A spacecraft of negligible mass relative to Earth moves radially outward from the planet
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A spacecraft of negligible mass relative to Earth moves radially outward from the planet. The total mechanical energy per unit mass E of the spacecraft is represented on an energy–distance diagram described as follows:
• The gravitational potential–energy curve follows U(r)=−rGME.
• A horizontal reference line at E=0J⋅kg−1 is drawn.
• A second horizontal line at E=−2.0×107J⋅kg−1 intersects the U(r) curve at a radial distance of 2RE from Earth’s center.
Assume no non-gravitational forces act after launch.
(a) Describe, in words, what the point of intersection at r=2RE and E=−2.0×107J⋅kg−1 implies about the spacecraft’s kinetic energy at that location.
(b) Using only the information given by the diagram, explain how you can determine whether the spacecraft’s trajectory is gravitationally bound or unbound at r=2RE.
(c) Suppose an engine burn at r=2RE instantaneously adds 3.0×107J⋅kg−1 of kinetic energy to the spacecraft. Explain what type of orbit will result after the burn and justify your answer by referring to the sign of the new total mechanical energy.