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 test-masses 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% 1σ accuracy in mass measurements, representing a significant improvement on the state of the art.

在没有专门的航天器会合任务的情况下，使用最先进的技术来精确测量小行星的质量是具有挑战性或不可行的，这些任务通常仅限于一个或几个小行星目标。或者，航天器飞越任务提供了访问多个小行星的可能性，但通常缺乏测量除最大小行星以外的所有小行星质量的敏感性。在这些相遇中，地球上的双向多普勒被用来测量小行星引起的航天器速度的变化。被称为光学重力测量 (OpGrav) 的技术旨在通过使用从航天器到一个或多个测试质量的光学测量来提高对飞越遭遇质量测量的这种灵敏度。在这项技术中，航天器在小行星飞越之前部署测试质量，然后使用机载望远镜在小行星遭遇之前和之后跟踪它们。测试质量可以比航天器通常选择的更靠近小行星，这样它们的轨迹就会发生可测量的偏转。本文提供了与 OpGrav 最相关的设计参数的定量灵敏度分析，包括小行星质量、飞越速度、测试质量数量、测试质量目标高度、测试质量部署时间和光学测量的节奏。此外，本文研究了实际测试质量部署误差对预期质量测量的影响。从广义上讲，该分析表明 OpGrav 在直径小五到十倍的小行星上提供了与现有技术相当的灵敏度，取决于是否部署了一个或三个测试质量。我们证明，在现实的任务假设下，使用 OpGrav 将允许所有以前的小行星飞越访问（其中大多数无法获得质量估计）达到超过 25% 1σ质量测量精度，代表对现有技术的显着改进。