Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter

Abstract

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, but which 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 systems of one degree of freedom whose dynamics is analyzed. * Ephemerides section,

Orbital Motion in Strongly Perturbed Environments

“…Europa is chosen as the nominal central body for large planetary satellites due to the great interest of sending an orbiter mission to this body to probe its interior ocean, and due to the fact that its orbital dynamics environment is quite interesting and has been considered in a number of papers [167,188,186,127,126,128,146,148,147,88,89,87] and theses [187,125,123]. We cover this topic in the remaining chapters as it represents another example of a strongly perturbed orbital system for spacecraft.…”

“…Others have performed detailed, higher-order averaging analysis (see [87]), which are of great interest and utility for the mission design and analysis of dynamics in this class of problem. The dynamics of low-altitude orbiters about Europa are found to be quite complex where orbits with inclinations within ∼50 • of polar can suffer impacts with that planetary satellite's surface in timespans of days to weeks.…”

Some orbital characteristics of lunar artificial satellites

“…The results allow us to find good conditions close to frozen orbits for future lunar missions. In other words [see references in: Abad et al (2009), Ferrer et al (2007, Lara et al (2010), Palacián (2007)], a better understanding of the physical phenomenon can be obtained and it allows the study of long-term stability of the orbits in the presence of disturbances that causes low changes in the orbital elements.…”

Exploring the long-term dynamics of perturbed Keplerian motion in high degree potential fields

“…The derivation and arrangement of Eqs. (36) is definitely simpler than corresponding expressions in [53]. We compare the efficiency of Eq.…”

“…Handling huge literal expressions cannot be avoided when higher orders of the perturbation approach are essential in the description of the dynamics [33,34,35,36,37]. On the contrary, in those cases in which the coupling of different perturbations is not of relevance in the analysis, the averaging procedure may preserve the main structural features of the potential model, thus avoiding the need of the typical blind computer-based, brut force approach.…”