A walk round an asteroid
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 3.2
Adapted from IOAA 2010 (Beijing), theory problem 6. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
A spacecraft lands on a spherical asteroid that does not rotate. The asteroid is 2.2 km across and its average density is 2.2 g/cm³. Can an astronaut walk once round its equator in 2.2 hours? Answer yes or no, and explain why with formulae and numbers.
- The radius is 1100 m, so the mass is
- The equator is
- By (S.19), the speed of a circular orbit just above the surface is
- The walk needs more than the orbital speed. At that speed the asteroid's gravity cannot hold the astronaut on a path that follows the curved surface, so each step would lift them off the ground.
AnswerThe answer is no. The walk needs 0.873 m/s, which is faster than the 0.863 m/s of a circular orbit at the surface, so the astronaut would leave the ground. Even an orbit just above the surface takes 2.23 hours to go round.
This problem also appears among the olympiad problems of Section 3.2, Energy and the vis-viva equation, which teaches the ideas it uses. Equation and figure numbers refer to the course.