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 √(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 √(2r2w2).
Thus we have
This page is maintained by Thomas Bending,
and was last modified on Thu 28 July 2022.
Comments, criticisms and suggestions are welcome. Copyright © Thomas Bending 2022