Speed of gravity and planetry orbits

[Platonist]

I was talking to someone online the other day, and they were claiming that general relativity must be wrong because it predicts that gravity must propagate at the speed of light, and he said this must be wrong, because if that were the case the Earth would be attracted to the place where the sun was eight minutes ago, and so orbit would not be possible.

I thought to myself 'hahaha you silly rabbit', I can easily answer that, and so I explained to him that it would be just the same situation as when if you tie a weight to the end of a string, and swing it round your head at a constant angular velocity, and if you start walking at a constant speed, the orbit of the weight could still be maintained at the same angular velocity, and that the two situations would be indistinguishable, and as the force cannot be propagted through the string instantaneously, this answers his query.

He couldn't really answer this point, but then later I started thinking more about this, and I realized my analogy was incorrect. The force vector in the string always points down the string towards the centre of motion, and the point is the string itself is also moving at a constant angular velocity, thereby ensuring that the force and centripetal acceleration vector is always pointing into the centre of the motion. This is not the case for the orbit of the Earth however, as there is no 'string' that is moving round with us.

Firstly of course, we need to determine a frame of reference. If you are on the Earth or on the sun (ouch, hot!) there is no problem as the solar system is basically at rest from your perspective. However let's imagine you are sitting on some rocky body, let's say 50 light minutes away looking down at the plane of the solar system as it goes moving by you at a constant velocity. Surely if gravity propagates at the speed of light, then the force vector on the Earth will be pointing to where the sun was eight minutes ago?

I'm sure my crazy friend is wrong, but I am stumped as to how, can anyone help?

 

[Jonathan Scott]

Gravity propagates at the speed of light, but there are effects not only due to the position of the source but also due to its velocity (a bit like magnetism in the electromagnetic field) and acceleration, which result in the resulting acceleration being almost exactly towards the expected position of the source at the current moment, taking the light speed delay into account.

 

[DrClaude]

Have a look at this old thread on the subject: https://www.physicsforums.com/threads/speed-of-gravity.634813/

 

[Platonist]

Thanks alot... can someone try to explain in simple terms how this comes about? Are we talking about complicated general relativity spacetime curvature which conspires to make it seem like it is propagting instantaneously? Is there anywhere whch might explain in simple terms how this comes about?

 

[Jonathan Scott]

You can visualise it by simply looking at it from the point of view of an observer moving with the same velocity as the current velocity of the sun, as from that point of view the sun is at rest, at least for a short period, and one would obviously expect the effective force on the planet to point to the sun's current position. When you look at that effect from the original rest frame of the solar system, and adjust the velocities of the sun and the planet accordingly, it means that the effective force on the planet is still directed towards the expected location of the sun at the current time.

 

[Platonist]

You can visualise it by simply looking at it from the point of view of an observer moving with the same velocity as the current velocity of the sun, as from that point of view the sun is at rest, at least for a short period, and one would obviously expect the effective force on the planet to point to the sun's current position. When you look at that effect from the original rest frame of the solar system, and adjust the velocities of the sun and the planet accordingly, it means that the effective force on the planet is still directed towards the expected location of the sun at the current time.

I can see how it works for an observer viewing the solar system in a frame of reference at rest with the solar sytem, but as I said above, just adjusting the velocities of the sun and Earth doesn't work. Constant velocities doesn't imply some extra force in fact in implies no extra force.

 

[Jonathan Scott]

You need a bit of Special Relativity to transform the acceleration vector to the solar system frame in a way which gives consistent results. That then gives a direction correction of the order of v/c where v is the speed of the sun perpendicular to the acceleration vector. So you can either look at this by saying that the acceleration vector has a small extra term v/c times the main acceleration in the direction of motion of the sun, or you can say that it points to where the sun will be now allowing for the light speed delay.

 

[nasu]

The idea of "not having an orbit" as an argument against relativity is flawed anyway.
If by "orbit" he means a closed orbit then, for an observer for which the sun moves, the Earth does not describe a closed orbit. Even if the gravity is instantaneous and using just classical mechanics.

In a similar way, in a frame fixed to the Sun, the Moon does not move on a closed orbit around the Earth but rather something like this.

And this is not a due to finite "speed of gravity".

 

[Jonathan Scott]

For more discussion see the Wikipedia article on Speed of Gravity. As Laplace worked out in 1805, combining Newtonian gravity with a finite speed results in orbits being far less stable than is actually observed unless the speed is extremely high. However, when relativity is taken into account the acceleration is effectively towards the current position of the source, which fixes the problem.

 

[A.T.]

general relativity must be wrong because it predicts that gravity must propagate at the speed of light

Gravitational waves propagate at c. The attraction causing orbits is not due to gravitational waves. This is similar to E-field vs EM-waves coming from a common moving source: They also can point at / arrive from a different directions.

 

[Platonist]

Thanks everyone. For the record I think 'Lorentz covariance' is meant to be the idea that explains this...

 

[cosmik debris]

The Earth/Sun system is similar to the situation of a charged particle moving in a static electric field, i.e. nothing is propagating between the Sun and the Earth. The Sun's gravitational field is just there and the Earth moves through it. Only if something disturbs this system does anything propagate then the changes propagate at c.

In the case of the charged particle system any acceleration of either the test charge or the source of the field will cause changes in the field to propagate at c. Since Gravitational radiation is quadrupole in nature rather than dipole as in the charge case, a change in the Earth or the Sun's acceleration is required. These changes propagate at c. There are small changes in acceleration in the Sun/Earth system but only change the orbit very slightly.