Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of the Generalized Law of Universal Gravitation with Allowance for the Ellipticity of Planet Orbits

Abstract

The precession of the perihelion of Mercury’s orbit is simulated numerically within the framework of the generalized law of universal gravitation in the field of the Sun and planets taking into account the ellipticity of the planet orbits and new data on the flattening, the mass of the Sun, and the gravitational constant. Calculations were carried out with increased accuracy (up to 19–20 decimal places) and iteration steps of 0.00005 s and 0.0001 s starting from the asteroid belt. It has been shown that the average precession of the perihelion of Mercury’s orbit in 100 years calculated within the framework of the generalized law of universal gravitation and averaged over long time periods from several hundred years to several thousand years taking into account the ellipticity of planet orbits is ~554.2”. This is less than the observed shift of the perihelion of Mercury’s orbit by ~19.9”. As is well known, the observed shift is ~574.1”. That is, the question on the adequacy of the generalized law of universal gravitation to the observances still remains open. However, it is possible that an object of small size (or several such objects) may be located inside Mercury’s orbit, and one more object, whose mass should not exceed at least ~0.2 of the Earth mass may be located at the diametrically opposite point of the Earth orbit behind the Sun. The results obtained are valid to within 1–2 decimal places.