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In the simulation of a solar or (galactic) system, when you calculate the position of a planet P at time t+dt, you only know the position of the other bodies in the system at time t, so you calculate the distance d between P and any other body Q at time t, and then the acceleration P receives from Q

If gravitation speed were infinite then that would be enough for accurate simulation

But if gravitation has a finite speed c, then P receives actually an acceleration from the position of Q when it was at time t-d/c, so you should keep all past positions in the memory of the computer ?

How in practice is this problem solved for precise simulation ? is it possible to calculate the speed of graviation this way, and is it equal to the speed of light ? (it could be a priori different)