Comparisons of the Cubed-Sphere Gravity Model with the Spherical Harmonics

Abstract

The cubed-sphere gravitational model is a modification of a base model, e.g., the spherical harmonic model, to allow for the fast evaluation of acceleration. The model consists of concentric spheres, each mapped to the surface of a cube and combined with an appropriate interpolation scheme. The paper presents a brief description of the cubedsphere model and a comparison of it with the spherical harmonic model. The model was configured to achieve a desired accuracy so that dynamical tests, e.g., evaluation of the integration constant, closely approximate that of the spherical harmonic model. The new model closely approximates the spherical harmonic model, with propagated orbits deviating by a fraction of a millimeter at or above feasible Earth-centered altitudes.

Hermitian approximation of the spherical divergence on the Cubed-Sphere

“…geodesic lines of the sphere S 2 equipped with the standard metric. Consider the two sets of great circles called C (1) i and C (2) j shown in Fig. 1.…”

“…• Gravitational field analysis: Specialized satellite data (from the COBE satellite) must be thoroughly worked out by interpolation and approximation [2].…”

A multiresolution model for small-body gravity estimation

“…Unlike the cubed-sphere gravity model, whose primary purpose is a fast evaluation of the gravity field (Beylkin and Cramer 2002;Jones et al 2010), the model of this paper is intended for estimation as it attempts to minimize the number of unknown parameters. We note that the radial part of this new model may be applied to the problem of fast evaluation as well.…”

Data Association Algorithms for Tracking Satellites

“…However, CelesTrak has compiled EOPs from all available sources to create a single file containing EOP data from 1962 up to predictions 1 year into the future. 1 The file maintained by CelesTrak is used by Analytical Graphics Inc. Satellite Tool Kit (STK), and TurboProp requires a periodic update of this file. Tools are provided for this, and are executed as part of the installation software.…”

“…This has enabled space situational awareness (SSA) research ongoing at CCAR. This research first came in the form of testing the prototype cubed-sphere model [1,2], which was designed for space surveillance and reduces the computation requirements of the gravity perturbation DISTRIBUTION STATEMENT A: Approved for public release, distribution is unlimited. 1 model.…”