Energy to Escape a Gravitational Field
Energy to Escape a Gravitational Field
Reaching infinity means the object finishes where gravitational potential energy is zero. Compare that final value with its negative starting energy.
Energy needed to reach infinity
- The increase in potential energy from radius r to infinity is shown below.
- An object that starts at rest at radius r must receive the same amount of energy to reach infinity with zero speed.
- If the object already has some kinetic energy, subtract it from the energy required to reach infinity (9702/42/F/M/24 Q1(b)(iii)).
- No extra energy is needed when the existing kinetic energy is at least as large as the required increase in potential energy.
Common mistake
and φ are negative; do not drop the minus sign. To find the energy supplied, use the change , not the value at one point.
Your turnquick check
A spacecraft moves from radius to radius and starts and ends at rest. Is its gravitational potential-energy change positive or negative? Must energy be supplied or removed?
Show worked answer
The change is positive: the potential energy becomes less negative as the spacecraft moves out. Energy must therefore be supplied.