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In deriving Kepler's third law (8.55) we made an
Chapter 8, Problem 8.15(choose chapter or problem)
In deriving Kepler's third law (8.55) we made an approximation based on the fact that the sun's mass Ms is much greater than that of the planet m. Show that the law should actually read 1.2 = [472/G 4s (m m)] a3, and hence that the "constant" of proportionality is actually a little different for different planets. Given that the mass of the heaviest planet (Jupiter) is about 2 x 1027 kg, while Ms is about 2 x 1030 kg (and some planets have masses several orders of magnitude less than Jupiter), by what percent would you expect the "constant" in Kepler's third law to vary among the planets?
Questions & Answers
QUESTION:
In deriving Kepler's third law (8.55) we made an approximation based on the fact that the sun's mass Ms is much greater than that of the planet m. Show that the law should actually read 1.2 = [472/G 4s (m m)] a3, and hence that the "constant" of proportionality is actually a little different for different planets. Given that the mass of the heaviest planet (Jupiter) is about 2 x 1027 kg, while Ms is about 2 x 1030 kg (and some planets have masses several orders of magnitude less than Jupiter), by what percent would you expect the "constant" in Kepler's third law to vary among the planets?
ANSWER:Step 1 of 2
If we consider the equation (8.54), the time period of oscillation of a planet around sun is given by,
But 
