Not too sure of your point regarding sat nav. The corrections are built in.

The extraterrestrial trajectory to Mercury has such a low velocity in terms of c,, time dilation is irrelevant. Earth control time delay is a factor but Newtonian calculations will land you where you need to be. You have to reach 0.8c before time and mass start getting interesting.

General relativity was profound and upset a key tenet of the Principia, that of absolute space, absolute time,absolute position. The conundrum is explained with Newton's bucket. But in the observable realistic achievement stakes, f=ma can help plot your trajectory with gravitational slingshot to such a local target quite easily. Interstellar distances with high acceleration, I grant you, we need to take time and mass as variables that would alter the target had we stuck with Newtonian calculations, but even then we would be introducing variables, not superseding.

It is disingenuous to suggest removal of the need for fixed state supersedes the gravity, force and mass concepts. The concepts are there, the mathematical relationships are there, the ratios between them represent his clarification.

Relativity did remove other sacred cows such as the ether, but we need to look at the work of Planck, through to Heisenberg onwards to begin to dismantle the Principia, as we look at the quantum world. Space probes are in the physical word though...