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

Content Provider	Springer Nature Link
Author	Lara, Martín Palacián, Jesús F. Russell, Ryan P.
Copyright Year	2010
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. 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.
Starting Page	1
Ending Page	22
Page Count	22
File Format	PDF
ISSN	09232958
Journal	Celestial Mechanics and Dynamical Astronomy
Volume Number	108
Issue Number	1
e-ISSN	15729478
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-06-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Restricted problems Hill’s problem Periodic orbits Stability Artificial satellites Perturbation methods Frozen orbits Satellite orbiter Mathematics Astronomy, Observations and Techniques Astrophysics and Astroparticles Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

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