Speed of gravity

[SAMU]

Since the Earth is moving around the Sun in its orbit at approximately 32000 mph or Apx. 9 miles per second and If the speed of gravity is the same as the speed of light then the moon, being one light second away, must be orbiting where the Earth was one second ago. That is to say 9 miles behind where we really are. Since, with lazer measurements, we can measure the distance to the Moon to an accuracy of a few feet. We should be able to check if the Moon is 18 miles closer to the earth when it is on the leading side of the Earth's orbit than it is when it is on the trailing side of the earth's orbit (averaging out the elipsis of the Moon's orbit). Or is the Moon the same distance from the Earth (on average) on both sides of its orbit? (the speed of gravity is infinite) Does anyone know if this measurement has ever been done?

If the speed of gravity is infitite then, by the process described in the earlier "speed of gravity" topic, signals, energy and possibly spacecraft can go faster than light.

[DStahl]

Ah! Very perceptive. The problem is, the laws of physics with respect to gravity and motion aren't quite as simple as they are presented in most undergraduate texts.

In particular, smooth motion of a massive body changes the behavior of its gravitational field slightly in a way that virtually perfectly cancels out the propagation time of the gravitational field. In other words, the Moon appears to orbit the instantaneous position of the Earth, and the Earth appears to orbit the instantaneous position of the Sun.

We had quite a discussion on this topic a while back.

The formulae describing this peculiar behavior of gravitational fields and moving bodies aren't ad-hoc or contrived; as I recall they are actually required if the conservation laws of physics as we understand them are correct. The same conservation laws require very similar corrections to the electrical fields of moving, charged bodies. In systems like closely orbiting neutron stars the gravitational cancellation mentioned above is not perfect, and the equations require that energy is lost by the system: that's the genesis of the famous gravitational waves, and the reason the measured decay of pulsar orbits is an important observation for relativity theory. This behavior of gravitational fields and moving objects is also, I think, the basis for the recent research which claimed to have measured the speed of gravitational propagation by deflection of light by Jupiter's gravity.

Interesting stuff! And not very intuitively obvious, either. On this page by Steve Carlip the effect is explained in plain English in terms of retarded fields; and on this Mathpages page it's explained with more mathematical examples in terms of lead-lag frequency response.

[beskeptical]

Not being a physicist, haven't a clue how it was done but I did see recent reports testing the speed of gravity. I assume that may have triggered this thought of yours?

Anyway, I did see recently that we can measure the distance to the Moon down to millimeters using laser pulses bounced off the mirror left on the Moon by the Apollo missions. Not that that is going to help here.

[crazy4space]

Since the Earth is moving around the Sun in its orbit at approximately 32000 mph or Apx. 9 miles per second and If the speed of gravity is the same as the speed of light then the moon, being one light second away, must be orbiting where the Earth was one second ago. That is to say 9 miles behind where we really are. Since, with lazer measurements, we can measure the distance to the Moon to an accuracy of a few feet. We should be able to check if the Moon is 18 miles closer to the earth when it is on the leading side of the Earth's orbit than it is when it is on the trailing side of the earth's orbit (averaging out the elipsis of the Moon's orbit). Or is the Moon the same distance from the Earth (on average) on both sides of its orbit? (the speed of gravity is infinite) Does anyone know if this measurement has ever been done?

If the speed of gravity is infitite then, by the process described in the earlier "speed of gravity" topic, signals, energy and possibly spacecraft can go faster than light.

All my planetary data says the earth is moving at 18.51 miles per second, which is closer to 55,000 miles per hour.

[DaveC]

All my planetary data says the earth is moving at 18.51 miles per second, which is closer to 55,000 miles per hour.

Well, if we assume the Earth's orbit is roughly circular, it travels about 300 million miles around the sun in a year. This works out to an orbital speed of about nine miles per second. I suspect your planetary data is providing the Earth's velocity relative to some "fixed" reference point like the galactic core? In fact we really don't have any idea how fast the Earth is moving, but for Samu's example, using the orbital speed works fine.

[RickNZ]

Hmmm giving gravity a speed points in the direction of a graviton existing however the view that gravity is simply an event due to a large body distortion of space-time then the speed of gravity is infinite, which backs perhaps indeed that the moon does orbit the instantanious position of the earth?

An uninformed guess here but perhaps when they calculated the speed of gravity they were simply witnessing the speed of light itself with the variation they noted being in fact the relative speed of jupiter?

[DStahl]

Even if gravity is viewed as a curvature of spacetime geometry the mathematical description of the curvature created by an object in smooth motion predicts that the vector of attraction will point at the instantaneous position of the object, and not its position at some time-minus-lightspeed-propagation-delay.

