Say I have a planet and shoot something with a given velocity, which is a significant portion of the escape velocity, in a given angle into the sky. It has some initial velocity and there is the force of gravity acting on it.
I simulated something like this before by creating my own Java vector class, and applying the force onto the velocity in small time intervals and then the velocity onto the position. It worked, but it took quite some time for a simple problem.
Is there any easier way to simulate more or less arbitrary trajectories in force fields?
I have Java, Python and Mathematica around, if any of those help.