Greetings, community. I'd like to ask a very simple question about gravity and the bending of spacetime.

What would happen if the sun disappeared at this very moment? Would the orbit of our planet be affected instantly and continue travelling across the space in a straight line, or is there some sort of speed limitation for gravity to take effect?

Looking forward to read your replies, and excuse me if the question was too obvious!
Regards,
Erick

DaveC426913
Gold Member
The question is not obvious, though it has been asked many times here on PF.

One caveat before I answer: the sun cannot simply disappear. The method by which the sun were removed from it position would also affect how the force of the sun's gravity would affect Earth.

That being said:

Gravitational waves travel at the speed of light. Any change in the sun's mass would take 8 minutes to affect Earth.

While current observations do not yet provide a direct model-independent measurement of the speed of gravity, a test within the framework of general relativity can be made by observing the binary pulsar PSR 1913+16. The orbit of this binary system is gradually decaying, and this behavior is attributed to the loss of energy due to escaping gravitational radiation. But in any field theory, radiation is intimately related to the finite velocity of field propagation, and the orbital changes due to gravitational radiation can equivalently be viewed as damping caused by the finite propagation speed. (In the discussion above, this damping represents a failure of the "retardation" and "noncentral, velocity-dependent" effects to completely cancel.)

The rate of this damping can be computed, and one finds that it depends sensitively on the speed of gravity. The fact that gravitational damping is measured at all is a strong indication that the propagation speed of gravity is not infinite. If the calculational framework of general relativity is accepted, the damping can be used to calculate the speed, and the actual measurement confirms that the speed of gravity is equal to the speed of light to within 1%. (Measurements of at least one other binary pulsar system, PSR B1534+12, confirm this result, although so far with less precision.)

If this result was only within 1%, how can scientists be so sure about the speed of propagation of gravitational waves? Could you possibly name me another experiment that has been done so I could read about it?

Thanks once again

russ_watters
Mentor
1% isn't a bad start and in any case provides a very definitive answer to your question of if it could be instantaneous.

I'm not very knowledgeable on the subject, but didn't Einstein's Theory of General Relativity predict the speed of gravity to be c?

From what I understand, gravity is not an object pulling on another object. The earth doesn't pull a person to it, but rather the earths mass distorts space and a person located in the distorted space is PUSHED to the earth by the distorted space. If the sun were to vanish, space would no longer be distorted and all the planets would travel a path determined by the other bodies nearby. How quickly this would happen after the sun is no longer affecting the earth is puzzling to me as well. I'm not quite sure if I buy the "gravity waves travel at the speed of light" statement either.

Nabeshin
I'm not quite sure if I buy the "gravity waves travel at the speed of light" statement either.

Speaking only from my personal experience with GR, I know that it's fairly straightforward to show that linearized gravitational waves (the simplest kind) travel at c.

Speaking only from my personal experience with GR, I know that it's fairly straightforward to show that linearized gravitational waves (the simplest kind) travel at c.

I believe there's more too it; that perturbations of the Minkowski metric are small.

Speaking only from my personal experience with GR, I know that it's fairly straightforward to show that linearized gravitational waves (the simplest kind) travel at c.

I understand what you're saying, but what perplexes me is that if gravify is basically the distortion of space/time, then a traveling gravity wave will be disorting time as it moves along. So if time is being distorted by the gravitational wave, then how can it's speed be determined with any amount of accuracy?

I understand what you're saying, but what perplexes me is that if gravify is basically the distortion of space/time, then a traveling gravity wave will be disorting time as it moves along. So if time is being distorted by the gravitational wave, then how can it's speed be determined with any amount of accuracy?

How do you measure time distance and velocity on the curved manifold of spacetime? The speed of light is, in general, only locally c. The same is true for gravity waves. If you project your local flat space over nonlocal space curved from gravity waves, you will not measure a velocity of c.

This is why small perturbations travel at approximately c for small applitude waves, and larger perturbations depend on what you mean by velocity.

In flat space-time the trace of the metric is (-1,1,1,1) and other terms are zero. A small perturbation would add huv to each term where all the huv<<1.

Nabeshin