# Thread: Newton's Action at a Didstance

1. ## Newton's Action at a Didstance

When calculating the orbit of planets, for instance, using the universal gravity force law, F = - Gm1m2/x^2 is it implicitly understood that the force exchange between m1 and m2 is instantaneous, otherwise presumtion and use of time delay in the force exchange [action/reaction] process will not result in a correct, that is observed orbital trajectory - if this be otherwise please provide a brief calculation indicating a contrary result.

This [apparently] being the case and a matter that Newton was loath to provide any opinion re 'action at a distance'. This being the case does it not appear that Gauss' gravitational potential field is an additional matter to which Newton would also not be eager to venture an opinion?

Please include a brief supporting ratiional in any response.

Thanx.

2. Actually F = - Gm1m2/x^2 is an approximation and a darn good one. If you want a more accurate way to calculate the orbit of an object you must use General Relativity and there is an implicit speed limit on gravity of c.

3. Newton said this:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”

That was in a letter to Dr Richard Bentley on 25 February 1692. He also said:

"Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?"

That's in Opticks, queries 20 and 21. Newton talks about an aethereal medium, but you can "translate" that into a gravitational potential field. With his reference to density, and mass density in the differential form of Gauss' law for gravity, I think Newton would venture an opinion.

4. Since the sun is virtually stationary to very good approximation, the lightspeed-delayed gravitational effects from its wobbling are practically negligible.

5. Originally Posted by geistkiesel
When calculating the orbit of planets, for instance, using the universal gravity force law, F = - Gm1m2/x^2 is it implicitly understood that the force exchange between m1 and m2 is instantaneous...
Yes. That's what Newton assumed.

This being the case does it not appear that Gauss' gravitational potential field is an additional matter to which Newton would also not be eager to venture an opinion?
Gauss's formulation of Newtonian gravity has exactly equivalent physics to Newton's.

Originally Posted by CptBork
Since the sun is virtually stationary to very good approximation, the lightspeed-delayed gravitational effects from its wobbling are practically negligible.
The Sun moves at about 200 km per second around the centre of the galaxy (from memory). I wouldn't call that "virtually stationary".

6. Originally Posted by James R
The Sun moves at about 200 km per second around the centre of the galaxy (from memory). I wouldn't call that "virtually stationary".
I am sure he means in something like the centre of momentum frame of the solar system.

7. Originally Posted by James R
The Sun moves at about 200 km per second around the centre of the galaxy (from memory). I wouldn't call that "virtually stationary".
Originally Posted by kurros
I am sure he means in something like the centre of momentum frame of the solar system.
Yep, just considering the solar system with an observer fixed at the sun's centre, with the planets orbiting at far, far less than lightspeed. For General Relativity purposes, I have a suspicion that even if the sun were wobbling back and forth at 200km/s relative to the solar system's centre-of-momentum reference frame, that's still less than 0.1% of lightspeed and wouldn't make a major difference to the resultant gravity. In any case, who cares how fast the sun is moving relative to our galactic centre, when no one's there to say how fast the galactic centre is moving for its own part?

When Einstein calculated the GR correction to the precession of Mercury's orbit, he treated the sun as a stationary body and applied the standard (non black hole) Schwartzschild solution, and the result was still nearly perfect, when added to the much larger precession caused by the presence of the other planets as calculated using the old Newtonian model.

8. m/m' m(h/v)(pp')(wave and fld)(geo)m' m(2h/v)(2w&f)(2pp')(2geo)m' m(h/v)^2(w&f)^2(pp')^2(geo)^2)m' m(h/v)^2+(h/v)^2*)(w&f)^2(w&f)^2*)(pp')^2)(pp')^2*)(geo)^2)(ge o)^2*)m' * is opposite, not anti.

