For a satellite of mass in an elliptical orbit

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

For a satellite of mass

m

in an elliptical orbit, its distance from the central body is

r_p

at perigee and

r_a

at apogee. Derive an expression for the ratio of its kinetic energy at perigee,

K_p

, to its kinetic energy at apogee,

K_a

, in terms of

r_p

and

r_a