Waltr said:
I was actually referring to Newtonian gravitation. Where it is considered a force. i was thinking more F=mg if m were to increase with speed so should the force.
You can't combine Newtonian gravitation with relativity; the two are inconsistent. And since the idea of mass increasing with speed only arises within relativity, you can't combine that idea with Newtonian gravity in a consistent way either.
Waltr said:
how fast the effect of gravity moves, like if the sun were to just vanish.
This probably does deserve a separate thread if you want to dig into it further, but I'll go ahead and make a long-winded post here anyway.
The "vanishing Sun" is a common scenario, but it has a fundamental problem: the Sun can't just vanish, because that would violate conservation of mass-energy. (In GR, this conservation law is a constraint that the stress-energy tensor must satisfy: if the Sun were to just vanish, the stress-energy tensor that describes the Sun would violate the constraint.) So you can't formulate the "vanishing Sun" scenario in a consistent way.
In fact, it turns out to be very difficult to formulate *any* kind of scenario like this for testing "the speed of gravity", precisely because of that conservation law; since the stress-energy tensor is the source of gravity, and since it's conserved, all sorts of obvious thought experiments about suddenly changing the source of gravity and watching the change propagate are actually impossible. For example, suppose we fire a big laser at the Sun in order to push it in some particular direction, so we can watch what happens to the orbits of the planets. The problem is that the laser beam itself carries energy, as does whatever is firing the laser, and if there's enough energy in the laser to push the Sun, there's enough energy in it to already be affecting the orbits of the planets way before it ever hits the Sun.
The best we can do (at least so far) at addressing the "speed of gravity" question is to attack it indirectly. One way is simply to ask GR, as a theory, what it says the speed of gravity is. The answer to that is unequivocal: GR says the speed of gravity is equal to the speed of light, in the following precise sense: Take any event in spacetime and ask what information you need to have in order to precisely determine the effects of gravity at that event. The answer is that all you need is information about the event's past light cone, i.e., about events in spacetime from which information can propagate to your chosen event at a speed less than or equal to the speed of light. You never need to know anything outside the past light cone.
Another way of attacking the question indirectly is to ask if there are other ways of observing the speed of gravity, given that we can't conduct the obvious sorts of experiments I described above. In situations where gravity is weak and all motions are slow, it turns out that the description of gravity given by GR is very close to the Newtonian description: in these situations, gravity can be considered to be a "force" in the usual Newtonian sense, and the speed of gravity question becomes a question about how fast this force propagates. Then we can use our Newtonian intuitions in the following way: a perfectly Newtonian force propagates instantaneously, so at any instant, the force on an object (such as a planet) due to a gravitating source (such as the Sun) should point directly at the source. But a force that propagates at a finite speed will have a time delay, so at a given instant, at the object, the force it feels should point, not at where the source is "now", but where the source was some finite time ago (the time it takes the force to travel the distance). The difference between these two directions (where the source is "now" and where it was a travel time ago) is called "aberration".
A number of people have used this intuition to argue that gravity must propagate much faster than light, because we do not, in fact, observe aberration of gravity--at least, we don't in almost all cases (but there are exceptions, which I'll get to in a minute). This contrasts sharply with light, for which we *do* observe aberration--for example, the direction in which we see light coming from stars changes as the Earth changes direction in its orbit around the Sun. However, when you look into the details, you find that there is another relativistic correction to the Newtonian behavior that is very important: the "force" of gravity in relativity does not just depend on the distance to the source, as it does in Newtonian theory. It also depends on the velocity of the object relative to the source.
It turns out that this velocity dependence, in the case of gravity, cancels out almost all of the aberration due to the finite speed of gravity, for cases where the velocity is only changing slowly (as it is for a planet orbiting the Sun). The small amount of aberration that remains shows up as a shift in the perihelion of the planet (the point where it comes closest to the Sun in its orbit), and just such a perihelion shift has been observed--first with Mercury (this was actually known well before Einstein developed GR, and was one of the first tests applied to the theory), but now, IIRC, it has been observed with other planets as well. So this is another indirect indication that gravity does in fact propagate at the speed of light.
The definitive treatment of all this is the paper by Carlip on Aberration and the Speed of Gravity:
http://arxiv.org/abs/gr-qc/9909087
It's somewhat technical but still very readable.
