A small research satellite of negligible mass relative to its planet travels in a closed
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A small research satellite of negligible mass relative to its planet travels in a closed, elliptical orbit. The closest approach (periapsis) is at distance rp from the planet’s center, and the farthest point (apoapsis) is at distance ra where ra>rp. Throughout the orbit the only significant force on the satellite is the planet’s gravitational attraction.
(a) Describe qualitatively how the satellite’s linear speed varies as it moves from periapsis to apoapsis.
(b) Explain why the magnitude of the satellite’s angular momentum about the planet’s center remains constant even though the satellite’s speed changes.
(c) At periapsis the satellite’s speed is vp. A brief sideways (tangential) force is applied to the satellite at periapsis, increasing the magnitude of its angular momentum. Without using algebra, state how vp is expected to change and justify your answer in words.