Q: What are the escape velocities for the earth, solar system and
[29 Nov 1999]
A: If we're a unit mass at distance r from an object of mass M and want to get to infinity then the potential energy required is the integral of MG / x2 between x = r and infinity, which is MG / r. To escape, our kinetic energy v2 / 2 must be equal to this.
If we're on the surface of the object, and it has surface gravity g, then g = MG / r2 so the potential energy required is gr and the escape velocity is sqrt(2gr).
If we're in a circular orbit around the object, then MG / r2 = rw2, where w is the angular velocity, so the potential energy required is r2w2 and the escape velocity is sqrt(2r2w2).
Thus we have
Back to puzzles
This page is maintained by Thomas Bending,
and was last modified on 30 December 2018.
Comments, criticisms and suggestions are welcome. Copyright © Thomas Bending 2018.