A model of the gravitational field of Amalthea. Part 1: Derivation

Mathematics

Scientific paper

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Amalthea, Density (Mass/Volume), Dynamic Characteristics, Gravitational Fields, Mathematical Models, Planetary Mapping, Shapes, Spherical Harmonics, Topography, Axes (Reference Lines), Cartesian Coordinates, Expansion, Jupiter (Planet), Legendre Functions, Moments Of Inertia, Numerical Integration, Radii

Scientific paper

Utilizing the topographic model of Jovian moon Amalthea (Stooke, 1994) and supposing that its mass density is constant we derived its basic geometrical and dynamical characteristics. For calculations the harmonic model of topography of the degree and order 18 was selected. The model appears to fit the entire surface to a mean accuracy of a few hundred meters, except in the regions localized around longitudes 0 deg and 180 deg. On the basis of the harmonic expansion of the topography we estimated the volume (V = 2.43 +/- 0.02 cu km) and the mean radius of topography r0 = (79 +/- 0.2) km. Generalized moments of inertia up to the order 2, principal moments of inertia and orientation of the principal axes with respect to the original reference frame were also calculated. The results show that although Amalthea has extremely irregular shape it may be treated dynamically as an almost symmetric body (B approximately equals C). Finally, the set of the Stokes coefficients up to the degree and order 9 was evaluated. The results are verified by direct numerical integration.

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