You are the science officer on a visit to a distant solar system. Prior to landi

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 1.8 × 10^7 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.7 × 10^11 m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 75.1 m/s^2. What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10^-11 N · m^2/kg^2)

A. (a) 9.1 × 10^25 kg, (b) 1.4 × 10^30 kg

B. (a) 1.7 × 10^26 kg, (b) 2.4 × 10^30 kg

C. (a) 9.1 × 10^25 kg, (b) 2.4 × 10^30 kg

D. (a) 1.7 × 10^26 kg, (b) 1.4 × 10^30 kg

Thank you! Please show all work and specify the correct answer choice at the end.

Explanation / Answer

acceleration due to gravity

g = GM/R^2

75.1 = 6.67*10^-11*M/(0.9*10^7)^2

M = 9.1*10^25 kg

------------

time period of planet =T = 2*pi*r^(3/2)/(sqrtGM)

402*24*60*60 = 2*pi*(1.7*10^11)^(3/2)/(sqrt(6.67*10^-11*M))

M = 2.4*10^30 kg

option C

C. (a) 9.1 × 10^25 kg, (b) 2.4 × 10^30 kg

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