Please answer all parts in detail A satellite of unknown mass is in a circular o

Question

Please answer all parts in detail

A satellite of unknown mass is in a circular orbit of radius R around a planet. The magnitude of the gravitational force exerted on the satellite by the planet is F. The amount of time the satellite takes to complete one revolution is T. Determine the mass M of the planet. Your answer should be in terms of, at most, R, F, and T. Show that if the satellite is close to the surface of the planet, the density rho = 3pi/GT2. Estimate the density of the Earth given T = 85 min.

Explanation / Answer

F= mv^2/r

v= sqrt(F*R/m)

T= 2*Pi*R/v = 2*pi*sqrt(mR/F)

mass of satellite = (T/(2*Pi))^2)*F/R

here, F = GmM/R^2

M= mass of planet

M= F*R^2/Gm = 4 *PI^2 *R^3/(G*T^2)

b)density = mass/volume = [4 *PI^2 *R^3/(G*T^2) ]/((4*Pi*R^3 )/3) = 3*pi/(GT^2)

c)density= 5432.56 kg/m3

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