In other words, the Earth is attracted to the Sun's position NOW, and not to the Sun's position 8 minutes in the past.

If, however, a Giant Purple Hand were to grab the Sun and yank it 30,000,000 kilometers to the Galactic North, then the Earth would not feel the difference in gravitational interaction for 8 minutes! (I think I recall that the Earth is 8 light-minutes from the Sun.)

Such a yank would be a non-periodic, irregular acceleration of the Sun, and in that case the mathematics of GR predict that the retarded-field equations would not cancel the change in position. The change in the gravitational field would indeed propagate at the speed of light--like a big ripple in the geometry of spacetime, moving outward from the Sun at precisely c. Needless to say, it's darned hard to check this prediction directly. However, the similar predictions made by electrodynamics theory are testable and are perfectly reflected in the well-known behaviors of a stationary charge, a moving charge, and an accelerating charge.

[later] To emphasize: SAMU's experiment will not give results that show the Moon orbiting the retarded position of the Earth. Relativity predicts that the Moon will orbit the Earth's instantaneous position, and that is what is observed. Yet, GR also predicts that for our purposes, and as commonly understood, changes in the gravitational field propagate at the speed of light.

[Kaptain K]

All my planetary data says the earth is moving at 18.51 miles per second, which is closer to 55,000 miles per hour.

Well, if we assume the Earth's orbit is roughly circular, it travels about 300 million miles around the sun in a year. This works out to an orbital speed of about nine miles per second. I suspect your planetary data is providing the Earth's velocity relative to some "fixed" reference point like the galactic core? In fact we really don't have any idea how fast the Earth is moving, but for Samu's example, using the orbital speed works fine.

Circumference = 2 x pi x radius = 2 x 3.1416... x 93 million miles = 584 million miles or ~ 6oo million miles

[Roy Batty]

Arrgh! they got it wrong
http://www.guntheranderson.com/v/data/galaxyso.htm

[Durandal]

Even if gravity is viewed as a curvature of spacetime geometry the mathematical description of the curvature created by an object in smooth motion predicts that the vector of attraction will point at the instantaneous position of the object, and not its position at some time-minus-lightspeed-propagation-delay.

In other words, the Earth is attracted to the Sun's position NOW, and not to the Sun's position 8 minutes in the past.

That makes sense. I takes two to tango. After all, it's not just Earth doing the gravitational attraction dance, the sun's center of gravity is attracted to the Earth as well. Does that mean that the interaction of gravitational fields is instantaneous while their propagation is not?

If, however, a Giant Purple Hand were to grab the Sun and yank it 30,000,000 kilometers to the Galactic North, then the Earth would not feel the difference in gravitational interaction for 8 minutes! (I think I recall that the Earth is 8 light-minutes from the Sun.)

Ah, but what about a Yellow Hand?

[irony]

If, however, a Giant Purple Hand were to grab the Sun and yank it 30,000,000 kilometers to the Galactic North, then the Earth would not feel the difference in gravitational interaction for 8 minutes! (I think I recall that the Earth is 8 light-minutes from the Sun.)

You mean that one that was telling Jupiter off a while back? :P

[RickNZ]

Dstahl: Are you saying that the earth can predict the location of the sun despite the 'updates' on the suns actual position having a 8 min delay. But if the sun was move unpredictably the earth would carry on behaving as if the sun hadnt moved untill it recieves an accurate update.

Has this theory been proven?

[R.A.F.]

But if the sun was move unpredictably the earth would carry on behaving as if the sun hadnt moved untill it recieves an accurate update.

It's even weirder than that, RickNZ. Picture this...if the Sun were to vanish for some reason, we here on Earth would not know anything was amiss for the 8 to 9 minutes it takes light to reach us from that distance. Say the Sun vanished 7 minutes ago. We would still feel its warmth, be influenced by it's gravity, and still be able to see it in the sky!
Of course in another minute we'd all be in for a big surprise!! Pretty weird huh?

If I'm wrong...Please, someone correct me.

[Senor Molinero]

It would seem to me that if the attraction vector points to the instantaneous position then the speed of propogation of gravity must be instantaneous also. Reason being that all of the gravitationally interacting objects are in motion. A SoL propagation would mean delayed updates of the major body's position and the whole universe would fall apart.
Just MHO !

