Grav,

I'm sorry -- I thought you were saying the precession just went as 1/r, but you were saying the precession *per orbit* went as ~1/r.

Well, that's what GR says (approximately). If you go through that link I posted above, the precession (per orbit) formula is approximately

theta = 6pi*r_s/L,

where r_s is the Schwarzchild radius, and L is the "semilatus rectum" of the ellipse, which for our purposes for a nearly circular orbit is about the average radius. Now, the Schwarzchild radius is just 2GM/c^2, which is about 1.5km for the sun.

Now, your formula, for that is v/c*R/L, where R is the radius of the sun goes, with v = 2piR/T --> 2piR^2/cT. Using your posted values for R and T, I get 4600m for that. So 4.6km/

Now, the GR value about is in radians per revolution, so we must divide by 2pi to get the "revs per rev" figure, that is just 3r_s = 4500m.

The slight difference between L and the radius makes it even closer for Mercury.

So Grav, it's coincidence that your R*v/c comes out to be about the same as 3*r_s for the sun.

Let's investigate this coincidence further, by looking at the ratio of your constant to 3r_s.

vR/c * (c^2/6GM) = c/6G * vR/M =

c/6G *wR^2/M

Now, if any of our intrepid astrophysicists can shed some light on this ratio of wR^2/M for stars, there might be some physics in this coincidence. Otherwise, it's just a coincidence for our sun.

Note that GR predicts this for any mass, rotation has nothing to do with GR's corrections. The above comes from the straight Schwarzchild metric. Now, frame dragging for a rotating mass would add some very small additional terms.

-Richard