Dynamics of Orbits Near 3:1 Resonance in the Earth-Moon System
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Dynamics of Orbits Near 3:1 Resonance in the Earth-Moon System Donald J. Dichmann & Ryan Lebois & John P. Carrico Jr
Published online: 5 August 2014 # American Astronautical Society (Outside the USA) 2014
Abstract The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next 20 years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincaré maps with twentyyear propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study. Keywords Resonant orbit . Periodic orbit . Stability . Bifurcation
Parts of this article appeared in “Lunar-Resonant Trajectory Design for the Interstellar Boundary Explorer (IBEX) Extended Mission”, AAS/AIAA Astrodynamics Specialist Conference, Girdwood AK, 2011, AAS11-454. D. J. Dichmann (*) Code 595.0, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA e-mail: [email protected] R. Lebois : J. P. Carrico Jr Applied Defense Solutions, 10440 Little Patuxent Parkway, Columbia, MD 21004, USA R. Lebois e-mail: [email protected] J. P. Carrico Jr e-mail: [email protected]
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J of Astronaut Sci (2013) 60:51–86
Introduction The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth near 3:1 resonance with the Moon, with spacecraft apogee oriented to stay away from the Moon. As described in [1–3], this type of orbit would be useful for space weather missions and shows remarkable stability over an interval of several decades. This article is an extension of [1], which reviews the trajectory trade study for the IBEX extended mission. The goal of this article is to obtain a better understanding of the dynamics of such an orbit, especially its stability. Toward this goal we study the dynamics of near 3:1 resonant periodic orbits, in the CR3BP for the Earth-Moon system. Poincaré recognized the central role of periodic solutions in the structure of a dynamical system [4]. As shown in [1], the actual IBEX orbit is quasi-periodic, not periodic. However it is common for a family of quasi-periodic orbits to exist near a periodic orbit in a Hamiltonian system
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