 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2013/8/a/solution

M_{E} = 4 π ρ R^{3} /3

and

r_{g} = η R

. Balancing the required centripetal acceleration with the exterior gravitational field gives

ω^{2} r_{g} = \frac{G M _{E}}{r _{g}^{2}}, η = (\frac{G M _{E}}{ω ^{2} R ^{3}})^{1/3} = (\frac{4 π Gρ}{3 ω ^{2}})^{1/3} .

The orbital plane must be equatorial and the motion prograde for the satellite to remain over one point. The uniform density assumption supplies

M_{E}

in terms of the specified

ρ

and

R

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