ch13-p053 - 53. (a) If we take the logarithm of Keplers law...

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where T E = 365.25 days is Earth’s orbital period and r E = 1.50 × 10 11 m is its mean distance from the Sun. In this case, it is perfectly legitimate to take logarithms and obtain o 21 log log log 33 EE M rT aT M §· =+ ¨¸ ©¹ © ¹ (written to make each term positive) which is the way we plot the data (log ( r E / a ) on the vertical axis and log ( T E /T ) on the horizontal axis). (b) When we perform a least-squares fit to the data, we obtain log ( r E / a ) = 0.666 log ( T E / T ) + 1.01, which confirms the expectation of slope = 2/3 based on the above equation. (c) And the 1.01 intercept corresponds to the term 1/3 log ( M o / M ) which implies 3.03 oo 3 10 . 1.07 10 MM M M = ¡ = × Plugging in M o = 1.99 × 10 30 kg (see Appendix C), we obtain M = 1.86 × 10 27 kg for Jupiter’s mass. This is reasonably consistent with the value 1.90
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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