D H said:
That's much closer, but it still isn't valid. That precession due to the other planets was calculated in a rotating frame in which those other planets are following orbits that deviate from Keplerian due to the frame rotation.
What, exactly, are you trying to accomplish, and why?
The value I calculated above is the observed value. The planets contribute 531.63±0.69 and GR 42.98±0.04.
Thus the remainder after these contributions are 0.48±0.94.
My goal is to determine the error in this measurement (whose meaning has been greatly clarified, thank you). Explaining my actual motivation would violate the rules of the forum :)
Instead, I will suggest that the observed precession of Mercury question has been answered and shift my focus towards understanding the PPN formalism. My basic question is now ho I get from the Schwarzschild metric to the PPN formula for the per orbit advance of \frac{2\pi m}{p}\left(2+2\gamma-\beta\right)?
Ok. That is more than is reasonable to expect an answer to here, but being able to do this is something I want to be able to do; and thus to be able to address my actual motives on my own.
My focus is on understanding the Eddington–Robertson–Schiff parameters. I have found where these are described as
ds^2=\left(1-2\frac{M}{r}+2\beta\frac{M^2}{r^2}\right) dt^2-\left(1+2\gamma\frac{M}{r}\right)(dx^2+dy^2+dz^2)
from which it is straightforward to calculate β and γ using the isotropic formulation of the metric. It is clear now that β is what I was referring to earlier as a second order effect. Am I reading this right, that Newtonian gravity about a point mass can be expressed (relative to the escape velocity [STRIKE]reference frame[/STRIKE] coordinate chart) by the metric:
ds^2=\left(1-2\frac{M}{r}\right) dt^2-(dx^2+dy^2+dz^2)
It seems like β might be 2 based on the precession formula above. Either way, that would be awesome insight!
Perhaps this new PPN formalism inquiry should be moved to a thread of its own.