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 2.2 * (10^11) m from its star with a period of 432 earth days. Once on the surface you find that the free-fall acceleration is 12.2 m/s^2. What is the mass of (a) the planet and (b) the star?

Mp = 1.48*10^23 Kg and M = 4.47*10^30 Kg

Explanation:

Given that

Diameter of planet D = 1.8*10^6m

Radius of planet Rp = 0.9*10^6m

Period of rotation of planet = 22.3 hrs = 80280s

Radius of orbit r = 2.2 * 10^11 m

Period of revolution around star T = 432days = 432*24*60*60 = 37324800s

Acceleration of gravity on the surface of planet gp = 12.2m/s^2

gp = GMp / (Rp) ^2

Mp = gp * (Rp) ^2 / G

= 12.2 * (0.9*10^6) ^2 : 6.67*10^-11

9.882*10^12 : 6.67*10^-11

Mp = 1.4*10^23 Kg

To determine the mass of the star, we consider the revolution of the planet around the star with period T

T^2 = (4π^2/GM) r^3

M = 4π^2r^3 : GT^2

M = 4π^2 * (2.2*10^11) ^3 : 6.67*10^-11 * (37324800) ^2

M = 4.47*10^30 Kg