table, and “Degrees” is the
value in column three of your data table. We want to solve for “P” which is the rotational
period:
P=
Time × 360 
Degrees
To continue our example that we started above, let’s pretend that we had a spot that
moved 30 degrees in 51.75 hours. The rotational period from this data would then be:
51.75 × 360
30
= 621 hours
P=
This hypothetical data tells you that it takes 621 hours for the spot to make a full
revolution. Repeat these calculations for each line of each data table. Enter your results
in column four (Period) of Data Tale 2.
4. Average Your Results
Each line of your data table probably gives you a slightly different rotational period.
That makes sense because there is always a margin of error in our measurements. You
can eliminate some of this error by averaging together all of your results for each spot.
Record the average period in hours.
To find out how many days it took for the spot to move use the information: 1 day=24
hours to convert the average period from hours to days. Record this value.
Part III: Drawing Conclusions
You have made some very important observations of the Sun that allowed you to see how
the Sun spins on its axis. Galileo did the very same thing with a crude telescope – poorer
than the simplest modern amateur telescope one can buy at the local discount store. The
lens in Galileo’s telescope (now housed in a museum in Florence, Italy) was less than two
inches in diameter!
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The images you have studied were taken with the most sensitive instruments from the
prime vantage point of a Sun-orbiting spacecraft. The quality of these images allowed
you to get a very good estimate of the period of the Sun’s rotation. It also allowed you to
study the rotation of features at different latitudes and different times. Now that you have
finished your calculations, respond to the following:
Questions
1. What causes these sunspot features on the solar surface? Why are sunspots dark?
2. What is the average rotation period in days for the three spots? From these values,
determine whether the approximate rotation period of the Sun is much longer,
much shorter, or about equal to one month?
3. Who was the first to use this method to determine the rotation period of the Sun?
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SUNSPOT DATA TABLES (for Part I)
Spot A
Image (MDI or EIT):______
Position
1
2
3
4
5
Longitude
Spot Latitude: _________
Date
Time
Spot B
Image (MDI or EIT):______
Position
1
2
3
4
5
Longitude
Spot Latitude: _________
Date
Time
Spot C
Image (MDI or EIT):______
Position
1
2
3
4
5
Longitude
Spot Latitude: _________
Date
Time
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ROTATIONAL PERIOD TABLES (for Part II)
Spot A
Positions:
1 to 3
2 to 4
1 to 5
Degrees
Time (hrs)
Period (hrs)
Average Period (hrs): ________
Average Period (days):________
Spot B
Positions:
1 to 3
2 to 4
1 to 5
Degrees
Time (hrs)
Period (hrs)
Average Period (hrs): ________
Average Period (days):________
Spot C
Positions:
1 to 3
2 to 4
1 to 5
Degrees
Time (hrs)
Period (hrs)
Average Period (hrs): ________
Average Period (days):________
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Lab Module 11
The Classification of Galaxies
Equipment
Website of galaxy images, color pencils, Hubble Tuning Fork Diagram
Objectives
Develop a classification scheme for galaxies and compare it to Hubble’s Tuning Fork
Diagram.
Background
In the 1700s, one of the ways astronomers distinguished themselves was by discovering
comets. Eighteenth century astronomers would scan the sky with their telescopes looking
for faint, fuzzy objects. Unfortunately for them, there are several fuzzy-looking objects
in the sky that are not comets- we know this because, unlike comets, these objects do not
move from night to night with respect to the stars in the sky.
From 1758 to 1782, a French astronomer named Charles Messier compiled a catalog of
these diffuse-looking objects, called nebulae, so that they would no longer be mistaken
for comets. Messier catalogued 110 total nebulae. Most of these objects are still known
by their Messier numbers.
Since the eighteenth century, astronomers with high powered telescopes have resolved
many Messier objects into globular and open star clusters. Other Messier objects are now
known to be areas of glowing gas around newly forming stars, or gas given off by stars
that have recently stopped burning. All of these types of objects are known to lie within
our galaxy, the Milky Way.
Several Messier objects do not fit into the classifications described above. These objects
are clearly not star clusters, nor are they associated with young stars or the remnants of
old stars. Astronomers labeled these objects “spiral nebulae” because many of them
exhibit spiral structure. What is the nature of these objects? Do they lie within the Milky
Way or outside of it? The latter question was hotly debated and remained unresolved
until 1923!
