Nonrelativistic contribution to Mercury’s perihelion precession

Abstract

We present here a calculation of the precession of the perihelion of Mercury due to the perturbations from the outer planets. The time-average effect of each planet is calculated by replacing that planet with a ring of linear mass density equal to the mass of the planet divided by the circumference of its orbit. The calculation is easier than examples found in many undergraduate theoretical mechanics books and yields results which are in excellent agreement with more advanced treatments. The perihelion precession is seen to result from the fact that the outer planets slightly change the radial period of oscillation from the simple harmonic period usually calculated for small displacements from equilibrium. This new radial period therefore no longer matches the orbital period and the orbit consequently does not exactly retrace itself. The general question of whether a given perturbation will cause the perihelion to advance or regress is shown to have the following answer: if a perturbing force is central and repulsive and also becomes stronger as the distance from the force center increases, the perihelion will advance. If the central perturbing force is attractive and also becomes stronger as the distance from the force center increases, the perihelion will regress.

Avanço do Periélio de Mercúrio – O Primeiro Sucesso da Teoria da Relatividade Geral de Einstein

“…No âmbito da mecânica clássica de Newton é possível, precisamente, modelar a força gravitacional que cada planeta deveria exercer sobre Mercúrio. Uma aproximação que considero bastante elegante, e acessível, foi publicada em 1979 (PRICE; RUSH, 1979). Os autores substituíram cada um dos planetas externos a Mercúrio por "anéis de massa" , cada um caracterizado por sua respectiva densidade linear de massa uniforme.…”

A Constructive Model of Newtonian Gravitation

“…At r>q 12 , mass fields are predominant. From (5), (6), and (7), gravitational force between objects O 1 and O 2 is: 1…”

“…An observer measures Mercury's orbital precession rate to be 5600 arc-secs/century. After filtering out the observer-planet relative motions, a 575 arc-secs/century is left over, which has been accounted for: 1) Price and Rush [7] show that the cumulative Newtonian gravity of planets Venus through Saturn contributes about 532 arc-secs/century. Each planet is replaced by a ring of uniform linear mass density to get a fairly accurate time-averaged effect of the moving planets.…”

The Saros cycle: obtaining eclipse periodicity from Newton's laws

“…Equation (18) implies (assuming that we have the correct sign in the bracket) an oscillation with period…”

“…The draconic month is obtained in section 3. following the techniques used in [17] for calculating the precession of the equinoxes. In section 4. we obtain the anomalistic month with tools developed for calculating the nonrelativistic contribution of the outer planets to Mercury's perihelion precession [18]. To the best of our knowledge, our procedure is the first direct calculation of the components of the Saros cycle using Newton's laws.…”