"Everything in the solar system orbits around that point."
Depends on exactly how pedantic you want to be. Technically everything in the solar system orbits the barycenter of the galaxy and intra-system movement is the same type of low-distance high-frequency wobbling the author chose to dismiss with regards to the motion of moons around planets.
If you get that pedantic you must delve into relativistic center of mass and center-of-momentum frame. The speed of gravity is the speed of light. Sun's gravity affects earth with 8 minute lag.
I'm told that you do the math at that level it's almost the same as in the Newtonian model, which is surprising. I never understood the math but it's related to the fact that changes in stress-energy tensor of matter are continuous. Mass+energy moves gradually from place to place, there are no sudden jumps. Earth accelerates towards point point where the Sun is in future. Not the same point as Newtonian mechanics with instant gravity says it should be, but close enough to hide relativistic effects of gravity most of the time.
Depends on exactly how pedantic you want to be. Technically everything in the solar system orbits the barycenter of the galaxy and intra-system movement is the same type of low-distance high-frequency wobbling the author chose to dismiss with regards to the motion of moons around planets.