I already read this Phys.SE question but my question is different. I'm well aware that the effect of gravity in GR gets transmitted from point to point at the speed of light. But let's ignore GR for now. What about Newtonian gravity?
Imagine a universe in which Newtonian gravity(but neither GR nor SR ) holds. Imagine also that there's only one object(say, a planet or anything with mass) in this universe. Suddenly another planet(or any object with mass) pops out into existence(yes I know, but ignore the conservation of mass for now). How long will it take for the gravity to affect those two objects. Is there any way to calculate it from Newton's law of gravitation?
It seems to that this equation does not say anything about how fast gravity should get transmitted. Or maybe In this Newtonian universe it cannot be calculated from theory but rather be measured experimentally?
A lot of people say it gets transmitted instantaneously, but from where does that follow? How does one prove this only assuming Newton's laws of motion and his gravity law as our axioms? And no don't tell me that $c$ is the upper limit, I'm assuming a Newtonian universe here.