  In this paper we study the brachistochrone problem in an inverse-square
gravitational field on the unit disk. We show that the time optimal solutions
consist of either smooth strong solutions to the Euler-Lagrange equation or
weak solutions formed by appropriately patched together strong solutions. This
combination of weak and strong solutions completely foliates the unit disk. We
also consider the problem on annular domains and show that the time optimal
paths foliate the annulus. These foliations on the annular domains converge to
the foliation on the unit disk in the limit of vanishing inner radius.
