# 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} }

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

### Special Relativity and the Precession of the Perihelion

- Physics, Education
- 2022

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…

### Attempt to obtain the general relativistic planet's motion by special relativity techniques

- Physics, GeologyAstronomische 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…

### Bound states of central force system in special relativity

- PhysicsPhysica 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,…

### Structure of the spacetime under gravitation obtained by purely dynamical method

- Physics, EducationGeneral 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…

### Lorentz’s 1895 transformations, Einstein’s equivalence principle and the perihelion shift of Mercury

- PhysicsEuropean 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…

### Analytical computation of the Mercury perihelion precession via the relativistic gravitational law and comparison with general relativity

- 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…