A simple bound for the variation at closest approach of a small body and star due to general relativity

Abstract

As a comet, asteroid or planet approaches its parent star, the orbit changes shape due to the curvature of spacetime. For comets in particular, the deviation at the pericentre may noticeably change their ephemerides and affect the dynamics of outgassing, tidal disruption or other processes which act on orbital timescales and are assumed to follow Newtonian gravity. By obtaining and analysing the unaveraged equations of motion in orbital elements due to the dominant post-Newtonian contribution (1PN), I derive a simple analytic expression for the maximum deviation in terms of only the stellar mass and eccentricity of the orbit. This relation can be used to assess the potential importance of including short-period relativistic terms in models containing comets, asteroids or planets, and help determine the level of precision needed in numerical integrations. The magnitude of the deviation in systems with Solar-like stars is typically comparable to the size of comet nuclei, and the direction of the deviation is determined by the eccentricity. I show that for eccentricities above a critical value of approximately 0.359, the direction is away from the star.

arXiv commentAccepted for publication in MNRAS Letters

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• Sublimation-induced orbital perturbations of extrasolar active asteroids and comets: application to white dwarf systems
• Tidal circularization of gaseous planets orbiting white dwarfs
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• White Dwarfs with Infrared Excess from LAMOST Data Release 5
• The white dwarf planet WD J0914+1914 b: barricading potential rocky pollutants?
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• Planetesimals drifting through dusty and gaseous white dwarf debris discs: Types I, II and III-like migration
• Disruption of exo-asteroids around white dwarfs and the release of dust particles in debris rings in co-orbital motion