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This is not a homework. In Chapter 8: Central-Force Motion, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, page 325, Problem 8-19, we are asked to calculate the mass of the planet Saturn. In the instructor's solution manual, the solution for this problem is:

m

m

I have tried to write m

Could anyone explain how could we obtain this ratio? Any help is much appreciated. Many thanks!

m

_{s}is the mass of Saturn.m

_{e}is the mass of Earth.I have tried to write m

_{s}and m_{e}in terms of the semimajor axis and the period and then dividing m_{s}by m_{e}, but I did not obtain the above result!Could anyone explain how could we obtain this ratio? Any help is much appreciated. Many thanks!