The existence of galaxies other than the Milky Way was first proposed in 1755 by
astronomer/philosopher Immanuel Kant. By the early 1900s, many astronomers
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postulated that spiral nebulae were in fact other galaxies that lay outside of the Milky
Way. Other Astronomers made convincing arguments against this hypothesis. They
argued instead that the Milky Way was essentially the entire Universe and that spiral
nebulae were components of our galaxy that just weren’t yet well-understood. The
answer to this argument rested in measuring the size of the Milky Way and the distances
to spiral nebulae, and comparing the two distance measurements.
The argument over the distances to spiral nebulae came to a head in April 1920 when
Harlow Shapley and Heber D. Curtis held a formal discussion of the matter which is now
known to astronomers as the Great Debate. Shapley argued in favor of spiral nebulae
being nearby objects that were scattered within the Milky Way. Shapley had measured
the Milky Way’s size at 60,000 light years across! He argued that if spiral nebulae were
as large as the Milky Way Galaxy, they must lie at inconceivable distances from us.
Contrarily, Curtis argued in favor of Kant’s theory that spiral nebulae were in fact distant
galaxies. He assumed that each of the spiral nebulae were about the same size.
However, he noted that spiral nebulae were observed as having different sizes. Curtis
suggested that the nebulae which looked smaller on the sky were actually much more
distant than the nebulae which looked larger. He concluded that there must be a huge
range in distances to spiral nebulae, and that these distances were far larger than the size
of the Milky Way.
Who won the great debate? Really, no one. Although Shapley and Curtis both gave
convincing arguments, neither of them was able to give a definitive answer to the
problem on the spiral nebulae distances. The matter remained unresolved until 1923
when Edwin Hubble provide us with an answer. (Edwin Hubble is the astronomer the
Hubble Space Telescope was named after).
Hubble was the first astronomer to measure the distance to a spiral nebulae. How did he
do this? Hubble was comparing the photographic images of the spiral nebula M31 (also
known as Andromeda) and noticed that one of the stars belonging to the nebula varied in
brightness from night to night. He recognized that this was a Cepheid variable star, or a
star which regularly gets dimmer and then brighter again. There is a known relationship
between the intrinsic brightness of a Cepheid variable star and period of its brightness
fluctuation (the time it takes to go from its brightest to its dimmest and back to its
brightest again). Hubble therefore calculated the Cepheid variable star’s intrinsic
brightness and compared this to the star’s observed brightness. He knew that the farther
away a star is, the dimmer it will appear. Hubble determined that the Andromeda nebula
is over 1,000,000 light years away! In comparison, the Milky Way was then thought to
have a diameter of 60,000 light years. Hubble knew the Andromeda nebula must
therefore be another galaxy which lies outside of the Milky Way. In fact, Andromeda is
one of the closest galaxies to the Milky Way, and on a very clear night, you can see it as a
faint, fuzzy blob in the sky. From Hubble’s discovery, extragalactic astronomy (the study
of celestial objects that lie outside of the Milky Way) was born.
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Part I. Developing your own Classification System
By making detailed observations of celestial objects and classifying them into different
groups, astronomers can concentrate on the object’s similarities and differences. They
can then make further observations and develop theoretical models that pinpoint why the
objects are similar or different. A star’s color may indicate its temperature; the shape of a
galaxy may indicate that new stars are forming inside it. These are the types of properties
that astronomers like to observe, catalog and compare. In this lab, you will classify the
objects that you see in the Planetarium and in the laboratory. When classifying galaxies,
you will develop your own system as well as compare your classification scheme with the
scheme developed by Hubble.
Step 1: You have been provided with a sample of images of nearby galaxies. Examine
their shapes closely and collaborate with the other students in your group to classify the
galaxies into morphological groups. Things to think about as you look at these images:
•
How many groups are you going to divide your sample of galaxies into? For
simplicity’s sake, you may want to stay within 5 groups, but the actual number
you decide on is your choice.
• What are the intrinsic shapes of these galaxies? Are they puffed up like grapes, or
are they flattened like compact discs? If they are flattened, you may consider how
your viewing angle affects your classification scheme (for instance, are you
seeing the galaxy from the side or looking down at it from the top?)
