When it comes to the speed of gravity, it appears we are in a quandary. Relativity says that nothing can travel faster than the speed of light. But if this is the case, orbits would decay very rapidly. They could never be as stable as they are observed to be.This is because if it takes time for the information that a body has moved to reach another through gravitation, a body will not be pulled to where the other is now (in its current position), but to where it was when the gravitational waves started out.
According to Newtonian gravity, the transmission is instantaneous. According to relativity, it appears to depend upon the situation, which is iffy at best. It says that gravitational waves travel at the speed of light, but that the effects of gravity are felt instantaneously. In other words, the warping of space-time moves with the body at all times, as if it were physically adhered to it. But then, how is the information transferred through such a permanent fixture to another when the body is in motion? And if this is the case, what is the meaning of gravitational waves (implying change of state through transmission)? This is the "scissors paradox".
I have determined (although some might disagree) that this is very similar to the effect that promoted relativity to begin with. That is, the Michelson-Morley experiment. In this, a light beam which was split, directed at perpendicular directions to each other, one in the direction of the motion of the Earth (through the ether) and the other perpendicular to this, and then realigned should have produced interference with each other which could be measured. However, no such interference could be found, just as no aberration is found with gravity. The underlying concepts are virtually the same.
Special relativity does very well when explaining the absence of interference in terms of time dilation and the contraction of distances in the line of motion, and has even resulted in the famous E=mc2. But when it comes to the aberration of gravity, it is a different matter. The time dilation necessary in order to explain it is on the order of billions of times greater, and vise versa for the distance contraction, so this is out of the question. And a non-Euclidean geometry would only serve to make matters worse, as a curved path only increases the time necessary for the interaction.
As far as the Michelson-Morley experiment is concerned, however, I believe I have found a flaw in the experiment. I have recreated it geometrically on paper and found that in any frame of reference other than at rest, it is in fact impossible to exactly realign the beams. That is to say, the two beams, once split, cannot be redirected by the mirrors so that they meet at the same point at final reflection and then travel in the same direction. The angles will instead diverge. The best we can do is to adjust the mirrors slightly so that the beams travel in the same final direction, but they won't meet at the same point at final reflection, and will travel parallel to each other as separate beams with a distance between them that increases with increased speed for Earth through the ether. We cannot even be sure that the angle of incidence equals the angle of reflection for all frames of reference.
What we need, then, is a way to measure the discrepencies of light for motion through the ether without the use of mirrors, the splitting of beams, or a measure of interference. How would we do that, you ask? Simple. No matter what the frame of refence, the Earth must travel with at least 1/10000 of the speed of light at some point in its orbit because of its revolutions around the sun. Let's consider this to be its velocity through the ether at the moment. If we were to direct a light beam down a ten meter long pole, that is directed perpendicularly to the motion through the ether, then according to the original expectations of the Michelson-Morley experiment and classical physics, the light would fall back away from the line of motion as it travels this distance since the Earth is moving forward during this time. When the pole is directed opposite this, the light will fall back the other way. The distance between these two points for this velocity as seen on a screen at the end of the pole will be 1/5 cm.
Of course, we would not originally know the velocity and direction of the Earth through the ether, but directing the pole at all possible angles will create a filled in circle on the screen at the end of the pole if all of the points are marked. The ratio of the radius of the circle to the length of the pole will equal the ratio of the velocity of the Earth through the ether to the speed of light. If the pole is then turned to where the light is pointed to the center of the circle and the light moves in the same direction as the pole when the pole is then turned away from the center, then the pole will be pointing in the direction of the Earth's direction of travel.
This experiment is so simple that it has probably already been tried (as at least 99% of what I propose seems to have already been thought of, but at least that shows I'm on the right track), but I have never heard of anything other than the Michelson-Morley experiment. With relativity being as successful as it seems to be, and with the aberration of gravity necessarily cancelling itself out, this probably will too (but it would still be an advantage to know for sure). But if it didn't, well, that would just be a whole different bag of tomatoes, wouldn't it? If it cancels itself out, then we must consider how gravity would do the same thing (time dilation and contraction aren't enough with gravity). If it doesn't, then we must show how the distance between two parallel beams of light cancel the interference that would otherwise be observed if they were aligned, and then somehow apply that to gravity.