Earlier quoted context omitted.
Remember that Newtonian concepts of gravity such as the equation g = Gm1m2/r^2 are only strictly valid within the Newtonian framework which, among other things, does assume that the effect of gravity is instantaneous. To derive accurate equations of motion under finite propagation speed of gravity, you need the machinery of general relativity. Of course, in mundane situations like the Earth-Sun system the two models…
Thank you for your answer. True, Newton basically uses "instant gravity", and his equations really do work. I don't know enough about general relativity I must say, I've just never been able to really get it.
One quite mundane situation where one does need GR is compensating for the clock drift of GPS satellites caused by their height and speed relative to a ground-based observer (time is relative, not absolute as Newton thought!) Because positioning critically relies on very precise clocks, a non-adjusted satellite positioning system would very quickly start giving completely inaccurate results.