A spacecraft of mass is initially so far from an asteroid that their mutual…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A spacecraft of mass 1.5×104kg is initially so far from an asteroid that their mutual gravitational potential energy may be considered zero. The asteroid has mass 8.0×1011kg and may be treated as spherically symmetric. The spacecraft is slowly moved radially toward the asteroid until the separation between their centers is 2.0km.
Assume any changes in the spacecraft’s kinetic energy during the approach are negligible.
(a) Derive an algebraic expression for the gravitational potential energy U(r) of the spacecraft–asteroid system as a function of the center-to-center separation r.
(b) Using your result from part (a), calculate the numerical value of the gravitational potential energy when r=2.0km.
(c) The spacecraft now fires its engines to move from r=2.0km to r=5.0km along the same radial line, again slowly enough that kinetic energy changes are negligible. Determine the work done by the engines during this maneuver, include the proper sign, and explain the physical meaning of that sign.