A few months ago I wrote a program which simulates how user-defined bodies moved under each other's gravities using Newton's Law of Gravitation. For each body, I calculated the total acceleration from all of the other bodies and moved it accordingly.
I would like to see if this can be done using General Relativity. Presumably, I would have to find each body's effect on spacetime and then calculate the body's acceleration/velocity as it moves over the warped spacetime. In the end, I would like to see if I can recreate Mercury's motion around the Sun, as calculated by Einstein.
If there is no single equation or set of equations which can be used to calculate the motion of a particle under gravity, I would love to see an example of where this has already been implemented.
