# CH08 - Chapter 8 The Family of Stars Motivation We already...

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The Family of Stars Chapter 8:

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We already know how to determine a star’s: Surface temperature Chemical composition Surface density In this chapter, we will learn how we can determine its: Distance Luminosity Radius Mass And how all the different types of stars make up the big family of stars. Motivation
Distances to Stars Trigonometric Parallax A star appears slightly shifted from different positions of the Earth on its orbit. The further away the star is (larger d), the smaller the parallax angle p. d = __ p 1 d in parsec (pc) p in arc seconds 1 pc = 3.26 LY

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Parallax
Parallax of stars near Orion (highly exaggerated)

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The Hipparcos Satellite European Space Agency Measured parallaxes of 2,539,913 stars. (99% of all stars to mag. 11) Extremely accurate parallax measurements on 120,000 stars. Failed to reach geosynchronous orbit due to booster failure. Worked anyway.
The Trigonometric Parallax Example: Nearest star, α Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 ly The Limit of the Trigonometric Parallax Method: With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc => This method does not work for stars further away than 50 pc.

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Intrinsic Brightness / Absolute Magnitude The more distant a light source is, the fainter it appears. The same amount of light falls onto a smaller area at distance 1 than at distance 2 => smaller apparent brightness. Area increases as square of distance => apparent brightness decreases as inverse of distance squared.
Standard Candles If we know how bright a candle is up close: We can measure its distance by how bright it appears to be far away:

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Brightness vs. Distance
Brightness vs. Distance Apparent brightness drops with the area of a sphere at distance r . Area = 4 π r2 # of photons passing through each sphere each second is the same. Flux = # of photons per second per unit area 1 / r2

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Brightness vs. Distance Q. If the distance to a given star were increased by a factor of two, how much would its brightness decrease?
Brightness vs. Distance Q. If the distance to a given star were increased by a factor of two, how much would its brightness decrease? A. By a factor of four! Apparent brightness 1 / r2

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Intrinsic Brightness / Absolute Magnitude The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): F ~ L __ d2 Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B.
Distance and Intrinsic Brightness Betelgeuse Rigel Example: App. Magn. mV = 0.41 Magnitude Difference Intensity Ratio 1 2.512 2 2.512×2.512 = (2.512)2 = 6.31 5 (2.512)5 = 100 App. Magn. mV = 0.14 For a magnitude difference of 0.41 – 0.14 = 0.27 , we find a flux ratio of (2.512)0.27 = 1.28

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Distance and Intrinsic Brightness Betelgeuse Rigel Rigel appears 1.28 times brighter
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CH08 - Chapter 8 The Family of Stars Motivation We already...

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