The speed of those ripples is determined the same way the speed of anything else is determined in relativity:
by their energy and their mass.
Since gravitational Waves are massless yet have a finite energy, they must move at the Speed of Light.
Which means, if we think about it, Earth isn’t directly attracted to the Sun’s location in space, but rather to where the Sun was located 8 minutes 20 seconds ago.
This is weird, and potentially a problem, because of how well studied the solar system is.
If the Earth were attracted to Sun’s position ~ 8 minutes ago using Newton’s laws, the orbits of planets wouldn’t match the observations.
There’s another way that General Relativity is different, however.
You also need to factor in the orbiting planet’s velocity as it moves around the Sun.
Earth, for example, since it’s also moving, kind of rides over the ripples through the space, coming down in a different spot from where it was lifted up.
There are 2 new effects going on in General Relativity that make this theory very different from Newton’s:
each objects velocity affects how it experiences gravity;
and so do the changes that occur in Gravitational Fields.
So, how do you calculate the curvature of Spacetime at any point in space?