• You may find that some of your galaxies do not easily fit into any particular
category. For this reason, it is completely acceptable to group these galaxies into
their own category- a weirdo category
Step 2: In your lab book write down the group names you have decided on. Develop and
describe the set of guidelines for classifying galaxy shapes for each group. Draw a
representative image of what that galaxy should look like.
Step 3: Classify the galaxies in the sample of images that you have been provided with
using the classification scheme that you have developed. You should write the NGC
number or Messier number of the galaxy under the group it belongs to.
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Part II. Comparing it with the Hubble Tuning Fork Diagram.
When you are ready, the instructor will give you a handout which represents the
classification scheme used by Edwin Hubble.
Using the information provided to you, classify each of the galaxies again, but this time
using the Hubble Tuning Fork Diagram.
Part III. Synthesis
Step 1: The instructor will provide a list of the correct Hubble types for all the galaxies,
write them down next to your guesses. Put a star next to the Hubble types (in column
4) that you got completely correct (that is you got both the class and subclass correct).
Circle the entire row if you guessed the class incorrectly. Do nothing to the row if
you just missed by a sub-class.
Step 2: The instructor will also explain the Hubble Tuning Fork diagram to you. Take
notes and include this information as part of your conclusion for bullet point #2.
Step 3: In your conclusion:
o Summarize your classification system. In your summary, discuss the number of
classes you came up with, the names of the classes, and the properties of each
class.
o Describe the differences between the classes and subclasses in Hubble’s
classification system (Just attach the notes from the mini-lecture your instructor
presented to you).
o Describe the similarities and differences between your system and Hubble’s. In
your discussion consider the differences/similarities in terms of the criteria you
used (e.g. were your classes based on shape, color, or both), the number of classes
you have, the level of detail of your classes (did you have classes and
subclasses?), etc.
o Describe how your guesses compared to the actual Hubble type. How many did
you guess exactly correct (that is you got the class and sub-class right)? How
many were you really far off from the actual type (i.e. you guessed the wrong
class completely)? Why do you think you misclassified these galaxies (the answer
to this question should come from the mini-lecture)?
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Galaxy Classification Table
NGC #
Your Class Name
Hubble Type
(Guess)
Hubble Type
(Actual)
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Lab Module 12
Classification of Messier
Objects
Hartnell Planetarium, color pencils, flashlight with red filter, computer
Objectives
Learn about the different types of Messier and be able to visually describe and identify
them. Use the Planetarium to identify and describe the properties of different Messier
Objects.
Background
In the 1700s, one of the ways astronomers distinguished themselves was by discovering
comets. Eighteenth century astronomers would scan the sky with their telescopes looking
for faint, fuzzy objects. Unfortunately for them, there are several fuzzy-looking objects
in the sky that are not comets- we know this because, unlike comets, these objects do not
move from night to night with respect to the stars in the sky.
From 1758 to 1782, a French astronomer named Charles Messier compiled a catalog of
these diffuse-looking objects, called nebulae, so that they would no longer be mistaken
for comets. Messier catalogued 110 total nebulae. Most of these objects are still known
by their Messier numbers.
By making detailed observations of celestial objects and classifying them into different
groups, astronomers can concentrate on the object’s similarities and differences. They
can then make further observations and develop theoretical models that pinpoint why the
objects are similar or different. A star’s color may indicate its temperature; the shape of a
galaxy may indicate that new stars are forming inside it. These are the types of properties
that astronomers like to observe, catalog and compare. In this lab, you will classify the
objects that you see in the Planetarium and in the laboratory.
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Lab Module 12: Classification of Messier Objects
Astronomy Laboratory Manual - Hartnell College
AST 1L
Part I. Distinguishing between different Messier Objects
Here the instructor will display the different Messier objects and galaxies on the screen.
Step 1: Using the worksheets provided, label the different Messier objects and Galaxies.
Use coloring pencils to color in the different Messier and Galaxies by comparing to the
colors seen on the screen.
Step 2: Describe in your groups visually what the Messier object or galaxy looks like.
Step 3: In the space provided in the worksheet, record the description that class presents
for each of the Messier objects and galaxies.
Part II. Planetarium
For this part, you will need to go to the planetarium. Images of Messier objects will be
projected onto the planetarium dome.
