Brownian Motion of Main-belt Asteroids on Human Timescales

Abstract High-precision astrometric data on main-belt asteroids (MBAs) enable new inferences on the gravitational and nongravitational forces present in this region. We estimate the typical Brownian motion due to mutual encounters among MBAs that cannot be predicted from the ephemeris of larger bodies and therefore serves as noise on inferences from the MBAs. The rms azimuthal shift σ ϕ of this “Brownian noise” is predicted using the distribution of known MBA orbits, combined with analytical propagation into future positional uncertainties—radial and vertical perturbations are much smaller. At current levels of asteroid-mass knowledge, we estimate that σ ϕ accumulates to 2–9 km, or 1–5 mas over T = 10 yr, increasing as T 3/2 . This must be taken into consideration for proper inferences from Gaia astrometry. Legacy Survey of Space and Time (LSST) data will, however, improve MBA mass knowledge enough to lower this Brownian uncertainty to 260–400 m, or 140–210 μ as, which in many but not all cases could be small enough to ignore in inferences using Gaia or LSST astrometry of MBAs. For full exploitation of Gaia and LSST MBA data, ephemeris models should include the ≈10,000 largest asteroids as active bodies with free masses, even if not all are well constrained. This will correctly propagate the uncertainties in these bodies’ gravity into desired inferences. The rms value of deflections from less massive MBAs is then just σ ϕ ≈ 17–60 m, or 9–40 μ as, depending on the mean mass of the MBAs at fixed absolute magnitude small enough to ignore until occultation-based position data become ubiquitously available for MBAs.