Neutron stars (heavy masses) in close orbit throw off huge amounts of gravitons. They spiral in and crash due to conservation of angular momentum.
If the Earth really were attracted to where the Sun was eight minutes ago - well, I admit I was wrong about them crashing into each other. The signs are the wrong way around :0) If gravity propagated outward from the Sun at the speed of light then its mostly radial effect would also have a small transverse component because of the motion of the target. This would act to speed up the Earth in its orbit, sending it slowly away from the sun.
How slowly? The magnitude of the tangential force acting on the Earth would be ES/GS of the Sun’s radial gravitational force, where ES is the earth's orbital speed and GS is the speed of Gravity.
ES = 30 kms/second. If GS = a mere 3 million kms a second then ES/GS is 1 in 10,000. 99.999 % of the Suns gravity would act radially on the Earth - the other fraction would run tangentially. Earth would gradually increase its distance from the sun, doubling the distance in about a millenia.
If GS is infinite, or very very large indeed, then the tangential force falls to zero, in line with observation.
If the Earth really were attracted to where the Sun was eight minutes ago - well, I admit I was wrong about them crashing into each other. The signs are the wrong way around :0) If gravity propagated outward from the Sun at the speed of light then its mostly radial effect would also have a small transverse component because of the motion of the target. This would act to speed up the Earth in its orbit, sending it slowly away from the sun.
Don't be silly. It isn't as if the Sun is on the telephone with the Earth asking it where to direct its gravitational force (which would cause a 16 minute delay for that conversation). If you consider gravity being propagated as a spherical wave front with no knowledge of what it is going to affect then all of your problems will go away. And if you want some actual calculations/derivations, read here. I also suggest you read up on how central forces work. This logic you used with gravity would cause the exact same problem in electrodynamics. But in those cases there would be a much larger fractional difference between the two objects. If your assumptions were true you would never see stable cyclotron motion (like an electron in a constant magnetic field).