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Unformatted text preview: 1) On Earth, we can measure 20,000 stars with parallaxes down to 0.&quot;01. The Hipparchos satellite measured 120,000 stars down to 0.&quot;0014. a) How much farther away could Hipparchos probe our galaxy relative to measurement on the Earth? Assuming both Earth and Hipparchos measurements use the earths orbit diameter as a baseline, the distances implied are: d=1/p pc where p is the parallax angle in arcseconds. For earth: d = 100 pc = 2.07x10 7 AU = 3.1x10 15 km For Hipparchos: d = 714 pc = 1.5x10 8 AU = 2.2x10 16 km Note how Hipparchos was able to observe 7.2 further in distance. Also notice that the distance from the sun to the center of our galaxy is about 8000 parsecs! That is still far beyond our reach, even with the Hipparchos satellite. b) What does the number of stars measured in both cases tell us about the shape of our galaxy? If the stars were evenly distributed in a spherical volume around the earth, the number of stars should be proportional to the volume or r 3 . So if Hipparchos was able to probe our galaxy 7.2 times further in radius it should have found 7.16 3 =367 times more stars. However, Hipparchos only found 6 times more stars. We can conclude that stars are not evenly distributed around us in a spherical volume. Actually we know that stars in our galaxy are distributed in a disk where the Sun and all the stars are rotating around the center of our galaxy. 2. Calculate the luminosity of the Sun using the amount of energy the Earth receives from it (1.37 x 10**3 Watt/m**2). This value, the Solar Constant, represents a quantity known as the apparent brightness. Our planet is r=1 AU or 1.5x10**11 m from the sun and it receives a flux of of F=1.37 x 10**3 Watt/m**2. So the luminosity of the sun should be L= Area x F = 4(Pi)r 2 x F where we have used the area of a sphere. So L is L=3.86 x 10**26 Watt = 3.86 x 10** 33 erg/s 3. Calculate the Solar luminosity using the Sun's radius and surface temperature. Compare this value with that of #2....
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 Spring '09
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 Quantum Physics, Hipparchos

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