Brachistochrone of a Spherical Uniform Mass Distribution
arXiv:math-ph/0611055
Abstract
We solve the brachistochrone problem for a particle travelling through a spherical mass distribution of uniform density. We examine the connection between this problem and the popular "gravity elevator" result. The solution is compared to the well known brachistochrone problem of a particle in a uniform gravitational field.
3 pages, 1 figure