Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter
- 185 Downloads
Preliminary mission design for planetary satellite orbiters requires a deep knowledge of the long term dynamics that is typically obtained through averaging techniques. The problem is usually formulated in the Hamiltonian setting as a sum of the principal part, which is given through the Kepler problem, plus a small perturbation that depends on the specific features of the mission. It is usually derived from a scaling procedure of the restricted three body problem, since the two main bodies are the Sun and the planet whereas the satellite is considered as a massless particle. Sometimes, instead of the restricted three body problem, the spatial Hill problem is used. In some cases the validity of the averaging is limited to prohibitively small regions, thus, depriving the analysis of significance. We find this paradigm at Enceladus, where the validity of a first order averaging based on the Hill problem lies inside the body. However, this fact does not invalidate the technique as perturbation methods are used to reach higher orders in the averaging process. Proceeding this way, we average the Hill problem up to the sixth order obtaining valuable information on the dynamics close to Enceladus. The averaging is performed through Lie transformations and two different transformations are applied. Firstly, the mean motion is normalized whereas the goal of the second transformation is to remove the appearance of the argument of the node. The resulting Hamiltonian defines a system of one degree of freedom whose dynamics is analyzed.
KeywordsRestricted problems Hill’s problem Periodic orbits Stability Artificial satellites Perturbation methods Frozen orbits Satellite orbiter
Unable to display preview. Download preview PDF.
- Aiello, J.: Numerical Investigation of Mapping Orbits about Jupiter’s Icy Moons. Paper AAS 2005-377, Aug 2005Google Scholar
- Casotto, S., Padovani, S., Russell, R.P., Lara, M.: Detecting a Subsurface Ocean from Periodic Orbits at Enceladus, AGU 2008 Fall Meeting, 15–19 Dec 2008, San Francisco, CAGoogle Scholar
- Cushman R.: Reduction, Brouwer’s Hamiltonian and the critical inclination. Errata 33, 297 (1984)Google Scholar
- Folta, D., Quinn, D.: Lunar Frozen Orbits, Paper AIAA 2006-6749, Aug 2006Google Scholar
- Kovalevsky J.: Sur la Théorie du Mouvement dun Satellite à Fortes Inclinaison et Excentricité. In: Kontopoulos, G.I. (eds) The Theory of Orbits in the Solar System and in Stellar Systems, IAU Symp. No. 25, pp. 326–344. Academic Press, London (1966)Google Scholar
- Lam, T., Whiffen, G.J.: Exploration of Distant Retrograde Orbits Around Europa, Paper AAS05-110, Jan 2005Google Scholar
- Lara, M., Palacián, J.F., Russell, R.P.: Averaging and Mission Design: the Paradigm of an Enceladus Orbiter, Paper AAS09-199, Feb 2009, 20 pages.Google Scholar
- Lo, M.W., Williams, B.G., Bollman, W.E., Han, D., Hahn, Y., Bell, J.L., Hirst, E.A., Corwin, R.A., Hong, P.E., Howell, K.C.: Genesis Mission Design, Paper AIAA-1998-4468, Aug 1998Google Scholar
- Paskowitz, M.E., Scheeres, D.J.: Orbit mechanics about planetary satellites including higher order gravity fields. Paper AAS 2005-190, Jan. 2005Google Scholar
- Szebehely V.: Theory of Orbits. The restricted problem of three bodies. Academic Press, New York (1967)Google Scholar
- Villac, B., Lara, M.: Stability maps, global dynamics and transfers. AAS Paper 05-378, Aug 2005Google Scholar