Small-Body Postrendezvous Characterization via Slow Hyperbolic Flybys

DOI: 10.2514/1.53722 The most crucial task for a spacecraft upon arriving at a small body is to determine the strength of the body's gravity field. This research proposes and models this initial characterization via a series of slow flybys and analyzes how rapidly the gravity field can be estimated and the precision to which it can be determined. Two analytical issues areaddressedinthispaperthatarepertinenttothedesignofthischaracterizationprocessandcanbeusedtoevaluate whether thereis aneed for lidarmeasurements. A new operational procedure calledV rangingis proposed, which can eliminate the need for lidar during the initial characterization phase. Following this, the characterization of the gravity field is addressed by performing a covariance analysis around three asteroids: Itokawa, Didymos, and Eros, representing a two-order-of-magnitude difference in size. I. Introduction T HEREisanincreasinginterestinstudyingsmall-bodysystems, such as asteroids and comets, with spacecraft rendezvous missions. On arrival to a small body, one of the most important tasks is for the spacecraft to characterize the body's environment to determine the gravitational parameterand the gravity field of the body. This is the major source of spacecraft perturbation when in proximity to the body, and lack of knowledge of thegravity field can delay the start of the main scientific mission. Thus, it is of interest to carry out this initial characterization of the body in as rapid amanner as is feasible and with minimum risk to the spacecraft. Estimation of thegravitationalparameterandgravitational fieldofabodygenerally uses a least-squares filter, most commonly a batch square-root infor- mation filter (SRIF) due to its numerical stability (1-3), assuming that the deviation from the true dynamics can be approximated within the linear range of the modeled nonlinear dynamics of the spacecraft (4). In addition to the gravity terms, other commonly estimated parameters in the filter are the spacecraft state, body's spin state, and navigationV maneuvers. The estimated parameters can be time-dependent as in spacecraft position and velocity, or time- independent (i.e., global) as in the higher-degree and higher-order gravity field. As will be shown later, a method for carrying out this initial estimation task throughaseriesof relativelyslow flybys ofthe body is proposed. We probe the level of characterization that can occur using this approach, and whether such an approach could eliminate the need for a dedicated orbital phase for some mission types. This topic is studied using both analytic and numerical methods. For definiteness, we assume that the target body is a near- Earth asteroid, with additional details on its size, shape, spin state, and heliocentric orbit given later. This paper consists of an analytical section and a numerical section, bothof whichwill discussthe estimation ofthesmall body's gravitational environment. The results presented here combine two previous conference papers (5,6). The first (analytical) part of the paperanalyzestheeffectivenessofperformingaprecisemaneuverto break the scale invariance in a hyperbolic flyby with optical-only observations. The goal of this analysis is to characterize the need for carrying a laser or radar ranging instrument to sense distance to the asteroid, and replaces this with a concept calledV ranging. A similar concept using optical-based navigation is also discussed by Alonso et al. (7) to estimate the relative position and attitude in the contextofformation flyingandValaseketal.(8)fortheapplicationof autonomous air refueling. Following this, we provideV ranging, which is a derivation of a new method to analytically estimate the precision of the gravitational parameter determination based on the geometry and time of the spacecraft trajectory around an asteroid. Specifically, wederiveanalytical expressionsfor the uncertainty of a small-body gravity field and spacecraft relative trajectory using Doppler tracking and optical navigation. The conventional method derivesby leveraging the property that the inbound and outbound hyperbolicvelocitiesV1 areequalinmagnitudeandseparatedbythe hyperbolic turn angle� . This method rendersas a function ofb1 (impact radius),V1, and change in hyperbolic velocityVflyby. Our new analytical estimate is based on the measured time of flight of a flyby trajectory to derive an expression for� . These two analytical expressionsforarecomparedwiththefullleast-squarescovariance discussedinthesecondpartofthispaperinordertodeterminewhich effect actually controls the full estimation.