Question

A planet's moon travels in an approximately circular orbit of radius 8.6 107 m with a period of 6 h 25 min. Calculate the mass of the planet from this information.

Answer 1

m v^2 / R = G M m / R^2 gravitational attraction = centripetal force

M = v^2 R / G solving for M

period = 6 h 25 min = (6 * 3600 + 25 * 60) sec = 23,100 sec = T

v = 2 pi R / T

M = 4 pi^2 R^3 / (G T^2)

M = 39.5 * (8.6E7)^3 / (6.67E-11 * 2.31E4^2)

M = 39.5 * 636 / (6.67 * 5.34) * 10^24

M = 7.05 * 10^26 kg