If gravity "travels" at $c$, and the sun is travelling "forward", does it mean the planets are actually orbiting various points "behind" the center of the sun? Does it also mean the sun is interacting with various points behind the planets? A line from the center of a planet, to a point behind the sun, would not be the same line as from the center of the sun to a point behind the planet. Does it mean there actually is no "common" point they both "orbit"? How is this stable?
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$\begingroup$ What do you mean by saying that the sun is travelling forward? $\endgroup$– PraharCommented May 30 at 11:55
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2$\begingroup$ Possible duplicate: physics.stackexchange.com/q/535344/180269 $\endgroup$– A.V.S.Commented May 30 at 15:01
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1 Answer
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@Prahar asked, "What do you mean by saying that the sun is travelling forward?"
That's easy. "Forward" is an arbitrary name for the direction in which the Sun is moving in the arbitrary coordinate system that you have chosen. We can imagine drawing a big letter "F" on the Sun ("F" for "front"), and "Forward" is motion in the direction of the "F".
The real problem is, suppose I choose a different coordinate system. In my coordinate system, the Sun is moving "Backward," (i.e., toward the letter "B" that I drew on the Sun directly opposite to your "F".)
If the point that the Earth orbits is somewhere on the the "B" side of the center of the Sun in your coordinate system, does that mean that the point the Earth orbits in my coordinate system is a different point? A point somewhere on the "F" side of the center?
How can the arbitrary choice of a coordinate system change the reality of what's happening?
It can't.
The answer is, Gravity does not move at the speed of light. Gravity does not move at all. What moves at the speed of light are disturbances in the gravitational field. If you grab hold of the Sun and give it a little shake, it will take about eight minutes at the speed of light before we here on Earth will feel the shake.
Otherwise, the Sun, and the shape that the Sun gives to the gravitational field, and the Earth, and the barycenter around which the Earth and the Sun mutually orbit all are co-moving, in whatever arbitrary coordinate system you choose.
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$\begingroup$ Aren't the disturbances a form of "information"? And wouldn't they seem to be coming from a point 8 minutes "behind" the sun? Your right, your F would just be an arbitrary term for the direction the sun is actually moving. Very hard to define that because it would all depend on your point of reference. However, the sun is moving, so it must be moving in some direction. Are you saying that Earth directly orbits the Sun, no matter what (the static gravity field), but any alterations in that field would be delayed by C? $\endgroup$ Commented Jun 11 at 12:27
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$\begingroup$ I'm not trying to be funny, but if Earth directly orbits the sun (or the barycentric point, which ever you desire), how then wouldn't we feel the shaking right away? I'm just confused as to how we can be "tied" to a point, but anything that happens at that point is delayed. $\endgroup$ Commented Jun 11 at 12:32
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$\begingroup$ @CuriousSteve, Re, "The Sun is moving, so it must be moving in some direction." You are denying the foundation upon which the theory of relativity is built, which is, that no inertial coordinate system is any more special than any other. There is no absolute motion in the theory of relativity. You can not say in which direction the Sun actually is moving. $\endgroup$ Commented Jun 11 at 13:17