The size of 3I/ATLAS from non-gravitational acceleration

Abstract

The third macroscopic interstellar object detected in the solar system recently passed through perihelion, with the best-fitting models of its trajectory now featuring non-gravitational accelerations. We assess how much mass loss is required to produce plausible non-gravitational acceleration solutions and compare with estimates of the mass loss. We find that they are consistent when the nucleus of 3I/ATLAS is around 1 km in diameter. For a recent solution with a time lag in the acceleration from Eubanks et al, we find diameters between 820 meters and 1050 meters, assuming an outgassing asymmetry factor $ζ=0.5$ and a density of the comet nucleus $ρ=0.5$ g cm$^{-3}$. The limits on the diameter scale as $(ζ/ρ)^{1/3}$. Substantial extrapolation is required in general to compare non-gravitational accelerations to mass loss rates, so reliable estimates of the mass loss rate at other stages of the comet's trajectory will substantially reduce the systematic uncertainty in this estimate.