Question

Suppose it is possible for a satellite to orbit around a spherical planet of uniform density with a minimum period of T_min = 0.177 days. What would the density of such a planet be?
__________ kg/m³

Answer 1

T = 0.177 days = 0.177 times 86400 = 15292l.8 sec Mass = density times volume M = S.V = S middot 4/3 pi R^2 According to kepler's law of planetary motion, T^2 = 4 pi^2 R^3/GM = 4 pi^2 R^3/G S 4/3 pi R^3 Therefore T^2 = 3 pi /G S Therefore S = 3 pi/T^2 G = 3 times 3.14/(15292.8)^2 times 6.67 times 10^- 11 S = 603.88 kg/m^3