# Eccentricity & GR precession; Mercury vs. GPB

1. Nov 21, 2008

### RandallB

Eccentricity & GR precession; Mercury vs. GP-B

How big a factor is the Eccentricity of Mercury orbit in contributing to its precession?

GR precession has been confirmed in the Gravity Probe B orbit even though it has an eccentricity of zero. The GP-B used a gyroscope to take the place of a detectable aphelion, while Earth has a nearly circular orbit with an eccentricity of 0.016 it gives measurable aphelion that allow modern observations the ability to see the small precession undetectably to 19 century astronomers.

Is it the large orbit eccentricity of 0.205 that gives Mercury such a large and easier to notice precession of 43 ArcSec/century?
I assume by moving up and down between different levels of GR curved space the effect on precession is magnified.

Does anyone have a reference to show or explain what how or what part of the GR formulas account for the eccentricity contribution?

If Mercury orbit was a more circular eccentricity of 0.01 what would the precession be?

If eccentricity is doubled to 0.41 is there some function to describe how much the precession would increase?

Last edited: Nov 21, 2008
2. Nov 21, 2008

### Jonathan Scott

Re: Eccentricity & GR precession; Mercury vs. GP-B

As far as I know (backed up by a quick look at Rindler "Essential Relativity"):

For a given orbital angular momentum, GR precession is not affected by the eccentricity. However, if you consider alternative orbits with varying eccentricity which have fixed semi-major-axis a instead of a fixed angular momentum, the precession is proportional to 1/a(1-e2).

The general (approximate) expression for the precession angle per orbit is:

6 pi (Gm/c^2)/(a(1-e2)).

(I tried to show the general expression in TeX but that seems to be broken at the moment, in that preview processing showed something completely different).

3. Nov 22, 2008

### JANm

Re: Eccentricity & GR precession; Mercury vs. GP-B

Thought there was a pi^3 in the precession angle formula; or is that the relativistic correction to this...