Dear physics stack exchange,
I've been trying to consider exactly how to program a gravitational simulation with time-retarded gravitational potential fields. Its proven difficult given each time one of the source masses is instantaneously accelerated the original sources potential fields spherically vanishes at a speed "c" from the last place it had its previous velocity and a new potential field moving at the new velocity is created also at a speed "c". It would be, however, computationally extreme to separately keep track of every instantaneous new field and how it's expanding or decaying. Especially because I hope to have the field determine the movement of multiple bodies and their new velocities resulting from time delayed changes to the overall net potential field. Put simply, is there a way of calculating the time retarded potential without it being so computationally extensive? Such as translating this into maybe something like an elastic PDE that could be solved by multidimensional finite difference methods.
If anyone can assist in either minor or major ways I would be grateful.
Sincerely, a freshman college student going on sophomore year
