1. Where M and m are the mass of the bodies
r is the distance between them and
G is the Gravitational Constant = 6.67 x N m2 kg-2

2. The simplest way to solve questions is to equate this formula to F = ma:

3. The centripetal force of the planets rotating about their axis and the gravitational force between 2 planets will be in equilibrium. Therefore we can use any of the following to help solve questions:

4. F = GMm r2 = mg
gsrs2 = goro2
GM = gr2
12 x = go
9.72x1014 = 9.025x1013go
GM is a constant value therefore gr2 at the surface will equal gr2 in orbit
go = ms-2

5. F = GMm r2 = mω2r = mg
T = 2π ωo
GM = ω2r3 = gr2
T = 2π 1.065x10−3
GM is a constant so:
ωo2ro3 = gsrs2
T = 5901 seconds
ωo2 = gsrs2 ro3
T = 1hr 38min
ωo2 = 12 x 9000, ,0003
ωo2 = 1.336x10-6
ωo = 1.065x10-3 rad/sec

6. F = GMm r2 = mω2r = mg
T = 2π ωo
ro = m
GM = ω2r3 = gr2
ωo = 2π T
Altitude =
GM is a constant so:
ωo = 2π 24x60x60
ωo2ro3 = gsrs2
Altitude = m
ro3 = gsrs2 ωo2
ωo = 7.27x10-5
ro3 = x (6380,000)2 (7.27x10−5)2
ro3 = 7.55 x 1022