A satellite is revolving in a circular orbit at a height h from the earth's surface, such that h R where R is the radius of the earth. Assuming that the effect of the earth's atmosphere can be neglected, the minimum increase in the speed required so that the satellite could escape from the gravitat…

Question

A satellite is revolving in a circular orbit at a height h from the earth's surface, such that h R where R is the radius of the earth. Assuming that the effect of the earth's atmosphere can be neglected, the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

Accepted Answer

(2) √gR(√2-1). For h R the orbit radius is effectively R, so the orbital speed is vₒ=√(GM)/R=√gR. The speed needed to escape from that same radius is vₑ=√(2GM)/R=√2gR. The satellite already has vₒ, so only the difference has to be supplied. Δ v=√2gR-√gR=√gR(√2-1).

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