9. Originally Posted by JJM
m/m' m(h/v)(pp')(wave and fld)(geo)m' m(2h/v)(2w&f)(2pp')(2geo)m' m(h/v)^2(w&f)^2(pp')^2(geo)^2)m' m(h/v)^2+(h/v)^2*)(w&f)^2(w&f)^2*)(pp')^2)(pp')^2*)(geo)^2)(ge o)^2*)m' * is opposite
Nope, it's drivel.

10. Originally Posted by origin
... If you want a more accurate way to calculate the orbit of an object you must use General Relativity and there is an implicit speed limit on gravity of c. ...
Is it possible to understand why there is no effect of the delay?

For example, if two equal mass, far from any other masses, co orbit each other with one light second separation between them, each will be attracted to the point where the other was one second earlier, and not directly to where it is now.

11. Originally Posted by Billy T
Is it possible to understand why there is no effect of the delay?

For example, if two equal mass, far from any other masses, co orbit each other with one light second separation between them, each will be attracted to the point where the other was one second earlier, and not directly to where it is now.
I am not sure what you are asking. Your first sentence seems to say there is no time affect and your subsquent comments indicate that there is a time component.

I am not the best person to ask anyway, I am not well versed in GR AT ALL. I would love to understand it a bit on a mathematical level but I don't have a year or 2 to lock myself in a room to work on it. My understanding is merely conceptual.

However it is my understanding that if the sun were to suddenly vanish, for instance, the earth would continue to merrily orbit for about 8 minutes and then suddenly its orbit would stop and it would 'fly off' in what ever direction it was when the gravitational field ceased to affect it.

12. Originally Posted by Billy T
Is it possible to understand why there is no effect of the delay?

For example, if two equal mass, far from any other masses, co orbit each other with one light second separation between them, each will be attracted to the point where the other was one second earlier, and not directly to where it is now.

Or, another way to phrase your question:

Is the sun attracted to:
(A) where the earth is now
or
(B) the point where the earth was eight minutes ago?

I also wonder if the difference would be discernible.

13. I found this quote from Sir Arthur Eddington:

"Finally is the force of gravitation propagated instantaneously,
or with the velocity of light, or some other velocity? Until
comparatively recently it was thought that conclusive proof
had been given that the speed of gravitation must be far higher
than that of light. The argument was something like this. If
the Sun attracts Jupiter towards its present position S, and
Jupiter attracts the Sun towards its present position J, the two
forces are in the same line and balance. But if the Sun attracts
Jupiter towards its previous position S', and Jupiter attracts
the Sun towards its previous position J', when the force of
attraction started out to cross the gulf, then the two forces
give a couple. This couple will tend to increase the angular
momentum of the system, and, acting cumulatively, will soon
cause an appreciable change of period, disagreeing with observation
if the speed is at all comparable with that of light. The
argument is fallacious, because the effect of propagation will not
necessarily be that S is attracted in the direction towards J'.
Indeed it is found that if S and J are two electric charges, S will
be attracted very approximately towards J (not J') in spite of
the electric influence being propagated with the velocity of
light. In the theory given in this book, gravitation is propagated
with the speed of light, and there is no discordance with
observation."

Space, Time, and Gravitation, 1920.

14. Originally Posted by Neddy Bate
Or, another way to phrase your question:

Is the sun attracted to:
(A) where the earth is now
or
(B) the point where the earth was eight minutes ago?

I also wonder if the difference would be discernible.
I believe the answers are approximately B and no. The difference in angle of the force is about 360*(1/(fraction of a year that 8 minutes is)) so pretty negligible, not to mention that the effect of the Earth on the sun is very negligible already.

I'm sure there must be some observable consequence of this gravitational delay though, perhaps in a more extreme situation. Aside from gravitational waves that is.

edit: in light of the above quote, I could be wrong. In fact maybe I am, you would think that a delay of days would have an appreciable effect on the orbit of pluto for example, (although I guess the force experienced is pretty low by then) and Newtonian gravity does such a good job that it seems that isn't the case.

