An international space agency is considering moving an aging communications satellite…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
An international space agency is considering moving an aging communications satellite from its current circular geostationary orbit of radius r1 to a disposal orbit of radius r2=2r1 around Earth. Assume Earth’s gravitational parameter is μE. The satellite’s mass is sufficiently small that its own gravity can be ignored.
(a) Derive a general expression for the change in total mechanical energy per unit mass, ΔE, required to move a satellite from one circular orbit of radius r1 to another circular orbit of radius r2. Express ΔE in terms of μE, r1, and r2. State clearly whether ΔE is positive or negative when r2>r1.
(b) Using your expression from part (a), evaluate ΔE per unit mass when r1 corresponds to a geostationary orbit (r1=4.22×107m) and r2=2r1. Provide a numerical result with proper units.
(c) Discuss the practical implications of the sign and magnitude of ΔE for planning the satellite’s end-of-life disposal maneuver. Include in your discussion whether propulsion work must be done on or by the satellite.