A satellite of mass m travels in an elliptical orbit around a planet of mass M. Its greatest and least distances from the planet are r1 and r2 respectively. Find the angular momentum L of the satellite about the centre of the planet.

m*sqrt(2*G*M*r1*r2/(r1 + r2))
m*sqrt(G*M*r1*r2/(r1 + r2))
m*sqrt(2*G*M*(r1 + r2)/(r1*r2))
m*sqrt(G*M*(r1 + r2)/(r1*r2))

Correct answer: m*sqrt(2*G*M*r1*r2/(r1 + r2))

Solution

At the farthest and nearest points the velocity is perpendicular to the radius. Use L = m*v*r equal at both points plus energy conservation to eliminate the speeds, giving L in terms of r1, r2.

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