# Perihelion precession from power law central force and magnetic-like force

## Abstract

By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury's 43''/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.

- Authors:

- Department of Physics, Nanjing University, 22 Hankou Road, Nanjing, 210093 (China)

- Publication Date:

- OSTI Identifier:
- 21541474

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.83.084008; (c) 2011 American Institute of Physics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTURBANCES; EXPANSION; NONLUMINOUS MATTER; ORBITS; PERTURBATION THEORY; PRECESSION; SCHWARZSCHILD METRIC; MATTER; METRICS

### Citation Formats

```
Xu Feng.
```*Perihelion precession from power law central force and magnetic-like force*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVD.83.084008.

```
Xu Feng.
```*Perihelion precession from power law central force and magnetic-like force*. United States. doi:10.1103/PHYSREVD.83.084008.

```
Xu Feng. Fri .
"Perihelion precession from power law central force and magnetic-like force". United States. doi:10.1103/PHYSREVD.83.084008.
```

```
@article{osti_21541474,
```

title = {Perihelion precession from power law central force and magnetic-like force},

author = {Xu Feng},

abstractNote = {By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury's 43''/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.},

doi = {10.1103/PHYSREVD.83.084008},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 83,

place = {United States},

year = {Fri Apr 15 00:00:00 EDT 2011},

month = {Fri Apr 15 00:00:00 EDT 2011}

}