The dynamical environment in the vicinity of small irregularly-shaped bodies with application to asteroids

Loic P.R Chappaz, Purdue University

Abstract

The study of the dynamical environment in the vicinity of a nonspherical body requires the development of adaptable models to accurately describe the irregularities of the body in terms of the gravitational potential. The most basic concept to construct the gravity force environment that governs the relative motion of two arbitrary bodies is Newton's universal law of gravitation. However, rather than modeling a body as a point mass, a distributed mass model is essential. Two different approaches, one based on gravity expansions, that is, spherical harmonics, and an alternative geometric model of the body, that is, a polyhedron model, are frequently employed to evaluate the gravitational potential for an irregularly-shaped body. Within this context, a simple model that incorporates spherical harmonics up to the second degree and order is employed as a first approximation for the dynamical behavior of a particle within the vicinity of an arbitrary body. Targeting schemes based upon differential corrections techniques are constructed to compute planar families of periodic orbits for sample bodies, with both retrograde and direct orbits. Examination of bifurcations within these families allows the numerical determination of spatial resonant periodic orbits. Exploiting information concerning the dynamical environment acquired from the families that are quickly generated using the second degree and order gravity model, similar families are then computed with the more detailed polyhedron model. The tools available to construct a wide variety of orbits in the vicinity of an irregularly-shaped body, also allow further exploration of the dynamical environment and serve as a basis for trajectory design.

Degree

M.S.

Advisors

Howell, Purdue University.

Subject Area

Aerospace engineering|Astrophysics

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