newtonian gravity - Let's say that the Sun moves away from us, this should cause a change in gravitational force, when will this change be noticed by us?

I have studied Newtonian physics, and was having a introduction to relativistic physics. I read a similar question in 'A brief history of Time' which is now not letting me sleep.

Answer

That change (aswell as any change in relative position of a mass) generates a perturbation (called gravitational waves) that propagates at the exact same speed as light. This means that the Earth wouldn't feel the change until 8 minutes had passed.

As the Sun gets farther the attraction would get weaker (by the square-law relation). But the important thing is that the time offset between the actual event as seen by the Sun and the event as seen from Earth would increase as they get farther (by means of a linear relation).

In general moving something as massive as the Sun so far that a change in the gravitational attraction gets noticed and doing it so quickly as to manifest itself in the Sun-Earth time-delay of 8 minutes requires a crazy amount of energy. If you do it slower you might be unable to see the offset in time between what happened in the Sun and what was perceived on Earth.

This requisite of moving a huge mass at huge speeds is met in some naturally ocurring scenarios, like for example black hole binaries (black holes orbiting each other). Only a black hole has the power to accellerate another black hole to those crazy speeds. In fact they are the strongest emmiters of gravitational waves.