[xenophiles]

...if gravity propagated at c, then the Earth would be attracted to where the Sun was eight minutes ago...

That's right, it is.

The result would be that the two bodies would develop a couple, and crash into each other.

That's right, given enough time. This has been experimentally observed in neutron stars spiraling toward each other. (Some gamma ray bursts may be from them colliding.)

A full, not-too-technical explanation of the experimental proofs for the very-fast speed of gravity can be found here[link]. Highly recommended.

I'm sorry to have to break it to you, but that essay is wrong. Gravity propagates at the speed of light.

[crazyshrink]

Assuming these scientists have it right and I am traveling in excess of the speed of light, where am I? Where I started, where I am going, or what?

And more importantly, how do I stop?

[agere_contra]

This has been experimentally observed in neutron stars spiraling toward each other.

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.