HW 7 - Evan Klein

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University of Michigan *

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102

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Astronomy

Date

Jan 9, 2024

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pdf

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4

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Problem 1 Table and Graph: Table 1: Main sequence Stars Star Name Lum. (Sol) Mass (Sol) Diam. (Sol) Lifetime Sirius 25 2 1.7 Rigil Kent. 1.5 1.1 1.2 Vega 37 2.1 2.3 Procyon 7.7 1.5 2 Achernar 3300 7 10 Altair 10.6 1.8 1.8 Pollux 32 1.9 8 Fomalhaut 17.7 2.1 1.8 Regulus 150 3.5 3.2 Castor 30 2.2 2.3 Elnath 70 4.5 5.5 Miaplacidus 210 3 5.7 Alnair 380 4 3.6 Alioth 108 3 3.7 Kaus Aust. 375 5 7 Alkaid 700 6 1.8 Menkalinan 48 2.4 2.8 Alhena 160 2.8 4.4 Peacock 2100 5 4.4
Problem 2: L = 1.78*M^3.66 The equation shows that mass and luminosity are exponentially proportional and that when we raise mass to the 3.66 power and multiply by 1.78, we get a pretty accurate estimate of luminosity. Alpha in this equation = 3.66 which is similar to the expected 3.5 exponent. I think that the dataset I used had a very clear correlation and that it would be hard for this obvious correlation to yield a vastly different exponent than what is expected. Problem 3: Beta = -2.66 T = M^-2.66 T = 5.62*M^-2.66 Beta = 2.66 The expected formula is nearly identical to the actual formula and they have the same exponent.
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