Looking at just the Earth-Sun interaction, Earth is moving in a gravitational field that is unchanging. It's not that Earth is being pulled towards where the sun was eight minutes ago, but rather that it continues to move in free-fall in a region of space-time that is curved in a time-invariant manner.

If the sun were to vanish completely, then an observer above the elliptic of the solar system would see Earth transition from an apparently curved orbit to a straight-line path approximately 8 minutes after the sun's vanishing.

Thank you for your answer. I've heard the "it's an unchanging gravitational field" argument before, but it doesn't really explain the question for me. If the suns gravity is a field, then why is the movement of that field (which is locked to the suns mass I presume) instantaneously "known" to the earth, so the earth "free falls" in the curved space time in the right direction holding its orbit. Why doesn't the earth, at 1 au, free fall into the space time curvature that was created by the sun 8 minutes ago? It certainly appears the earth "knows" where the sun is now, which would imply instant information travel.

I also think you contradict yourself in your last statement, in which you say that the gravitational field of the sun does take 8 minutes to reach earth.

“Instant” is not a concept that makes sense with relativity. One observer’s “instant” is another observer’s “back in time.”

I’m not totally sure why this doesn’t result in spiraling into the sun as you describe, but I think it’s because the sun’s gravitational field is basically constant, and it’s changes which propagate at the speed of light.

Why would being 8 minutes out of date result in an unstable orbit?

Why wouldn't it? It's not obvious to me one way or the other: it's a small perturbation, over billions of years, of the same period as the period of the orbit itself. It's plausible that it might be unstable.

Remember that Newtonian concepts of gravity such as the equation g = Gm1m2/r^2 are only strictly valid within the Newtonian framework which, among other things, does assume that the effect of gravity is instantaneous. To derive accurate equations of motion under finite propagation speed of gravity, you need the machinery of general relativity. Of course, in mundane situations like the Earth-Sun system the two models give nigh identical results.

Thank you for your answer. True, Newton basically uses "instant gravity", and his equations really do work. I don't know enough about general relativity I must say, I've just never been able to really get it.

His equations work in the limit of slow speeds and low masses; GR keeps giving valid predictions in cases Newtonian mechanics breaks down. Famously, Newton cannot explain the slight observed precession of Mercury’s orbit which is something GR predicts precisely. But the effect is tiny and in almost all cases you don’t need a full relativistic treatment to predict the motions of Solar System bodies sufficiently accurately.

One quite mundane situation where one does need GR is compensating for the clock drift of GPS satellites caused by their height and speed relative to a ground-based observer (time is relative, not absolute as Newton thought!) Because positioning critically relies on very precise clocks, a non-adjusted satellite positioning system would very quickly start giving completely inaccurate results.

I'll let someone else answer your question, but if you enjoy thinking about these things, you might enjoy this vsauce video about the "speed of dark": https://www.youtube.com/watch?v=JTvcpdfGUtQ

Thank you, I will watch it when off of work.

I think this helps answer your question https://physics.stackexchange.com/questions/252015/gravity-v...

Thanks! That's a long read. I've started at the original question, but it'll take a while to process.

I don't think that time shifting the gravity vector has a measurable effect on the orbit. Indeed, the vector is 1au*c late in real life, but we didn't know that for sure until the recent neutron star collision observation.

As you're always working with a fixed temporal distance, wouldn't that basically negate any instability? There'd never be a gravitational "correction", as that 8 minute offset would never shift.

Well, real orbits are not perfectly circular (and many stable orbits are far from circular) so the distance (temporal and spatial) certainly changes.

That's true - you'd have a possible gravitational blue/red shift at different points.

Gravitational waves aren't how gravity propagates, however. They are really only relevant in exotic situations like mergers of massive compact objects, where spacetime is warped enough that orbits aren't stable and the bodies spiral inwards, radiating their excess gravitational potential energy in the form of gravitational waves.

If gravitational waves are not how gravity propagates, how does gravity propagate?

In general relativity gravity is curvature of spacetime caused by mass-energy. Changes in curvature propagate at c, the speed of causality. Gravitational waves are a special case of those changes predicted by GR, inspiraling massive objects making the spacetime around them ”ring” like a bell.

An eventual theory of quantum gravity may entail another viewpoint of gravity as a quantum field and mediated by a hypothetical graviton. But as of now we don’t have a good idea of what such a theory might look like; unifying QM and GR is famously one of the great unsolved problems in physics.

"In general relativity gravity is curvature of spacetime caused by mass-energy. Changes in curvature propagate at c, the speed of causality."

I really hope you meant speed of light there.

Regardless, this thing is still a mystery to me. Why, if gravity propagates at c (or, better perhaps: Changes in the space-time curvature, which is caused by mass-energy, propagate at c), why doesn't the earth spiral into the sun or away from it? If the earth is attracted to the point where the sun was eight minutes ago and not to where it is right now, it's orbit should not be stable. It's a very big difference compared to the "gravity is instant" way of Newton.

The speed of light in a vacuum is c, which is the speed of information, or the speed of causality

I used the term "speed of causality" on purpose; that's what c is really about. The fact that the speed of light in vacuum happens to be c is just a side effect of photons being massless.

Thank you again for your of answering my questions. So.. well.. What is this speed of causality then? Can we put a number on it?

Besides this all, I still can't get anyone to give me a clear cut and dried answer on my original question. If gravity is instant in the Newtonian model, and that gives us stable orbits and all that, how does that translate to the Einsteinian model, where there's an upper speed limit of c? So, why would that even work, if the gravity of the sun takes 1au/c to get here and be felt by the earth? Or, is gravity somehow "above" this speed limit?