The nature of the orbits of charged dust injected into the Jovian magnetosphere during the tidal break-up of comet Shoemaker-Levy 9

Assuming that the spin and magnetic axis of Jupiter are strictly parallel and that the grain charge remains constant we have derived two integrals of the 3D equations of motion of charged dust grains moving within the co-rotating regions of the Jovian magnetosphere taking into account both planetary gravitation and magnetospheric rotation. We then apply this model to study the fate of fine dust injected into the Jovian magnetosphere as a result of the tidal disruption of comet Shoemaker-Levy 9 during its first encounter with Jupiter in July 1992. This analysis, which uses the integrals of the equation of motion rather than the equation of motion itself as was done by Horanyi (1994), does not allow us to calculate the orbits or the orbital evolution of the grains. But it does allow us to construct the spatial regions to which the grains are confined, at least initially before evolutionary effects take over. We have chosen three points along the path of the disintegrating comet for the injection of dust and used two values for the uncertain floating potential of the dust in the inner Jovian magnetosphere. Grains can have three different fates, depending on their size, their acquired potential and their point of injection. While the smallest grains are quickly lost by collision with the planet at high latitudes independent of the sign of their charge, those in an intermediate but narrow size range, injected near the equatorial plane can be trapped in a region close to it, this being true for both positive and negative grains. While somewhat larger positive grains may be initially ejected outward by the co-rotational electric force, similar negative grains, pulled inward by this force collide with the planet at low latitudes. In all cases the largest grains, which are dominated by planetary gravity, initially escape from the inner magnetosphere by following in the path of the comet.Using a detailed time dependent numerical calculation of the jovicentric orbits of the charged dust debris of the disintegrating comet, that allows for variation in the grain potential, while also allowing for perturbations of the grain orbits due to solar radiation pressure and solar gravity Horanyi (1994) found that grains in the size range (1.5m <a < 2.5m) which initially make large excursions from the planet, will eventually form a ring in the radial range 4.5R _J <r < 6R _J . Our present analytical calculation cannot make such a prediction about the evolutionary fate of the dust debris. It can, however, estimate the size of the grains that are initially confined to regions near the points of injection, before evolutionary effects become important.