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.
Skip Nav Destination
Article navigation
June 1979
Papers|
June 01 1979
Nonrelativistic contribution to Mercury’s perihelion precession
Michael P. Price;
Michael P. Price
Ritter Astrophysical Research Center, The University of Toledo, Toledo, Ohio 43606
Search for other works by this author on:
William F. Rush
William F. Rush
Ritter Astrophysical Research Center, The University of Toledo, Toledo, Ohio 43606
Search for other works by this author on:
Am. J. Phys. 47, 531–534 (1979)
Citation
Michael P. Price, William F. Rush; Nonrelativistic contribution to Mercury’s perihelion precession. Am. J. Phys. 1 June 1979; 47 (6): 531–534. https://doi.org/10.1119/1.11779
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Ergodic Lagrangian dynamics in a superhero universe
I. L. Tregillis, George R. R. Martin
All objects and some questions
Charles H. Lineweaver, Vihan M. Patel
The most efficient thermodynamic cycle under general engine constraints
Christopher Ong, Shaun Quek
A story with twists and turns: How to control the rotation of the notched stick
Martin Luttmann, Michel Luttmann
The spinorial ball: A macroscopic object of spin-1/2
Samuel Bernard-Bernardet, Emily Dumas, et al.
In this issue: January 2025
Joanna Behrman, Pierre-François Cohadon, et al.
Related Content
Einstein's perihelion formula and its generalization
American Journal of Physics (April 2015)
Advance of perihelion
American Journal of Physics (September 2013)
Elementary theory of perihelion precession
American Journal of Physics (October 1983)
Precession of the perihelion of Mercury
American Journal of Physics (December 1988)
Relativistic And Thermal Effects In The Orbital Dynamics Of Low‐Perihelion Near‐Earth Asteroids
AIP Conference Proceedings (December 2010)