Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics

Abstract

Milgromian dynamics (MD or MOND) uniquely predicts motion in a galaxy from the distribution of its stars and gas in a remarkable agreement with observations so far. In the solar system, MD predicts the existence of some possibly non-negligible dynamical effects, which can be used to constrain the freedom in MD theories. Known extreme trans-Neptunian objects (ETNOs) have their argument of perihelion, longitude of ascending node, and inclination distributed in highly non-uniform fashion; ETNOs are bodies with perihelion distances greater than the orbit of Neptune and with semimajor axes greater than 150 au and less than $\sim1500$ au. It is as if these bodies have been systematically perturbed by some external force. We investigated a hypothesis that the puzzling orbital characteristics of ETNOs are a consequence of MD. We set up a dynamical model of the solar system incorporating the external field effect (EFE), which is anticipated to be the dominant effect of MD in the ETNOs region. We used constraints available on the strength of EFE coming from radio tracking of the Cassini spacecraft. We performed several numerical experiments, concentrating on the long-term orbital evolution of primordial (randomised) ETNOs in MD. The EFE could produce distinct non-uniform distributions of the orbital elements of ETNOs that are related to the orientation of an orbit in space. If we demand that EFE is solely responsible for the detachment of Sedna and 2012 VP$_{113}$, then these distributions are at odds with the currently observed statistics on ETNOs unless the EFE quadrupole strength parameter $Q_{2}$ has values that are unlikely (with probability < 1$\%$) in light of the Cassini data.