Classical Dynamics of Particles and Systems · Problem 8-23

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-satellite-radial-velocity

Problem

An Earth satellite moves in an elliptical orbit with a period

\tau

, eccentricity

\varepsilon

, and semimajor axis

a

. Show that the maximum radial velocity of the satellite is

2\pi a\varepsilon/(\tau\sqrt{1-\varepsilon^2})