Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_238

3/238 A satellite is placed in a circular polar orbit a distance \( H \) above the earth. As the satellite goes over the north pole at \( A \), its retro-rocket is activated to produce a burst of negative thrust which reduces its velocity to a value which will ensure an equatorial landing. Derive the expression for the required reduction \( \Delta v_A \) of velocity at \( A \). Note that \( A \) is the apogee of the elliptical path.