Step 1: Working with your group members, classify the images of the Messier objects.
•
•
If it is a star cluster, write down whether it is a globular cluster or open cluster.
If it is a galaxy, describe what kind of galaxy it is.
Step 2: Sketch the object in the following boxes provided. Also, describe what the object
looks like in the space provided and record the name of the constellation that it is in and
the season it will be visible.
Step 3: After everyone has finished classifying the objects, the images will be shown in
the planetarium again. The instructor will tell you the correct class of object that you are
observing. In the space provided, write down the correct name. Do not erase your own
attempt to classify the object!
Part III. Conclusion
In your conclusion, include:
o What was Messier originally looking for before he discovered the Messier
objects?
o How many Messier objects are there?
o List the main types of Messier objects and describe some of their properties.
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Planetarium
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
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Astronomy Laboratory Manual - Hartnell College
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Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
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Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
Your Classification:
Name of Object:
Constellation:
Season:
Visual Description of Object:
Actual Classification:
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Lab Module 13
Large Scale Structure of the
Universe
This material is adapted from the CLEA (Contemporary Laboratory Exercises in Astronomy) module, The
Large Scale Structure of the Universe; Department of Physics, Gettysburg College, Gettysburg, PA.
Equipment
This experiment uses a Windows computer, the CLEA program Large Scale Structure, and a scientific
calculator. (Note that the computer mentioned above may provide such a calculator.)
Objective
•
•
•
•
•
•
•
Find galaxies in a restricted area of the sky using a list compiled by earlier observers.
Take spectra of these galaxies using simulated telescopes and
spectrometers.
Recognize the principal features of galaxy spectra.
Measure the wavelengths of principal spectral lines in galaxies.
Calculate the redshift, z, and the radial velocities of the galaxies.
Plot radial velocities and positions on a wedge diagram.
Interpret the distributions of galaxies you see on the wedge diagram.
Background
Drawing a map of the universe is not an easy task. Understanding why it is difficult, however, is rather
simple. Consider how hard it is to determine the shape and extent of a forest when one is standing in the
middle of it. Trees are visible in all directions, but how far do they extend? Where are the boundaries of the
forest, if any? Are there any clearings or any denser groves, or are the trees just scattered uniformly about
at random? A terrestrial surveyor might answer these questions by walking around the forest with a
compass and transit (or, more recently, a Global Positioning System or GPS receiver), mapping carefully
where everything was located on a piece of ruled paper. But consider how much more difficult it would be
if the surveyor were tied to a tree, unable to budge from a single spot. That’s the problem we earthbound
observers face when surveying the universe. We have to do all our mapping (of galaxies, of course, not
trees), from a single spot,—out solar system—located about 2/3 of the way between the center of the Milky
Way galaxy and its edge.
Two of the three dimensions required to make a 3-dimensional map of the positions of the galaxies in
universe are actually fairly easy to determine. Those two dimensions are the two celestial coordinates,
Right Ascension and declination, that tell us the location of a galaxy on the celestial sphere. Over the years,
by examining photographs of the heavens, astronomers have compiled extensive catalogs that contain the
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coordinates of hundreds of thousands of galaxies. They estimate that there are hundreds of billions of
galaxies that lie within the range of our best telescopes.
More is needed, however. The two celestial coordinates just tell us in what direction to look to see a galaxy.
A third number—the distance of the galaxy—is necessary in order to produce a reliable map. Unfortunately
the distance of galaxies is not immediately obvious. A small, faint galaxy nearby can appear much the same
as a large, luminous galaxy much further away. Except in the very nearest galaxies, we can’t see individual
stars whose luminosity we can use to estimate distance. How then can we determine galaxy distances
reliably?
The solution to this problem is to make use of the expansion of the universe to give us a measure of
distance. By the expansion of the universe we mean the fact that the overall distance between the galaxies
is getting larger all the time, like the distance between raisins in a rising loaf of bread. An observer on any
galaxy notes that all the galaxies are traveling away, with the most distant galaxies traveling the fastest.
The increase of galaxy speed with distance was first noted by astronomer Edwin Hubble in the 1920 who
measured the distances of nearby galaxies from the brightness of the Cepheid variable stars he could seen
in them. He measured the speeds (technically called the radial velocities) of the galaxies by measuring the
wavelengths of absorption lines in their spectra. Due to the Doppler effect, the wavelengths of absorption
lines are longer (shifted in toward the red end of the spectrum), the faster the galaxy is moving away from
the observer. One of Hubble’s first graphs, showing the increase of radial velocity with distance, is shown
below.
