2009
Jumping off a planet
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section S2
Adapted from IOAA 2009 (Tehran), theory problem 3. We have restated it in our own words and kept the original data. The solution was last checked on 16 October 2026.
Estimate the radius of a planet from which a person could escape by jumping straight up. Assume that the planet has the same density as Earth.
Estimate the take-off speed of a jump on Earth. How does the escape speed of a planet of fixed density depend on its radius?
- A good jump lifts the centre of mass by about 0.5 m, which we state as an assumption. Energy conservation on Earth gives the take-off speed
- A planet of radius
- Setting
AnswerThe planet could have a radius of about 1.8 km. Any sensible jump height is acceptable if it is stated, and the radius changes only as the square root of the height.
This problem also appears among the olympiad problems of Section S2, Exam technique and the problem-solving method, which teaches the ideas it uses. Equation and figure numbers refer to the course.