The easiest way to set up the equations of motion in polar co-ordinates is to use the Euler-Lagrange equation.
http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
The Mathematica function EulerEquations will generate them from the Lagrangian, which is the kinetic energy minus the potential energy, in the coordinates of interest.
The analytic solution, an ellipse, is obtained by a change of variable u = 1/r.
