Motions of Satellites and Asteroids Under the Influence of Jupiter and the Sun: I. Stable and Unstable Satellite Orbits

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Abstract
An attempt is made to find which initial jovicentric orbital elements give rise to stable satellite orbits about Jupiter. The orbits of a large number of hypothetical satellites of Jupiter with various values for their initial semi-major axes, inclinations and eccentricities are computed and the effect of varying these initial elements on a satellite's subsequent behaviour is demonstrated. The orbits of the satellites are taken to be examples of the elliptical restricted three-dimensional three-body problem with the Sun and Jupiter as the two massive bodies. The equations of motion of the satellite are solved numerically by De Vogelaere's method.

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