T HE instrument requirements for a scientific mission about Europa constrain the orbit design to a subset of limited values of the orbital elements. Near-circular, low-altitude, high-inclination orbits are normally required for mapping missions, and spacemission designers try to minimize the altitude variation of the satellite over the surface of the body by searching for orbits with small eccentricity and with a fixed argument of periapsis. These orbits are usually called frozen orbits [1–3]. However, due to third-body perturbations, high-inclination orbits around planetary satellites are known to be unstable [4–6], and thus emerges the problem of maximizing the orbital lifetime. One proposed approach to maximize orbit lifetime resorts to dynamical systems theory. This approach has been shown to be useful in orbit maintenance routines, in which the stable manifold associated with unstable nominal orbits provides a efficient way of maximizing time between maneuvers [7]. In the same fashion, paths in the plane of argument of periapsis and eccentricity that yield long lifetime near polar orbits around Europa have been recently identified [8]. In this paper we take a different approach. Periodic orbits around Europa are known to exist and have been previously used in the investigation of stability regions around Europa [9–11]. Periodic orbits in the rotating frame are ideal, nominal, repeat ground-track orbits that, for long enough repetition cycles, are suitable for mapping missions. We compute low-altitude, near-circular, highly inclined, repeat ground-track, unstable periodic orbits, and find that these kinds of solutions enjoy long lifetimes. Our procedure is based on fast numerical algorithms that are easily automated. The numerical search for initial conditions of repeat ground-track orbits is very simple and feasible even for higher-order gravity fields [12,13]. Safe recurrences for computing the gradient and Hessian of the gravitational potential can be found in the reference list (see, for instance, [14] and references therein). For our search, we use a simplified dynamical model that considers the mean gravitational field of a synchronously rotating and orbiting moon, and take into account the perturbations of the third body in the Hill problem approximation [5,15,16]. Tests on the validity of the solutions aremade in an ephemerismodel that includes perturbations of the sun, the other Galileans, the nonsphericity of Jupiter, the other gas giants, and a Europa gravity model that is consistent with synchronousmoon theory andNASA’sGalileo close encounters [17]. In passing from the simplified to ephemeris model we introduce a one-dimensional parameter scaling of the initial conditions that proved efficient in the past [10]. On one side it provides a simple and feasible optimization for a given epoch. But it also shows how isolated the optimized solution is in the ephemerismodel, thus giving a reasonable estimation of the robustness of the solution in the presence of realistic perturbing forces. With respect to theEuropa gravityfield, it turns out that theGalileo flyby data cannot detect valid signatures for any gravitational terms for Europa beyond , J2, and C2;2 [17]. However, based on observations of other celestial bodies, it seems reasonable to speculate that Europa could be top or bottom heavy [18], and previous studies have shown that J3 can play an important role [8,18,19]. Therefore, we study the influence of J3 in the proposed orbits, and find repeat ground-track orbits with higher eccentricities than the second-order gravity field solutions, but with similar lifetimes.
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Jan 1, 2012
D Dalal + 2
Open Access