# Modified Newtonian Gravity, Wide Binaries and the Tully-Fisher Relation

## Abstract

**:**

## 1. Introduction

^{2}[15]. Tight constraints have been, experimentally, imposed on the cross-sections for their weak interactions with nucleons [16,17]. In the DAMA/LIBRA experiment, an annual modulation was detected that was considered to arise from the interaction of DM particles in the Galactic halo with the detector mass as the velocity of the Earth varies along its orbit. However, this modulation has been fitted using conventional interactions with muons and neutrinos [18]. Moreover, other experiments have not been able to reproduce the results of DAMA/LIBRA after adequate corrections for surface effects and the expected background [19,20].

^{2}making them a form of “warm dark matter” (WDM). This term implies that the particles presently move at velocities similar to that of stars and gas clouds within galaxies. On the other hand, their spectra can be very different from a Maxwellian distribution [36]. Sterile neutrinos might be a way to overcome the cuspy-halo problem [35].

^{2}sterile neutrino. This interpretation is—surely—too hasty and premature. Gu et al. [43] suggested a conventional mechanism in atomic physics (charge exchange with bare sulfur ions) that can explain the generation of this particular line. Other authors have found no evidence of such a line in stacked galaxy spectra [44] or from our own Galaxy, which should be emitting such X-rays from all directions of the Galactic halo [45].

## 2. Modified Newtonian Gravity

## 3. Wide Binaries and the Tully-Fisher Relation

#### 3.1. The Tully-Fisher Relation

#### 3.2. Radial Velocity Perturbations of Proxima Centauri

## 4. Modified Newtonian Gravity and the Anomalous Perihelion Precessions in the Solar System

## 5. Discussion

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Scaled extra scalar potential for a point source (solid line) vs. the approximation in Equation (13) (dashed line).

**Figure 2.**Observations of Hernández et al. [72] for the relative velocity of two binary stars of mass equal to that of the Sun at separations ranging from $0.07$ pc to 4 pc. The estimated relative velocities are shown as open circles, with uncertainty corresponding to the shaded area. Predictions of Newtonian theory are given by the lower dashed line. The dotted line is the MOND prediction and the solid line is the prediction of the MNG as discussed in this paper for $\kappa =3.109$ and $\beta =8737$ AU. Notice the similarity of the predictions of MNG with MOND without the external field effect as discussed by Banik and Zhao [80]. This could falsify the MNG model in light of the data release 2, as discussed by Pittordis and Sutherland [81].

**Figure 3.**Perturbation in the radial velocity of Proxima Centauri as a consequence of the extra forces of MNG model as a function of time.

**Table 1.**Orbital parameters for the osculating keplerian orbit of Proxima Centauri at present as given by Kervella et al. [88]. The angles are written in sexagesimal degrees.

Parameter | Value and Units | Plus Error | Minus Error |
---|---|---|---|

a Semi-major axis | 8700 AU | $+700$ AU | $-400$ AU |

e Orbital eccentricity | $0.5$ | $+0.08$ | $-0.09$ |

P Period | $547,000$ years | $+66,000$ years | $-40,000$ years |

${T}_{0}$ Epoch of periastron | $283,000$ years | $59,000$ years | $-41,000$ years |

I Orbital inclination | ${107.6}^{\circ}$ | $+{1.8}^{\circ}$ | $-{2.0}^{\circ}$ |

$\Omega $ Longitude asc. node | ${126}^{\circ}$ | $+{5}^{\circ}$ | $-{5}^{\circ}$ |

$\omega $ Argument of periastron | ${72.3}^{\circ}$ | ${8.7}^{\circ}$ | ${6.6}^{\circ}$ |

$RV$ Radial velocity | $-21.7$ km/s | $+0.027$ km/s | $-0.027$ km/s |

**Table 2.**Prediction of the MNG model and MOND for the extra anomalous advance of the perihelion of the planets in comparison with the observations in the EPM2008 and EPM2011 ephemerides. In the case of EPM2017 only the formal uncertainties are given as deduced by Iorio [98].

Planet | MNG (mas cy${}^{-1}$) | MOND | EPM2008 | EPM2011 | EPM2017 |
---|---|---|---|---|---|

Mercury | $-0.034$ | $0.02$ | $-3.6\pm 5.0$ | $-2\pm 3$ | $0.008$ |

Mars | $-0.271$ | $-0.09$ | $0.1\pm 0.5$ | $-0.02\pm 0.037$ | $0.003$ |

Jupiter | $-1.713$ | $-0.65$ | − | $58.7\pm 28.3$ | $33.9$ |

Saturn | $-4.307$ | $3.12$ | $-6\pm 2$ | $-0.32\pm 0.47$ | $0.067$ |

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Acedo, L.
Modified Newtonian Gravity, Wide Binaries and the Tully-Fisher Relation. *Universe* **2020**, *6*, 209.
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Modified Newtonian Gravity, Wide Binaries and the Tully-Fisher Relation. *Universe*. 2020; 6(11):209.
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