Question

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.60×107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.10×1011 m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 12.2 m/s2 .

Part A: What is the mass of the planet?

Part B: What is the mass of the star?

Answer 1

A)

Mass, m = g R^2/G

m = (12.2) (0.8 x 10^7)^2/(6.67 x 10^-11) = 1.17 x 10^25 kg

B)

Mass, M = (4 pi^2 R^3)/(GT^2)

M = (4 pi^2 x (2.1 x 10^11)^3)/(6.67 x 10^-11 x (402 x 86400)^2)

M = 4.54 x 10^30 kg

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