Orbital perturbations due to massive rings

TL;DR

This paper analytically investigates the long-term orbital perturbations caused by a homogeneous circular ring on a test particle, deriving bounds on the ring's mass from planetary perihelion precession data, applicable to natural and artificial matter distributions.

Contribution

It extends previous analyses by considering non-coplanar configurations and applies the results to set upper bounds on ring masses from Solar System observations.

Findings

Derived analytical expressions for orbital perturbations due to rings.

Set upper bounds on ring masses based on perihelion precession data.

Applicable to both baryonic and non-baryonic dark matter distributions.

Abstract

We analytically work out the long-term orbital perturbations induced by a homogeneous circular ring of radius Rr and mass mr on the motion of a test particle in the cases (I): r > R_r and (II): r < R_r. In order to extend the validity of our analysis to the orbital configurations of, e.g., some proposed spacecraftbased mission for fundamental physics like LISA and ASTROD, of possible annuli around the supermassive black hole in Sgr A* coming from tidal disruptions of incoming gas clouds, and to the effect of artificial space debris belts around the Earth, we do not restrict ourselves to the case in which the ring and the orbit of the perturbed particle lie just in the same plane. From the corrections to the standard secular perihelion precessions, recently determined by a team of astronomers for some planets of the Solar System, we infer upper bounds on mr for various putative and known annular matter distributions of natural origin (close circumsolar ring with R_r = 0.02-0.13 au, dust ring with R_r = 1 au, minor asteroids, Trans-Neptunian Objects). We find m_r <= 1.4 10^-4 m_E (circumsolar ring with R_r = 0.02 au), m_r <= 2.6 10^-6 m_E (circumsolar ring with R_r = 0.13 au), m_r <= 8.8 10^-7 m_E (ring with R_r = 1 au), m_r <= 7.3 10^-12 M_S (asteroidal ring with R_r = 2.80 au), m_r <= 1.1 <= 10^-11 M_S (asteroidal ring with R_r = 3.14 au), m_r <= 2.0 10^-8 M_S (TNOs ring with R_r = 43 au). In principle, our analysis is valid both for baryonic and non-baryonic Dark Matter distributions.