Hubble’s redshift-distance relation gives us the key
to the third dimension. Since the distance of a galaxy
is proportional to its velocity, we can simply take a
spectrum of it, measure the amount of the spectral
lines are redshifted, and use that as a measure of
distance. We plot the position of galaxies in three
dimensions, two being the Right ascension and
declination of the star, to create a three-dimensional
and
being the
redshift
(or velocity,
or distanc
mapthe
of third
the universe
which,
hopefully,
will reveal
the
size and scope of its major structures.
Figure 1
Radial Velocity vs. Distance
Of course one needs to observe the spectra of a lot of galaxies in order to trace out the contours of the
universe. This was a time-consuming process in the beginning; Hubble sometimes had to expose his
photographic plates for several hours in order to get data on just one galaxy. But by the 1980’s techniques
of spectroscopy made it possible to obtain galaxy spectra in a matter of minutes, not hours, and several
teams of astronomers began undertaking large map making surveys of the galaxies. One of the most
important of these pioneering surveys was undertaken by John Huchra and Margaret Geller at the HarvardSmithsonian Center for Astrophysics in Cambridge, MA. The CfA Redshift Survey (which provides much
of the data for this exercise), surveyed all the brighter galaxies in a limited region of space, in the direction
of the constellation Coma.
The maps produced by the CfA Redshift Survey and other groups revealed that the galaxies were not
distributed at random, but rather were concentrated in large sheets and clumps, separated by vast expanses,
or voids, in which few, if any, galaxies were found. One large sheet of galaxies, called the “Great Wall”,
seemed to span the entire survey volume.
Even with modern techniques, surveying thousands of galaxies takes a great deal of time, and the task is far
from complete. Only a tiny fraction, about 1/100 of 1%, of the visible universe has been mapped so far.
Describing the large scale structure of the universe on the basis of what we currently know may be a bit
like describing our planet on the basis of a map of the state of Rhode Island. But some of the major
conclusions are probably quite sound.
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In the exercise that follows, you will conduct a survey of all the bright galaxies in a catalog covering the
same region of the sky as the original CfA redshift survey. We’ve reduced the number of galaxies in our
catalog, and made the operation of the instrument a bit simpler, but the fundamental process is the same as
that used today to gauge the overall structure of the universe we live in.
Introduction
Overall Strategy
The software for the Large Scale Structure of the Universe lab puts you in control of any one of three
optical telescopes, each equipped with a TV camera (for seeing what you’re pointed at) and an electronic
spectrometer that can obtain the spectra of light collected by the telescope . Using this equipment, you can
conduct a survey of a sample of galaxies in a restricted portion of the sky. You will obtain spectra for all
the galaxies in that region, measure the wavelengths of prominent spectral absorption lines, and use the
data to determine the redshift and radial velocities of each galaxy. From this, you will construct a map of
the distribution of galaxies in the region. The map will show some of the major large-scale features of the
universe, and you will be able to
determine characteristic shape and size of
these features by thoughtful examination
and analysis.
The slice of sky we are surveying stretches
60 degrees in the east-west direction (from
Right Ascension 12 H to 16 H) and 5
degrees in the north-south direction (from
declination +27° to declination +32°). This
region of the sky was chosen primarily for
convenience: it is high in the sky in the
northern hemisphere, and it is not obscured
by gas and dust in our own galaxy.
Figure 2
Portion of the Sky Used in this Survey
Moreover some of the richest nearby groupings of galaxies, in the direction of the constellation Coma, lie
in this direction. There are over 200 galaxies in our sample. For the purposes of this exercise, you can
assume that this is all the galaxies that we can see through the telescope. In fact there are many more than
this in the real sky, but we have omitted many to make the measurement task less tedious. This isn’t that
unrealistic, because even under the best conditions, astronomers’ catalogs of galaxies never can include all
the galaxies in a given volume of space. Faint galaxies, or ones which are spread out loosely in space may
be hard to see and may not be counted. Still, our sample contains enough galaxies to show the large-scale
features of the visible universe in this direction. It is your assignment to discover those features for
yourselves.
