The radius of a planet is R1, the autobiographical period is T1, it has a satellite, the orbit radius is R2, the cycle around the planet is T2, if the gravitational constant is g, find the average density of the planet

The radius of a planet is R1, the autobiographical period is T1, it has a satellite, the orbit radius is R2, the cycle around the planet is T2, if the gravitational constant is g, find the average density of the planet


Gravity provides centripetal force: GMM / r2 ^ 2 = m * R2 * (2pi / T) ^ 2 can get m =
If the radius of the planet is R1, the volume v = 4 * pi * R1 ^ 3 / 3;
Then the density p = m / v



If M1 = 2M2, R1 = 4r2, the ratio of their periods T1: M2 is 1:1
The masses of the two planets are M1 and M2, and their orbital radii around the sun are R1 and R2, respectively, if M1 = 2M2
, R1 = 4r2, then what is the cycle ratio T1: T2


Kepler's law, a cubic / T is constant, circular orbit, semimajor axis a = R, so T1: T2 = (R1 / r2) ^ 3 / 2 = 8