A satellite is launched in the equatorial plane so that it can transmit signals up to latitude 60° on Earth. Its orbital speed is v = √[GM/(αR)], where R is Earth's radius. Find α.
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Mains Advanced

Question

A satellite is launched in the equatorial plane so that it can transmit signals up to latitude 60° on Earth. Its orbital speed is v = √[GM/(αR)], where R is Earth's radius. Find α.

G1 Physics · Accepted Answer

For the limiting line of sight, the satellite-Earth geometry givₑ orbital radius r = 6R. Circular-orbit speed is v = √(GM/r) = √[GM/(6R)]. Comparing with v = √[GM/(αR)] givₑ α = 6.