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As described in Section 5.5, the ability of general relativity to explain the discrepancy
between the observed perihelion precession rate of Mercury, and that calculated from Newtonian mechanics,
was one of the first major successful tests of this theory. However, given that the Newtonian precession rate is
about ten times larger than the general relativistic correction, it is necessary to calculate the Newtonian rate to great accuracy
in order for this particular test to be convincing. In this Appendix, we perform such a calculation, adapting the method
outlined by Stewart (Stewart 2005).
Let
and
be the position vectors of Mercury and some other planet in the solar system, respectively, relative to the Sun.
Furthermore, let
,
, and
be the masses of Mercury, the other planet, and the Sun, respectively.
According to the analysis of Section 10.2, the vector
evolves in time according to

(B.1) 
where
. Here, the disturbing function due to the
other planet takes the form

(B.2) 
where
.
Next: Time evolution of eccentricity
Up: Perihelion precession of Mercury
Previous: Perihelion precession of Mercury
Richard Fitzpatrick
20160331