Precession of the perihelion of Mercury’s orbit

The precession of the perihelion of Mercury’s orbit is calculated using the Laplace–Runge–Lenz vector. An approximate calculation that assumes the orbits of the perturbing planets are circular and coplanar with Mercury’s orbit is within 4.4% of the correct value. A complete calculation that uses the correct elliptical orbit and orientation for each of the perturbing planets is then presented. The precession due to a perturbing planet is proportional to the mass of the planet and is approximately inversely proportional to the cube of its semimajor axis.