# Impact of Lorentz Violation Models on Exoplanets’ Dynamics

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## Abstract

**:**

## 1. Introduction

## 2. Definition of the Perturbing Acceleration

## 3. The Method of Radial Velocity

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | For an unperturbed Keplerian ellipse in the gravitational field of a body with mass M, it is ${n}_{\mathrm{b}}=\sqrt{GM/{a}^{3}}$. |

2 | Notice that all the following results hold for the binary’s relative orbit; the resulting shift for the stellar RV can be straightforwardly obtained by rescaling the final formula by the ratio of the planet’s mass to the sum of the masses of the parent star and of the planet itself. |

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**Table 1.**Estimates for ${\overline{s}}^{\mu \nu}$ for exoplanets with small eccentricity. The parameters to be used in Formulas (30)–(32) can be found at http://exoplanet.eu, accessed on 7 November 2022.

Planet | e | $\left(\right)open="\langle "\; close="\rangle ">\Delta {\mathbf{v}}_{\mathit{z}}$ (m/s) | ${\overline{\mathit{s}}}^{\mathit{\mu}\mathit{\nu}}$ |
---|---|---|---|

SDSS 1604 + 1000 b | 0.04 | 1 0.1 0.01 | ∼${10}^{-5}$ ∼${10}^{-6}$ ∼${10}^{-7}$ |

GJ 367 b | 0 | 1 0.1 0.01 | ∼${10}^{-6}$ ∼${10}^{-7}$ ∼${10}^{-8}$ |

WASP-19 b | 0.0046 | 1 0.1 0.01 | ∼${10}^{-6}$ ∼${10}^{-7}$ ∼${10}^{-8}$ |

Kepler-411 e | 0.016 | 1 0.1 0.01 | ∼${10}^{-5}$ ∼${10}^{-6}$ ∼${10}^{-7}$ |

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Gallerati, A.; Ruggiero, M.L.; Iorio, L.
Impact of Lorentz Violation Models on Exoplanets’ Dynamics. *Universe* **2022**, *8*, 608.
https://doi.org/10.3390/universe8110608

**AMA Style**

Gallerati A, Ruggiero ML, Iorio L.
Impact of Lorentz Violation Models on Exoplanets’ Dynamics. *Universe*. 2022; 8(11):608.
https://doi.org/10.3390/universe8110608

**Chicago/Turabian Style**

Gallerati, Antonio, Matteo Luca Ruggiero, and Lorenzo Iorio.
2022. "Impact of Lorentz Violation Models on Exoplanets’ Dynamics" *Universe* 8, no. 11: 608.
https://doi.org/10.3390/universe8110608