The region you’re going to be examining is shape like a thick piece of pie, where the thickness of the pie
slice is the declination, and the length of the arc of crust represents the right ascension. The radius of the
pie, the length of the slice, is the furthest distance included in the survey.
Technical Details
How does the equipment work? The telescope can be pointed to the desired direction either by pushing
buttons (labeled N,S,E,W) or by typing in coordinates and telling the telescope to move to them. You have
a list of all the target galaxies in the direction of Coma with their coordinates given, and you can point the
telescope to a given galaxy by typing in its coordinates. The TV camera attached to the telescope lets you
see the galaxy you are pointed at, and, using the buttons for fine control, you can steer the telescope so that
the light from a galaxy is focused into the slit of the spectrometer. You can then turn on the spectrometer,
which will begin to collect photons from the galaxy, and the screen will show the spectrum—a plot of the
intensity of light collected versus wavelength. As more and more photons are collected, you should be able
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to see distinct spectral lines from the galaxy (the H and K lines of calcium), and you will measure their
wavelength using the computer cursor. The wavelengths will longer than the wavelengths of the H and K
labs measured from a non-moving object (3970.0 and 3933.3 angstroms), because the galaxy is moving
away. So for each galaxy you will have recorded the wavelengths of the H and K lines.
These are all the data you need. From them, you can calculate the fractional redshift, z (the amount of
wavelength shift divided by the wavelength you’d expect if the galaxy weren’t moving) and the radial
velocity, v, of the galaxy from the Doppler-shift formula.
You’ll display your map as a two-dimensional “wedge diagram” (see figure 3 on the following page). It
shows the slice of the universe you’ve surveyed as it would look from above. Distance is plotted out from
the vertex of the wedge, and right ascension is measured counterclockwise from the right.
As you plot your data, along with that of your classmates, you’ll be able to see the general shape of the
clusters and voids begin to appear.
Figure 3
The Wedge Diagram
I. Taking Spectra With the CLEA Computer Program
Beginning Your Observations
Welcome to the observatory! The program you are going to use simulates the operation of a modern
digitized telescope and spectrometer. Let’s begin by obtaining the spectrum of a galaxy and measuring its
redshift. You’ll then be on your own as you and your classmates gather all the remaining data needed to
map out your sample of the universe.
Step 1: Open the Virtual Educational Observatory (VIREO) program by double clicking on the VIREO
icon on your computer screen. Click on login in the MENU BAR and type and enter your names and lab
table as requested. Click OK when ready.
Step 2: Click on File Run Exercise The Large-Scale Structure of the Universe
THE VIRTUAL OBSERVATORY CONTROL SCREEN
Choosing the Virtual Observatory option brings up the Virtual Observatory Control Screen (figure 1),
which is the base of control for the various functions of VIREO.
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Figure 1: The Virtual Observatory Control Screen
1.
2.
3.
4.
Select a telescope: From the Virtual Observatory Control screen, select one of the three available
telescopes by clicking on Telescopes, Optical, Access 4.0 Meter. The larger the telescope, the
brighter the images and the shorter the exposure times. You can always return to this screen to
choose a larger telescope if you find that the objects you are studying are too faint for the
telescope you are using.
Open the dome shutters: so that the telescope can see the sky by clicking on the Dome
open/close switch at the upper right. The dome shutters will slide open, revealing the night sky.
The bright stars you see are those crossing your meridian at the present time for your location, as
you would see them if you were standing in the dome.
Access the Telescope Control Panel: Turn on the optical telescope control panel button at the
lower right of the Observatory control screen. The telescope Control Panel Screen will open. You
can now use the telescope.
General description of the Telescope Control Panel. Controls on the telescope control panel
allow you to move the telescope to different parts of the sky, switch the view between the widefield finder and the narrow-field telescope view, and access optical instruments such as the
photometer, spectrometers, and cameras. Large digital displays show Universal Time, Sidereal
Time, as well as the Right Ascension and Declination the telescope is pointed at. Smaller displays
show the Julian Day to six decimal places (essentially a fraction of a second), and a display at the
upper right shows local standard time. A central window shows, in a “TV-camera” view, what the
sky the telescope sees through the finder or narrow-field telescope, depending on which is
selected. In the TV view, north is to the top, and east is to the left, which is the standard
orientation in most telescopes and astronomical images.