[Klausnh]

I’ve always understood that the rate of space-time movement is not limited by c only objects moving within space-time are limited by c. If that’s correct, why couldn’t gravitational attraction be instantaneous. I also recall reading that it is theoretically possible to travel to other stars by enclosing an object in a space-time “bubble” and moving that bubble at greater than c. Unfortunately, I don’t remember where I read that

[JS Princeton]

I’ve always understood that the rate of space-time movement is not limited by c only objects moving within space-time are limited by c. If that’s correct, why couldn’t gravitational attraction be instantaneous. I also recall reading that it is theoretically possible to travel to other stars by enclosing an object in a space-time “bubble” and moving that bubble at greater than c. Unfortunately, I don’t remember where I read that

If Einstein's General Theory of Relativity is true, gravity should propogate at the speed of light. However, it might not be true. So far, though, we have no evidence to show it to be measurably false.

[DStahl]

RickNZ: "Dstahl: Are you saying that the earth can predict the location of the sun despite the 'updates' on the suns actual position having a 8 min delay. But if the sun was move unpredictably the earth would carry on behaving as if the sun hadnt moved untill it recieves an accurate update."

Yes. That's what I'm saying. Because the Sun is in predictable motion its gravitational field is distorted in a predictable way. Same with Jupiter, and that's what the researchers in the speed-of-gravity observation mentioned above were relying on.

RickNZ: "Has this theory been proven?"

No theory is proven, I suppose, but retarded-field theory predates General Relativity and the aspects of the theory which describe the retarded-field behavior of charged particles has been tested until Heck won't have it. I believe it was also proven (mathematically) in the early part of the 20th Century that the conservation laws of physics would be incorrect if retarded-field phenomena were not part of the universe.

My point is, this is not a wild speculation but an awfully solid if somewhat esoteric part of physics. Kip Thorne once explained it in a slightly different way: If I recall, he said that the slight distortion in spacetime curvature created by the predictably moving Sun is already in place at the Earth's location, and so there is no 'prediction' on the part of the Earth, just an automatic following of the existing shape of spacetime. He differentiated between components of the gravitational field, but I don't remember the terms he used in his email--similar to 'dynamic' and 'static' components, though.

We get into an experimental bind when we try to test the gravitational aspects of retarded fields directly, because anything we can jerk around at will is too small to give us a measureable gravitational wave and anything large enough to give such a wave only ever moves in smoothly accelerating orbits, which according to the equations give the effect of changing the vector of attraction as described above. Sheesh. Why were we not provided with a proper manual for the testing of the universe?

Tom Van Flandern, astronomer-turned-gadfly, asserts that gravity does propagate virtually instantaneously. Steve Carlip and others have taken the trouble to provide concise, careful refutations of Van Flandern's work; most physicists I have emailed about it have said that what Van Flandern proposes is flat wrong: it is incorrect physics, and shows a poor understanding of the math involved.

But this is NOT easy stuff for the layman! In fact, Newton--who was inestimably smarter than Van Flandern--hated the idea of instantaneous propagation of gravity, but didn't have the tools to come up with retarded field theory. "I refuse to speculate" about the propagation of gravitation, he said: Non fingo hypotheses.

Here's a quotation from this short essay by Steve Carlip, Matthew Weiner, and Geoffry Landis:

"In general relativity...gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a 'force' in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the 'force' in GR is not quite central -- it does not point directly towards the source of the gravitational field -- and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result. [ie, instantaneous propagation--DS]"

"This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction 'conspire' to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations. Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light." (emphasis added)

----

I swear, I am not making this up!

[John Kierein]

Look at it this way. If you are on a train going at a constant velocity, facing forward and toss a ball straight up in the air it comes down to you straight, not behind you. The train drags both you and the ball along together. So also the sun drags the earth and the earth drags the moon. Thus the constant velocity wrt the cosmic microwave background is carried "instantaneously". But it's a little different story with accelerations. If the train is braking, the ball doesn't come straight down back to you, it flies to the front of you, if you are in a seat belt. However if you are jumping up in the air at the same time the train braking occurs, the ball and you are accelerated wrt the train the same and the ball comes down straight to you as well. So the earth and moon act like you and the ball and the sun acts like train; there is no difference in the motion due to the velocity of the sun. There is also no diference in the motion of the moon wrt earth due to any acceleration of the sun; but both the earth and moon should feel a time lag if the sun accelerates.

A fun book to read is "Pushing Gravity" edited by Matt Edwards. Van flandern has a paper in it that says that gravity should travel faster than c. I have a paper that says that gravity should travel at c. We both say gravity is a push. I identify what causes the push; Van Flandern hasn't a clue what causes it, but speculates that the cause must be travelling faster than c.

[SAMU]

[quote="crazy4space
All my planetary data says the earth is moving at 18.51 miles per second, which is closer to 55,000 miles per hour.[/quote]

You're right, my mistake. I forgot the 2 in the formula to solve for mps, ie 2xRxpi=C/365/24/60/60=mps.

Which yields of course apx. 18 mps.