Mass in Gravitational Field - Verlet ODE Solver

The Verlet methods to integrate ODEs guaranty energy conservation. Using such methods addresses most of the issues described in the problem of a mass in a gravitational field described in a previous section

• Exercise Replace the RK4 ODE solver step by a Velocity Verlet step in the code orbit.c. This code is found in the previous section

• Exercise Run the code over a range of initial velocity $v$ .

The code uses a slightly smaller $dt$ as compared to the $dt$ in the RK4 solution. This is because the Velocity Verlet method is a much lower order ODE solver. Notice however that the code is much batter at maintaining closed orbits even for high excentricity orbits.

A hallmark of the Velocity Verlet method is the conservation of energy.

• Exercise Plot the energy time-series. Note the recurrence of the same value of the energy.

This code is also time-reversal invariant.

• Exercise Check the time reversal invariance of the code. Do the same check with the RK4 based code.