• Corpus ID: 119289003

# Kepler's Orbits and Special Relativity in Introductory Classical Mechanics

@article{Lemmon2010KeplersOA,
title={Kepler's Orbits and Special Relativity in Introductory Classical Mechanics},
author={Tyler J. Lemmon and Antonio R. Mondragon},
journal={arXiv: Earth and Planetary Astrophysics},
year={2010}
}
• Published 24 December 2010
• Physics, Geology
• arXiv: Earth and Planetary Astrophysics
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic momentum of Special Relativity and Newtonian gravity. The corresponding equations of motion are solved in a Keplerian limit, resulting in an approximate relativistic orbit equation that has the same form as that derived from General Relativity in the same limit…
6 Citations

## Figures from this paper

per revolution, where G is Newton’s gravitational constant, M is the (rest) mass of the Sun, the orbit has semimajor axis a and eccentricity , c is the speed of light in vacuum, and T 2 = 4πa/GM
• Y. Kubo
• Physics, Geology
Astronomische Nachrichten
• 2022
It is attemptedto derivethe generalrelativistic (GR) equationof motion for planet and its solution solely by the special relativity (SR) techniques. The motion of a planet relative to the sun and
• Physics
Physica Scripta
• 2022
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a massive body. Then,
• Y. Kubo
• Physics, Education
General Relativity and Gravitation
• 2019
By comparing the special relativistic motion of a planet with respect to the sun and that of the sun to the planet, it is concluded that the spatial and time scales in the spacetime under the
• Physics
European Journal of Physics
• 2018
As a continuation of previous papers emphasizing the interest of historical issues for the present teaching of mechanics (Kepler’s equant model, Newton’s derivation of planetary motions, Lorentz’s
• Physics
• 2015
Let $r(\varphi)$ denote the orbit of Mercury. We compare the formulae obtained via general relativity for $r(\varphi)$ and for the corresponding perihelion precession angle $\Delta \varphi$, with the