Two satellites, Satellite A of mass and Satellite B of mass
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two satellites, Satellite A of mass m and Satellite B of mass 3m, each travel in separate circular orbits of the same radius r measured from Earth’s center. Ignore the gravitational influence of any body other than Earth on the satellites.
(a) Derive an expression for the instantaneous acceleration of Earth toward Satellite A in terms of G, ME (Earth’s mass), m, and r.
(b) Derive the corresponding expression for the instantaneous acceleration of Earth toward Satellite B.
(c) Determine the ratio aE,B/aE,A of the accelerations found in parts (a) and (b).
(d) Explain, without additional calculation, why the center of mass of the Earth–satellite system remains on a fixed circular path about Earth’s center for either satellite despite the difference in satellite mass.