The Challenge of Measuring Asteroid Masses with Gaia DR2 Astrometry

The Gaia second data release (DR2) contains high-accuracy astrometric measurements of thousands of solar system bodies. These measurements raise the possibility of determining asteroid masses by modeling scattering events between massive objects observed by Gaia. In this paper, we identify promising encounters between small asteroids that occur during DR2 and quantify the various errors involved in mass determination. We argue that, in the best case, Gaia astrometry can provide constraints as tight as approximate to 1 km on the positions of asteroids. Further, we find that even with general relativistic corrections, integrations of the solar system accumulate 1 km errors after 700 days. While not a problem for modeling DR2 astrometry, future Gaia data releases may require models accounting for additional effects such as gravitational harmonics of the sun and planets. Additionally, due to suboptimal astrometric uncertainty, the geometry of the observations, and the Gaia observing pattern there are much looser constraints as a result in most cases, with constraints being several orders of magnitude weaker in some cases. This suggests that accurate mass determination for the smallest asteroids will require additional observations, either from future Gaia data releases or from other sources. We provide a list of encounters that are most promising for further investigation.