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5.
6.
Figure 2: The Optical Telescope Control Screen
Controls on the Telescope Control Panel
• Tracking Control: Must be turned on to access other controls. Without it, the telescope
does not track the stars. Without the tracking on, you will be able to see stars drift across the
field of the TV monitor from east to west at the rate of 360° per day.
• Telescope Motion: The four N-E-S-W buttons move the telescope to the north, east, south, or
west. The Slew Rate slider controls the speed of the motion. The telescope can also be
moved to specific spots in the sky using the Slew… option, by typing in coordinates, or by
selecting objects from a hot list.
• View: The slider selects between a wide-field finder view, and a narrow field telescope view.
A display under the slider shows the width of the field of view. Change to Telescope view to
access the instruments.
• Instrument: The slider selects the available instruments for the telescope, including the
Aperture Photometer, single-slit Spectrometer, multi-aperture Spectrometer, CCD camera,
and IR camera. Clicking the Access button under the slider will bring up a control screen for
the instrument chosen.
Selecting the Galaxies from the Sample List
• On the telescope control window, click on Slew Observation Hot List Load Hot
List and then the Survey Field that has been assigned to you by your instructor.
• Then click on Slew Observation Hot List and View/Select from List
• Record the name, Right Ascension, and Declination of your galaxy in Table 1.
• Click on Yes, when it asks you to Slew telescope to Target Coordinates.
USING THE SPECTROMETER
Make sure you are in the Telescope Control screen,that the telescope is tracking, that you are pointed at the
approximate coordinates of the object of interest, and that the telescope is set for the narrow-field
(“Telescope”) view. Access the spectrometer by setting the Instrument slider to Spectrometer, and click
the Access button. The Spectrometer Control window should appear.
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Figure 4: The Spectrometer Control Window
Controls on the Spectrometer Control Screen:
• Spectrum Display: Displays the spectrum being obtained. The spectrometer is a photon-counting
spectrometer, so when the spectrum is actually accumulating counts this display shows the individual
counts in each channel as dots. When the spectrum is complete (or paused) the points are connected,
and the overall pattern of the spectrum can be seen. The display axes are wavelength in Ångstroms,
along the y axis, and relative intensity, on the y axis---which is the number of counts in a channel
normalized to the maximum counts in all the channels.
• Photon Count: Displays the total number of photons recorded by the spectrometer.
• Photons Per Channel (avg): Displays the total number of photons divided by the number of channels
in the spectrum.
• Integration Seconds: Displays the total length of time the spectrum has been accumulating
• Signal to Noise Ratio: a measure of the strength of the spectrum you have collected. In order to
clearly measure the wavelengths of the calcium lines, you will need to obtain a signal to noise of about
15 or so.
• Go/Stop buttons: Start and stop the observations. The stop button pauses the accumulation of photons,
but the start button can be pressed again if more counts are desired (e.g. to achieve a higher signal to
noise ratio.)
A window should open, showing you the spectrometer display. The spectrometer breaks up the light
coming in the slit into its component wavelengths and measures the number of photons (the intensity)
coming in at each wavelength. If we tell the spectrometer to start counting, it will begin to collect light and
display it on the graph of intensity versus wavelength that you see on the screen.
Taking Spectra:
1. Using the NESW buttons on the Telescope Control screen, position the object of interest
directly in the center of the slit marked by two red lines on the TV display window. Note that
the spectrometer is only sensitive to light that enters through the slit. If you point it at the
blank sky, you will get background noise. If you are observing an extended object like a
galaxy, you will get the strongest signal if you center on the brightest part of the object. When
you have the telescope in the desired position, simply press Go, and watch the spectrum
accumulate. You can press Stop at any time to examine the spectrum, and take a longer
exposure if you wish to increase the signal to noise ratio.
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2.
To save it for further measurement for redshift, line strength, or spectral classification, choose
the options on the File Data  Save Spectrum drop-down menu. The spectrum can be
saved under a name determined by the user or under a default name by the software.
The spectrum of the galaxy will exhibit the characteristic H & K calcium lines which would normally
appear at wavelengths 3968.847 Å and 3933.67 Å, respectively, if the galaxies were not moving. However,
the H & K lines will be red shifted to longer wavelengths depending on how fast the galaxy is receding.
