The effect of zonal harmonics on dynamical structures in the circular restricted three-body problem near the secondary b
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(2020) 132:45
ORIGINAL ARTICLE
The effect of zonal harmonics on dynamical structures in the circular restricted three-body problem near the secondary body Luke Bury1
· Jay McMahon2
Received: 22 January 2020 / Revised: 6 August 2020 / Accepted: 25 August 2020 © The Author(s) 2020
Abstract The circular restricted three-body model is widely used for astrodynamical studies in systems where two major bodies are present. However, this model relies on many simplifications, such as point-mass gravity and planar, circular orbits of the bodies, and limiting its accuracy. In an effort to achieve higher-fidelity results while maintaining the autonomous simplicity of the classic model, we employ zonal harmonic perturbations since they are symmetric about the zaxis, thus bearing no time-dependent terms. In this study, we focus on how these perturbations affect the dynamic environment near the secondary body in real systems. Concise, easily implementable equations for gravitational potential, particle motion, and modified Jacobi constant in the perturbed model are presented. These perturbations cause a change in the normalized mean motion, and two different formulations are addressed for assigning this new value. The shifting of collinear equilibrium points in many real systems due to J2 of each body is reported, and we study how families of common periodic orbits—Lyapunov, vertical, and southern halo—shift and distort when J2 , J4 , and J6 of the primary and J2 of the secondary body are accounted for in the Jupiter–Europa and Saturn–Enceladus systems. It is found that these families of periodic orbits change shape, position, and energy, which can lead to dramatically different dynamical behavior in some cases. The primary focus is on moons of the outer planets, many of which have very small odd zonal harmonic terms, or no measured value at all, so while the developed equations are meant for any and all zonal harmonic terms, only even terms are considered in the simulations. Early utilization of this refined CR3BP model in mission design will result in a more smooth transition to full ephemeris model. Keywords Zonal harmonics · Circular restricted three-body problem · Orbital perturbations · Periodic orbits
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Luke Bury [email protected] Jay McMahon [email protected]
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Office 422 Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO 80303, USA
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Office 461 Aerospace Engineering Sciences Building, 3775 Discovery Dr, Boulder, CO 80303, USA 0123456789().: V,-vol
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L. Bury, J. McMahon
1 Introduction The circular restricted three-body problem (CR3BP) is a useful platform for understanding and designing trajectories in the presence of two large, perturbing bodies (Szebehely 1967; Koon et al. 2006). Widespread use of the CR3BP has given rise to the field of low-energy trajectory design, which can help minimize fuel usage and allow access to a wide variety of orbital geometries (Howell 1983; Koon et al. 2006; Parker et al. 2013; Vaquero Escribano 2013; Bosanac 2016; Restrepo
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