Comparing Two Paths

A mass $M$ is fixed at the origin in the $xy$ coordinate system. At time $t = 0$ , another mass $m$ begins at a radius $r_0$ with respect to the origin, with a speed $\dot{r}_0$ directed radially away from the origin.

Under the influence of gravity, the particle travels away from the origin, comes to a stop, and eventually returns to where it started at time $t = T$ . The "action" for this path is:

$S_1 = \int_0^T (E - U) \, dt \\ E = \frac{1}{2} m \, \dot{r}^2 \\ U = -\frac{G M m}{r}$

Consider another path whose endpoints have exactly the same space and time coordinates as for the first path, but with the particle being completely at rest the whole time. Let the action for this path be $S_2$ . We know that the second path is non-physical, and it should therefore have a larger action than the first path does.

What is $S_2 - S_1$ ?

Details and Assumptions:
1) $M = m = G = r_0 = \dot{r}_0 = 1$