# Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity

## Abstract

**:**

## 1. Introduction

## 2. The Torsion and Contortion Tensors in Riemann–Cartan Spacetime

## 3. Parametrization of Torsion in Spherically-Symmetric and Axisymmetric Spacetimes

## 4. Autoparallel Trajectories and Perturbation Theory

## 5. Results

**Table 1.**Corrections to the secular node precessions as obtained in the INPOP10a ephemeris and predictions of the torsion gravity model discussed in this paper in milliarcseconds per century.

Planet | $\Delta \dot{\Omega}$ (INPOP10a) | $\Delta \dot{\Omega}$(Torsion Gravity) |
---|---|---|

Mercury | $1.4\pm 1.8$ | 0.30 |

Venus | $0.2\pm 1.5$ | $2.14\times {10}^{-2}$ |

Earth | $0.0\pm 0.9$ | $-1.70\times {10}^{-4}$ |

Mars | $-0.05\pm 0.13$ | $2.62\times {10}^{-3}$ |

Jupiter | $-40\pm 42$ | $1.51\times {10}^{-5}$ |

Saturn | $-0.1\pm 0.4$ | $1.31\times {10}^{-5}$ |

**Table 2.**Corrections to the secular perihelion precessions as obtained in the INPOP10a and EPM2011ephemerides and predictions of the torsion gravity model discussed in this paper in milliarcseconds per century.

Planet | $\Delta \dot{\omega}$ (INPOP10a) | $\Delta \dot{\omega}$ (EPM2011) | $\Delta \dot{\omega}$ (Torsion Gravity) |
---|---|---|---|

Mercury | $0.4\pm 0.6$ | $-2.0\pm 3.0$ | −0.622 |

Venus | $0.2\pm 1.5$ | $2.6\pm 1.6$ | $-4.28\times {10}^{-3}$ |

Earth | $-0.2\pm 0.9$ | $0.19\pm 0.19$ | $-1.03\times {10}^{-4}$ |

Mars | $-0.04\pm 0.15$ | $-0.02\pm 0.037$ | $-4.9\times {10}^{-3}$ |

Jupiter | $-41\pm 42$ | $58.7\pm 28.3$ | $-3.48\times {10}^{-5}$ |

Saturn | $0.15\pm 0.65$ | $-0.32\pm 0.47$ | $-2.69\times {10}^{-5}$ |

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix: Relation among the Sun’s System of Reference and the Orbital Coordinates

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Acedo, L.
Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity. *Universe* **2015**, *1*, 422-445.
https://doi.org/10.3390/universe1030422

**AMA Style**

Acedo L.
Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity. *Universe*. 2015; 1(3):422-445.
https://doi.org/10.3390/universe1030422

**Chicago/Turabian Style**

Acedo, Luis.
2015. "Autoparallel vs. Geodesic Trajectories in a Model of Torsion Gravity" *Universe* 1, no. 3: 422-445.
https://doi.org/10.3390/universe1030422