Local Representation of the Geopotential by Weighted Orthonormal Polynomials

Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies

“…Interpolation-based methods, as developed in Junkins [8] and Engels and Junkins [9], compute gravitational forces by differentiating a polynomial fit of the geopotential in a (small) region of space. With their approach, accurate gravity models around spherical bodies can be represented with relatively low-degree polynomials, and force evaluations are reduced to efficient polynomial evaluations.…”

“…Given the nearly ellipsoidal shape of the Earth, [8,9] divide space with a regular grid in ellipsoidal coordinates. Orthogonal polynomials are used as an interpolation basis for the interpolation of the geopotential.…”

“…This section briefly reviews key features of two gravitational force representations that are relevant to this research: the polyhedral method developed by Werner [5] and Werner and Scheeres [4] and the interpolation method proposed by Junkins [8] and Engels and Junkins [9].…”

“…The idea of locally representing gravitational fields using interpolation has already been investigated by Junkins [8] and Engels and Junkins [9] in the context of inertial navigation around Earth. These methods, however, rely on the nearly spherical shape of the Earth, and do not transfer directly to the case of arbitrarily shaped bodies.…”

“…Before presenting these results, we review two computational models relevant to the formulation of our method: the polyhedral method of Werner and Scheeres [4] and the interpolation method of Engels and Junkins [9]. In Sec.…”