# Speed of Gravity

1. Dec 27, 2006

### quantum123

Is the speed of gravity infinite? Relativity says no and it is equals to c.
Take a look at this scenario, planet jupiter and the sun is rotating around their center of mass.
If speed of gravity is not infinite, then the direction of force on the bodies will not be central, resulting in a torque, and the orbit will not be stable and will collapse.
Yet, we have stable orbits in the solar system everyday, and so relativity must be wrong!:surprised
Can anyone solve the paradox?

2. Dec 27, 2006

### D H

Staff Emeritus
DO the math to show the "orbit will collapse". While you are at it, google precession of Mercury.

3. Dec 28, 2006

### MeJennifer

It is not a paraodx, not only is there precession the orbit decays as well.

4. Dec 28, 2006

### quantum123

Are you saying that even the solar system will decay like the binary star system while emitting gravitational radiation, but only more slowly? How slowly? What about the atomic orbits?

5. Dec 28, 2006

### cesiumfrog

Cute :rofl:

Those subatomic particles are strongly charged too, if they were going to emit radiation you'd expect them first and foremost to do it electromagnetically.

6. Dec 28, 2006

### Hans de Vries

The solution to this is very well know. Your question comes back regularly

You do make a good point, but for both gravitation and electric fields we
can say the following:

The force field of a moving mass/charge always points towards/away from
the location where the mass/charge will be when it continues to move in
a straight line.

Since the orbit of Jupiter is very large, the points where Jupiter and the Sun
will be if they continue to move in straight lines is so close to their actual
positions that the orbit is stable (enough).

Infinite range fields like the electric and gravitation fields adhere to the
so-called Wave Equation also known as the d'Alembertian, For the electric
potential for instance we have:

$$\frac{\partial^2 V}{\partial t^2} - c^2 \frac{\partial^2 V}{\partial x^2} - c^2 \frac{\partial^2 V}{\partial y^2} - c^2 \frac{\partial^2 V}{\partial z^2} \ =\ \frac{q}{\epsilon_o}$$​

It is this wave equation which causes the potential V to propagate with
the speed c originating from the charge q. It is also the wave equation
which causes the force field (the electric field) to point to the location
where the charge would be if it continuous to move in a straight line.

Regards, Hans

Last edited: Dec 28, 2006
7. Dec 28, 2006

### disregardthat

How do we measure the acceleration of the gravity's force? At one distance from a planet the acceleration is X'm\s^2. At another place further away it is Y*m\s^2. So (as I just found out in the math forum) there have to be a "jerk" a rising of acceleration.

So if one object use twenty seconds from the place where it feels Y*m\s^2 (let's say that is 5m\s^2 to the place where it feels x*m\s^2 (let's say that is 10m\s^2) the math would be like this:

(10m\s^2 - 5m\s^2) \ (20-0) = 5m\s^2\20 = 0.25m\s^3

So the jerk would be 0.25m\s^3, right?

But I don't know excactly how the gravity works. Does even the jerk accelerate as we get closer to the planet? Have it been done any mathematical research on this?

8. Dec 28, 2006

### pervect

Staff Emeritus
As other posters have mentioned, this is a frequently asked question. It is answered in the sci.physics.faq

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

The basic point is that you can't properly measure the speed of gravity by the "direction of the gravitational force". A more detailed explanation expands on this remark by pointing out that you can't measure the speed of light by the "direction of the electromagnetic force" either.

9. Dec 28, 2006

### yogi

There are no really good experiments that directly measure the velocity of forces - we can measure the velocity of waves directly, and forces indirectly, but the issue will not be satisfactorily resolved until there is some unequivocal test to establish the speed at which forces are propagated. Van Flanderen and others claim that since the Solar Gravitational force on the earth points directly at the earth rather than its retarded position, it must be instantaneous - but the reasoning fails to take into account the nature of the field. Interestingly, some well knows physics writers such as Sears have stated in their early works that gravitational effects appear to occur instantaneously

10. Dec 28, 2006

### pervect

Staff Emeritus
Sure there are - at least I think the experiments for measuring the speed of electromagnetic forces are both good and direct.

What we do to measure this speed (which turns out to be the speed of light, as the disturbances propagate as waves) is to perturb a system where different parts of the system are coupled by electromagentic forces _here_ and measure the time it takes for the pertubation of the system to reach _there_.

Very simple, very direct, and it yields an answer of 'c' (in a vacuum - the disturbances actually propagate slightly slower in a medium).

What gives the wrong answer is to use a model of force that insists that the force between two particles points in the apparent (sometimes called retarded) direction of the source. This is basically a bad assumption, and the FAQ does a reasonable job (IMO) of explaining why. (Because momentum is conserved, we can expect the force to always point in the instantaneous direction of the source, not the retarded direction. Sometimes people arive at this bad model by using too literal a model of virtual particles. However they arive at the model, it's not a good model.)

We can, in principle, do much the same thing with gravity - to perturb a system, and measure the amount of time it takes the pertubation to propagate - except that we can't with our current technology create a big enough disturbance. In fact, we can't currently detect naturally occuring disturbances. So, we probably need to wait till gravity wave detectors (such as LIGO) come online, then we will be able to measure the disturbances from catastrophic astronomical events like binary inspirals. We still won't be able to directly cause measurable gravitational radiation ourselves, but we will be able to detect naturally occuring sources.

Then we'll just have to wait until we get both a gravity wave detection and an optical detection of the same (catastrophic) event, and we'll have fairly direct evidence that the speed of gravity is equal to 'c' (assuming that GR is correct), or not 'c' (if GR happens to be wrong). But my money is on GR.

11. Dec 28, 2006

### nakurusil

Van Flandern's claims have been debunked repeatedly. Here is an example by Steve Carlip.