Photons are collected one by one. We must collect a sufficient number of photons to allow identification of
the wavelength. Since an incoming photon could be of any wavelength, we need to integrate for some time
before we can accurately measure the spectrum and draw conclusions. The more photons collected, the less
the noise in the spectrum, making the absorption lines easier to pick out.
Taking Spectra:
1. On the main VIREO Exercise Window- click on Tools Spectrum Measuring
2. FileDataLoad Saved Spectrum. Choose one of the galaxy spectrum files.
3. Locate the H and K absorption lines and click on the dip for each absorption line. The value
of the wavelength for the absorption line should appear.
4. Record the measured values of the K and H wavelengths in Table 1.
II. Calculating the Recessional Velocities of your Galaxies
Note the following information:
The laboratory wavelength, λK of the K line of calcium is 3933.67 Å.
The laboratory wavelength, λH of the H line of calcium is 3968.85 Å.
Step 1: You have now measured the wavelengths of the K and H lines in the spectrum of NGC 4278, and
have entered these wavelengths into columns 6 and 7 of the data sheet, Table 1. You’ll note that your
measured wavelengths are longer than the “laboratory” wavelengths listed above, because the galaxy is
moving away. You next want to calculate absolute redshifts, ∆λK and ∆λH for each line, where
(1) ∆λΚ = λK measured - λK laboratory and ∆λΗ = λH measured - λH laboratory
Step 2: Next you calculate the fractional redshifts, zH and zK which are what astronomers use when they
use the term redshift in general. The fractional redshifts are just the absolute redshifts divided by the
original laboratory wavelengths, or, in algebraic notation:
(2) zK = ∆λΚ / λK laboratory and zH = ∆λΗ / λH laboratory
Step 3: You can calculate the radial velocity of the galaxy of each redshift using the Doppler shift formula:
(3)
v K = c zK
and
v H = c zH
Step 4: Finally you can average the two velocities to get a more reliable value.
(4) vave = (vH + vK) / 2
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You now have measured and analyzed the data for one galaxy. The numbers you will want to plot in
your wedge diagram, eventually, will be the Right ascension and the velocity of each galaxy. Since the
slice of the universe is thin in Declination, we will assume that all the galaxies we measure lie roughly in
the same plane.
Step 5: Have your instructor check your calculations before moving on to the next galaxy.
Collecting Data for a Wedge Plot
Step 6: When you have measured, calculated, and saved the velocities for each galaxy in your sample, you
are ready to pool your data with others in the class, and plot up a wedge diagram.
Step 7: Plot up the RA versus velocity on the wedge plot for all your galaxies EXCEPT NGC4278 (#24).
As you enter the dots for the galaxies in your survey the shape of the large-scale distribution of matter
should gradually appear. You will now want to examine the plot and see what it reveals about the largescale structure of the universe.
III. Interpreting the Wedge Plot
Carefully examine the wedge diagram you and your classmates have produced. Though you have only
plotted 200 or so representative galaxies, the features you see are distinctive. Once your classmates have
finished plotting their points on the wedge plot, answer the questions below.
Questions
1. Does matter in the universe appear to be randomly distributed on the large scale, or are there clumps and
voids?
2. The most densely populated region of the diagram (which appears like the stick figure of a human), is the
core of the Coma Cluster of galaxies. What are the approximate Right Ascension and velocity coordinates
of this feature?
3. You can use Hubble’s velocity-distance relation to determine the distances of objects in the chart.
v=HD
where H is the Hubble constant which tells you how fast an galaxy at a given distance is receding due to the
expansion of the universe. The value of H is not well known, and there is a great deal of dispute about it,
but a value of H=75 kilometers/sec/megaparsec is a reasonable figure. (1 megaparsec = 106 parsecs).
Using this value of H, calculate the distance to the Coma Cluster.
4. Using the velocity-distance relation, how far is the farthest galaxy included in this study? How much
smaller is this distance than the limit of the observable universe, which is about 4.6 x 103 Megaparsecs?
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Table 1.
GALAXY
NAME
RA
h:m:s
DEC
o
:′:″
λk
meas
λH
meas
∆λk
∆λH
zk
zH
vk
vH
vavg
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