Determinations of asteroid masses using mutual encounters observed in the Legacy Survey of Space and Time

Using published simulations of the 10-year Legacy Survey of Space and Time (LSST), we forecast its ability to determine the masses of individual main-belt asteroids (MBAs) through precise astrometry of any pairs of the ~1.2 million known MBAs undergoing close gravitational encounters during the survey. The uncertainty $\sigma_I$ on the impulse applied to a tracer asteroid by its deflector is derived from the Fisher matrix of the tracer's astrometric data, including an azimuthal acceleration $A_2$ from the Yarkovsky effect as a free parameter for each tracer. If only LSST observations are available, $\sigma_I \approx7\times10^{-6}\,{\rm m}\,{\rm s}^{-1}$ for MBAs at apparent magnitude $m_V<19.5,$ degrading ~10x for $m_V=23.$ These tracers yield a median uncertainty on the mass of an MBA of $\approx4\times10^{-14}M_\odot,$ with a wide range of variation depending on the ``luck'' of close encounters. Roughly 125 MBAs obtain mass measures with S/N>5. If pre-LSST astrometry yields a strong constraint on the state vector of the tracer MBA at the start of LSST, then these values improve to median $\sigma_M\approx1.3\times10^{-14}M_\odot$ and 310 MBAs at S/N>5, with >1/2 of these having S/N>10. These yields would be a ~10-fold increase in the number of known asteroid masses, including a nearly complete knowledge of MBAs with H<7.5. If pre-LSST data are sufficient to start constraining the Yarkovsky effect, another factor $\sim1.5$ can be gained. Tables of the measurable deflector MBAs and their tracers are provided.