please post clearly clac- based physics problem After getting your Ph.D. (in the

Question

please post clearly clac- based physics problem

After getting your Ph.D. (in the distant future) you become the Science Officer on a starship. You and your away team land on a new planet in a far solar system. Prior to landing you measure the planet's diameter to be 1.8 times10^7 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits at 2.2 times10^11 m from its star with an orbital period of 402 earth days. Note: all orbits are circular. Once on the surface you find that the acceleration due to gravity is 12.2 m/s^2. a) What is the mass of the planet? b) What is the mass of the star?

Explanation / Answer

(A) accleration due to gravity = G M / R^2

12.2 = (6.67 x 10^-11) (M) / (1.8 x 10^7 / 2)^2

M = 1.482 x 10^25 kg

(B) for orbit around the start,

Gravitational force on planet = centripetal force

G M_star M / r^2 = M w^2 r

and w = 2pi / T = 2 pi / (402 x 24 x 3600 s ) = 1.809 x 10^-7 rad/s

G M_star = w^2 r^3

(6.67 x 10^-11) (M_star) = (1.809 x 10^-7)^2 (2.2 x 10^11)^3

M_star = 5.224 x 10^30 kg   

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