Sedna and the cloud of comets surrounding the Solar System in Milgromian dynamics

Abstract

We reconsider the hypothesis of a vast cometary reservoir surrounding the Solar System - the Oort cloud of comets - within the framework of Milgromian Dynamics (MD or MOND). For this purpose we built a numerical model of the cloud assuming QUMOND, a modified gravity theory of MD. In the modified gravity versions of MD, the internal dynamics of a system is influenced by the external gravitational field in which the system is embedded, even when this external field is constant and uniform, a phenomenon dubbed the external field effect (EFE). Adopting the popular pair $\nu (x)=[1-\exp (-x^{1/2}){]}^{-1}$ for the MD interpolating function and $a_0=1.2\times 10^{-10}$ m s${}^{-2}$ for the MD acceleration scale, we found that the observationally inferred Milgromian cloud of comets is much more radially compact than its Newtonian counterpart. The comets of the Milgromian cloud stay away from the zone where the Galactic tide can torque their orbits significantly. However, this does not need to be an obstacle for the injection of the comets into the inner solar system as the EFE can induce significant change in perihelion distance during one revolution of a comet around the Sun. Adopting constraints on different interpolating function families and a revised value of $a_0$ (provided recently by the Cassini spacecraft), the aforementioned qualitative results no longer hold, and, in conclusion, the Milgromian cloud is very similar to the Newtonian in its overall size, binding energies of comets and hence the operation of the Jupiter-Saturn barrier. However, EFE torquing of perihelia still play a significant role in the inner parts of the cloud. Consequently Sedna-like orbits and orbits of large semi-major axis Centaurs are easily comprehensible in MD. In MD, they both belong to the same population, just in different modes of their evolution.

19 pages, 1 table, 21 figures; v3 - minor corrections, typos

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