15. Originally Posted by CptBork
In any case, who cares how fast the sun is moving relative to our galactic centre, when no one's there to say how fast the galactic centre is moving for its own part?
It's important for the reason given in the Eddington quote, above.

16. Originally Posted by James R
It's important for the reason given in the Eddington quote, above.
You could just as easily pick the galactic centre as your centre-of-mass frame, and then I believe its own accelerations are of negligible consequence to Sol's orbit. If want to see substantial consequences from the speed-of-light delay, I think you need to look at systems such as binary stars.

17. Actually, CptBork, I think the problem doesn't arise in general relativity, although I'm not sure of the exact reasons. That is, gravity acts as if it was instantaneous and Newtonian, despite the finite propagation speed of gravitons.

As far as I am aware, there are good mathematical and theoretical proofs of this, though I haven't seen them myself.

Nevertheless, it is certainly a problem worth considering.

18. Originally Posted by Neddy Bate
Or, another way to phrase your question:

Is the sun attracted to:
(A) where the earth is now
or
(B) the point where the earth was eight minutes ago?

I also wonder if the difference would be discernible.
Originally Posted by kurros
I believe the answers are approximately B and no.
It should be closer to A actually, at least if you go by analogy with the electric field in electrodynamics. If you have a charge moving at a constant velocity, the electric field always points towards or away from where the charge is now, even though causal influences only propagate at c in electrodynamics. The only implication of that is that if you took a charge with a constant velocity and made it start accelating, then for a while the electric field some distance away would continue to point where the charge would be now if it hadn't started accelerating (there's an applet here illustrating this). For two charges orbiting one another, each charge does get pulled in a direction a little behind where the other is, but only by an amount that depends on its acceleration and not directly on its velocity. I'd hazard a guess that in GR the effect might be even weaker, since as far as GR is concerned a planet in orbit is following a freefall trajectory and isn't accelerating.

19. Originally Posted by James R
Actually, CptBork, I think the problem doesn't arise in general relativity, although I'm not sure of the exact reasons. That is, gravity acts as if it was instantaneous and Newtonian, despite the finite propagation speed of gravitons.

As far as I am aware, there are good mathematical and theoretical proofs of this, though I haven't seen them myself.

Nevertheless, it is certainly a problem worth considering.
Coming back to our solar system model, the sun's been sitting there making a dent in spacetime for billions of years, so the lightspeed delay has very little impact.

Edit: And in other reference frames, like one in which the Earth and sun are both hurtling at ~200km/s around the galactic core, the spacetime curvature is such that in the sun's centre-of-mass frame, you still get the (almost) Newtonian result- GR is set up to work that way pretty much by definition.

20. przyk:

Originally Posted by przyk
It should be closer to A actually, at least if you go by analogy with the electric field in electrodynamics. If you have a charge moving at a constant velocity, the electric field always points towards or away from where the charge is now, even though causal influences only propagate at c in electrodynamics.
Suppose at t=0, I'm sitting at position (x,y)=(0,1 light seconds) from an electric charge which is moving along the x axis in the x direction at a speed of 0.5c (let's say). The charge is located at (x,y)=(0,0) at t=0.

Are you saying that at t=1 second the electric field at my position will point towards the point (x,y)=(0.5 light seconds, 0)? Note that the distance from my location to the charge at t=1 second is 1.12 light seconds.

If that's what you're saying, can you please explain why this is the case?

CptBork:

Originally Posted by CptBork
Coming back to our solar system model, the sun's been sitting there making a dent in spacetime for billions of years, so the lightspeed delay has very little impact.
But depending of your frame of reference, that dent is either stationary or moving.

Edit: And in other reference frames, like one in which the Earth and sun are both hurtling at ~200km/s around the galactic core, the spacetime curvature is such that in the sun's centre-of-mass frame, you still get the (almost) Newtonian result- GR is set up to work that way pretty much by definition.
Can you explain why this is the case, and how the GR result differs from the Newtonian one?

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