Abstract
A recent study of a sample of wide binary star systems from the Hipparcos and Gaia catalogues has found clear evidence of a gravitational anomaly of the same kind as that appearing in galaxies and galactic clusters. Instead of a relative orbital velocity decaying as the square root of the separation, ΔV∝r−1/2, it was shown that an asymptotic constant velocity is reached for distances of order 0.1 pc. If confirmed, it would be difficult to accommodate this breakdown of Kepler’s laws within the current dark matter (DM) paradigm because DM does not aggregate in small scales, so there would be very little DM in a 0.1 pc sphere. In this paper, we propose a simple non-Newtonian model of gravity that could explain both the wide binaries anomaly and the anomalous rotation curves of galaxies as codified by the Tully-Fisher relation. The required extra potential can be understood as a Klein-Gordon field with a position-dependent mass parameter. The extra forces behave as 1/r on parsec scales and r on Solar system scales. We show that retrograde anomalous perihelion precessions are predicted for the planets. This could be tested by precision ephemerides in the near future.
Highlights
In the 1930s, the astronomer Fritz Zwicky conducted pioneering work in which he examined the validity of the virial theorem for the Coma galaxy cluster, unveiling a surprising anomaly.Zwicky discovered that galaxies within the cluster move much faster than predicted by the gravitational attraction of the observed luminous matter [1]
The objective of this paper is to propose a modified Newtonian model that accounts for the flat rotation curves both for the scale of wide binary stars and galaxies
Most researchers adhere to Zwicky’s initial hunch that the failure of the virial theorem in clusters was caused by a large mass of dark matter that was not taken into account in the calculations
Summary
Zwicky discovered that galaxies within the cluster move much faster than predicted by the gravitational attraction of the observed luminous matter [1]. Famous for his bold proposals, he interpreted this observation as the consequence of a vast amount of matter that cannot be directly observed in the cluster. In 1936, Smith replicated Zwicky’s work to estimate the mass of the Virgo cluster. He concluded that a great mass of intergalactic material should be present within the cluster [2]
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