Optical Gravimetry mass measurement performance for small body flyby missions

It is challenging or infeasible to precisely measure the mass of small asteroids using the state-of-the-art without a dedicated spacecraft rendezvous mission, which are typically limited to one or a few asteroid targets. Alternatively, spacecraft flyby missions offer the possibility of visiting multiple asteroids but typically lack the sensitivity to measure mass for all but the largest asteroids. In these encounters, Earth-based two-way Doppler is used to measure a change in the spacecraft's velocity imparted by the asteroid. The technique known as Optical Gravimetry (OpGrav) seeks to increase this sensitivity of mass measurements from flyby encounters using optical measurements from the spacecraft to one or more test-masses. In this technique, the spacecraft deploys the testmasses prior to an asteroid flyby and then tracks them before and after the encounter using an on-board telescope. The test-masses can pass much closer to the asteroid than a spacecraft would typically choose such that their trajectories are measurably deflected. This paper provides a quantitative sensitivity analysis of the design parameters most relevant to OpGrav, including asteroid mass, flyby velocity, number of test-masses, test-mass target altitude, test-mass deployment time, and the cadence of optical measurements. Additionally, this paper investigates the effect of practical test-mass deployment errors on the expected mass measurement. Broadly speaking, this analysis shows that OpGrav provides comparable sensitivity to the existing technique at asteroids that are five to ten times smaller in diameter, depending on whether one or three test-masses are deployed. We demonstrate that under realistic mission assumptions, the use of OpGrav would have allowed all previous flyby visits of asteroids, most of which were not able to obtain mass estimates, to achieve better than 25% 1 sigma accuracy in mass measurements, representing a significant improvement on the state of the art.