Gravity Propagation: How Does Time Affect Orbital Modeling?

[TheGalaxyOfGold]

I was thinking about the idea of looking up at a particular minuscule spot in the sky to see a particular planet at a very precise time, say, with a telescope. I was considering how light takes a matter of minutes to reach us. But then, remembering that gravitational forces must travel through space in order to be realized by the orbiting object some minutes later. This sort of ran me for a loop where I couldn't reason whether the gravitational force acting on an object, which traveled at the speed of light to get there and be realized is really calculated properly in models considering a planet has moved by the time the force arrives. Of course, I'm sure there are models that understand this well, and probably it's not as convoluted a question as it seems to me, but how does the propagation of gravity taking time to get to its destination affect a model that is intended to accurately play out the orbits of planets according to their present (not observed) position, with respect to, say TBD.

Perhaps I'm calling out a silly time scale to use. Please correct me if so.

 

[Bandersnatch]

In Newtonian mechanics, gravity is instantaneous. It has to be in order for orbits to be stable.
In GR, it travels at the speed of light. However, in GR, there is also a velocity-dependent component to gravity, and those interactions cancel out the aberration from the finite speed.
So both theories give the same results, and one can e.g. send ships to other planets using only Newtonian mechanics.
This paper: https://arxiv.org/abs/gr-qc/9909087 shows this mathematically.

 

[TheGalaxyOfGold]

Thank you!