Solar oblateness and Mercury's perihelion precession

The Keplerian laws of planetary motion are solutions of the two-body gravitational problem. Solar oblateness resulting from the rotation of the Sun distorts the gravitational force acting on a planet and disturbs its Keplerian motion. An analytic solution of a planetary orbit disturbed by the solar gravitational oblateness is derived. In addition to short- and long-periodic disturbances there are secular disturbances, which lead to a perihelion precession and a nodal regression as well as to a mean-motion advance. The magnitude of the short-periodic perihelion precession could disturb observations of the secular effect if the survey is shorter then one Julian year. Transformation of formulae from the solar equatorial plane to the ecliptic plane is discussed. Numerical estimates of the secular perihelion precessions of Mercury, Venus and Mars are in good agreement with published results, confirming our theory. Inversely, the solar oblateness could be determined through observation of the perihelion precession of a planet. The solution is also valid for satellite orbits in the solar gravitational field.