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Transcript
Unit 10: Measuring the Properties of Stars Mr. Ross Brown Brooklyn School for Law and Technology In this unit we will learn about: • How we measure stars’ distances using parallax • Why a star’s color indicates temperature & how to use Wien’s law to determine temperature • The difference between luminosity and brightness • How we can measure radius using temperature • The magnitude system of star brightness • Stellar spectra and how it indicates surface temperature • Luminosity classes • How we estimate stellar masses • The H-R diagram for inferring a star’s size and evolutionary state How do we measure a star’s distance • 7 March 2016 • Do now: Why is it important to know a star’s distance from Earth? What other things can we calculate if we know the distance? How do we measure a star’s distance • For nearby stars…. – Triangulation • Lay out a right triangle, whose one side we know How do we measure a star’s distance • Parallax – Method of triangulation that uses an apparent change in an object’s position as the observer’s position changes. How do we measure a star’s distance • Parallax is small across such large distances. Rather than measure it in degrees, we measure it in fractions of degrees called “arc seconds” (1/3600 of a degree, 1/60 of an arc minute) Homework #17 • 7 March 2016 • How is a parsec defined? How big is a parsec compared to a light year? How do we measure a star’s distance • We define a parallax (p) as ½ the angle by which it appears to shift. From this, we measure a star’s distance (d) as 1/p where p is in arc seconds and d is parsecs. dpc=1/parc seconds • One parsecs = 3.26 light-years (3.09*1013 km) How do we use a star’s light to learn about its properties? • 14 March 2016 (Happy Pi Day!) • Do now: How can we tell how hot something is without using a thermometer or touching it? How do we use a star’s light to learn about its properties? • Temperature – Stars are VERY hot – Hotter blue, cooler red How do we use a star’s light to learn about its properties? • Using color more precisely – Wien’s Law: longer wavelength = cooler temperature How do we use a star’s light to learn about its properties? • Luminosity: the amount of energy an object radiates – Lightbulb = 60-75 watts – Sun = 4* 1026 watts – Luminosity measures how fast an object consumes its fuel How do we use a star’s light to learn about its properties? • Luminosity measured via inverse-square law • Its distance and apparent brightness How do we use a star’s light to learn about its properties? • Radius – If two stars have the same temperature but one is more luminous, the more-luminous star must have a larger surface area, thus a larger radius How do we use a star’s light to learn about its properties? • Stefan-Boltzmann Law – If two stars have the same size but the surface of one is hotter, the hotter star will have greater luminosity In what other ways can we measure a star’s properties? • 15 March 2016 (Beware the Ides of March!) • Do now: Which star is cooler and many times brighter than Earth’s Sun? a) Barnard’s Star b) Betelgeuse c) Rigel d) Sirius In what other ways can we measure a star’s properties? • Direct measurement of radius – (Yesterday we used luminosity and StefanBoltzmann Law to arrive at radius) – We can be more precise by using Angular Size In what other ways can we measure a star’s properties? • Challenges to using angular size – Due to distance, fuzzy images, even with telescopes – Large ground-based telescopes get better images, but the atmosphere blurs them some – Computer can de-blur it a little In what other ways can we measure a star’s properties? • We need a HUGE telescope • Or TWO telescopes, far apart, combined with computers In what other ways can we measure a star’s properties? • Star radii differ greatly – Most are roughly the size of our Sun – Some, like Betelgeuse, are hundreds of times larger. These are Giants – Smaller stars, including our Sun, are Dwarfs, or Dwarves In what other ways can we measure a star’s properties? • The Magnitude System of measuring brightness – 150 BCE, Greek astronomer Hipparchus – Brightest is magnitude 1, dimmest is magnitude 6 In what other ways can we measure a star’s properties? • Is the Magnitude System the best system? – Apparent magnitude is a function of luminosity and distance – The scale is “backward,” with the lowest number representing the brightest stars – Magnitude differences represent ratios • Each magnitude represents a factor of 2.512 Homework #18 • 15 March 2016 • What is the H-R Diagram? What are its axes? How can we differentiate between classes of stars? • 16 March 2016 • Do now: What are dimensions across which we can differentiate one star from another? How can we differentiate between classes of stars? • The Hertzsprung-Russell Diagram (H-R) – 1912 – If we plot stars according to luminosity and temperature, the follow a smooth curve How can we differentiate between classes of stars? • The H-R Diagram – Bright stars on top, dim on bottom – Hot stars on left, cool on right – Blue on left, red on right • Temperature-wise, this is opposite other graphs – The curve on which most stars (90%) are depicted is the Main Sequence How can we differentiate between classes of stars? How can we differentiate between classes of stars? How can we differentiate between classes of stars? • 17 March 2016 • Do now: On what factors does the luminosity of a star depend? How can we differentiate between classes of stars? • Luminosity depends on a star’s surface area and temperature – If stars are the same temperature and one is brighter, it must have a larger radius – This is a Giant – Cool giants are Red Giants – Hot stars that are dim must have smaller radii – Dwarfs – If it’s hot yet dim, White Dwarf How can we differentiate between classes of stars? • What can we surmise about mass and density and luminosity? • The Mass-Luminosity Relation • Larger mass = greater luminosity How can we differentiate between classes of stars? • Luminosity Classes How can we differentiate between classes of stars? – 18 March 2016 – Do now: What are the various methods we use for determining stellar quantities? How can we differentiate between classes of stars? • Methods of determining stellar quantities – Distance – Temperature – Luminosity – Composition – Radius – Mass – Radial Velocity How can we differentiate between classes of stars? • The Method of Standard Candles – Think about oncoming headlights as you drive How can we differentiate between classes of stars? • Method of Standard Candles – If we know luminosity and brightness, we can calculate distance How can we differentiate between classes of stars?
