What is the observed precession of Mercury?

[D H]

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?

 

[utesfan100]

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.

 

[utesfan100]

I found this article, showing that the upcoming BepiColumbo mission aims to very accurately measure the orbital elements of Mercury which, when combined with observations of other planets to reduce the uncertainty of the effect of the gravitational tugs, will allow for improved estimates of γ and β, able to test the Lense-Thirring effect.

http://www.aanda.org/index.php?opti...l=/articles/aa/ref/2005/07/aa1646/aa1646.html

It would seem this test of GR is not as irrelevant as the previous discussion indicated, but we will have to wait until 2020 for this test to again become relevant relative to present methods for determining the PPN parameters. (Though shouldn't this data be attainable from Messanger?)

 

[utesfan100]

Thank you, everyone, for your help. I now understand the answers to questions I was wanting to ask, but did not even know the right terms to ask about.

I found the article below greatly helped in outlining the calculation of the precession for the PPN parameters γ and β.

http://www.math.washington.edu/~morrow/papers/Genrel.pdf

In particular, the metric does not need to be solved for because we already have the parametrized estimate. Further, the integral can be simplified by using the u=1/r substitution and finding the change in ω for the ellipse (like almost every other treatment of the Kepler problem does.)

My previous objection that this equation based on the PPN parameters depends on the theory is valid, but only if the theory adds terms to the Lagrangian to model something like gravitons carrying part of the field. For PPN this is not the case.