Newton's laws of motion in 3+1 dimensions ?

[jk22]

If it were supposed that time were a 4th non-spatial dimension how would it influence the gravitational movement ?

The problem I have when trying to solve this invented problem is that Newtonian physics works in coordinates and that there are a lot of ways to find 4d 3+1 hyperbolic-spherical coordinates.

Which one should be used to start the calculations ?

 

[Dale]

It sounds like you are thinking of Newton-Cartan gravity.

https://en.m.wikipedia.org/wiki/Newton–Cartan_theory

 

[haushofer]

Newton-Cartan gravity however is at the level of dynamics fully equivalent to Newtonian gravity as you know it (to answer the question in the OP).