Computer-developed construction of analytic expressions for the coordinates and partial derivatives of Jupiter's Galilean satellites

Abstract

In his effort to develop series expressions for the coordinates of the Galilean satellites accurate to one are second (Jovicentric), R. A. Sampson was forceda priori to adopt certain numerical values for several constants imbedded in his theory. His final numerical values for the series expressions are not amenable to adjustment of the constants of integration nor of physical constants which affect the motion of the satellites. A method which utilizes computer-based algebraic manipulation software has been developed to reconstruct Sampson's theory, to remove existing errors, to introduce neglected effects and to provide analytical expressions for the coordinates as well as for the partial derivatives with respect to orbital parameters, Jupiter and satellite masses, Jupiter's oblateness (J ₂,J ₄) and Jupiter's pole and period of rotation. The computer-based manipulations enable one to perform, for example, the approximately 10⁸ multiplications required in calculating some perturbations (and their partial derivatives) of Satellite II by Satellite III with ease, and provide algebraic expressions which can readily be adjusted to generate theories corresponding to revised constants of integration and physical parameters.