Long-term capture orbits for low-energy space missions

Carletta, Stefano; Pontani, Mauro; Teofilatto, Paolo

doi:10.1007/s10569-018-9843-7

Cited by 6 publications

(6 citation statements)

References 38 publications

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“…A second canonical transformation T 2 : (Q, P) → (x, y), originally proposed by Siegel and Moser [41] and extensively used for the CR3BP [29,33,42], allows expressing Ĥ(2) as the sum of three terms…”

Section: Topological Characterization Of Low-energy Trajectoriesmentioning

confidence: 99%

“…Applying the transformation T 2 developed by Siegel and Moser [41], the Hamiltonian variables are transformed as follows (see [29,40] for the derivation of matrix T 2 )…”

Section: Appendix B Canonical Transformationsmentioning

confidence: 99%

“…In fact, the phase space description derived for the CR3BP in the surrounding of the libration point L 1 (or L 2 ) can actually provide pivotal results for the design of missions also in the presence of non negligible, but limited, eccentricity in the motion of the primaries [28] and gravitational attraction from a fourth body [29]. This result has its foundation on a theorem by Conley and Easton [30], stating that the basic topological properties of the phase space flow of the CR3BP are persistent in the presence of perturbations, whose validity was verified also by means of numerical analyses [31,32].…”

Section: Introductionmentioning

confidence: 99%

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Characterization of Low-Energy Quasiperiodic Orbits in the Elliptic Restricted 4-Body Problem with Orbital Resonance

2022

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In this work, we investigate the behavior of low-energy trajectories in the dynamical framework of the spatial elliptic restricted 4-body problem, developed using the Hamiltonian formalism. Introducing canonical transformations, the Hamiltonian function in the neighborhood of the collinear libration point L1 (or L2), can be expressed as a sum of three second order local integrals of motion, which provide a compact topological description of low-energy transits, captures and quasiperiodic libration point orbits, plus higher order terms that represent perturbations. The problem of small denominators is then applied to the order three of the transformed Hamiltonian function, to identify the effects of orbital resonance of the primaries onto quasiperiodic orbits. Stationary solutions for these resonant terms are determined, corresponding to quasiperiodic orbits existing in the presence of orbital resonance. The proposed model is applied to the Jupiter-Europa-Io system, determining quasiperiodic orbits in the surrounding of Jupiter-Europa L1 considering the 2:1 orbital resonance between Europa and Io.

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Section: Topological Characterization Of Low-energy Trajectoriesmentioning

confidence: 99%

“…Applying the transformation T 2 developed by Siegel and Moser [41], the Hamiltonian variables are transformed as follows (see [29,40] for the derivation of matrix T 2 )…”

Section: Appendix B Canonical Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characterization of Low-Energy Quasiperiodic Orbits in the Elliptic Restricted 4-Body Problem with Orbital Resonance

2022

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“…The single-launch deployment strategy proposed here is developed based on the characterization of low-energy trajectories which cross the phase space surrounding the libration point L 1 , named the equilibrium region [34,35]. Operating in the dynamic framework of the elliptic restricted four-body problem (ER4BP), which is significantly more accurate than the CR3BP to model the Sun-Earth-Moon system, it is proved that a satellite can be transferred from a low-energy trajectory to an orbit with desired semimajor axis, eccentricity, inclination, and RAAN by providing a single ∆V when crossing the equilibrium region.…”

Section: Introductionmentioning

confidence: 99%

A Single-Launch Deployment Strategy for Lunar Constellations

Carletta

2023

Applied Sciences

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Satellite constellations can provide communication and navigation services to support future lunar missions, and are attracting growing interest from both the scientific community and industry. The deployment of satellites in orbital planes that can have significantly different inclinations and right ascension of the ascending node requires dedicated launches and represents a non-trivial issue for lunar constellations, due to the complexity and low accessibility of launches to the Moon. In this work, a strategy to deploy multiple satellites in different orbital planes around the Moon in a single launch is examined. The launch vehicle moves along a conventional lunar escape trajectory, with parameters selected to take advantage of gravity-braking upon encountering the Moon. A maneuver at the periselenium allows the transfer of the spacecraft along a trajectory converging to the equilibrium region about the Earth–Moon libration point L1, where the satellites are deployed. Providing a small ΔV, each satellite is transferred into a low-energy trajectory with the desired inclination, right ascension of the ascending node, and periselenium radius. A final maneuver, if required, allows the adjustment of the semimajor axis and the eccentricity. The method is verified using numerical integration using high-fidelity orbit propagators. The results indicate that the deployment could be accomplished within one sidereal month with a modest ΔV budget.

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“…The analytical results show that loose captures allow some flexibility in the choice of capture orbit and can significantly reduce propulsive costs over tight captures. In reference (Carletta et al, 2018), they investigate the dynamical conditions corresponding to long-term ballistic capture in the three-dimensional circular restricted three-body problem and develop powered permanent capture strategies. In reference (Wafaa et al, 2018), a restricted 2 1 2 body problem is proposed as a possible mechanism to explain the capture of small bodies by a plane, which is possible for both prograde and retrograde orbits.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of lunar capture braking method based on particle swarm optimization

Bai

Guo

Zhang

et al. 2019

AEAT

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Purpose The purpose of this paper is to verify the feasibility of lunar capture braking through three methods based on particle swarm optimization (PSO) and compare the advantages and disadvantages of the three strategies by analyzing the results of the simulation. Design/methodology/approach The paper proposes three methods to verify capture braking based on PSO. The constraints of the method are the final lunar orbit eccentricity and the height of the final orbit around the Moon. At the same time, fuel consumption is used as a performance indicator. Then, the PSO algorithm is used to optimize the track of the capture process and simulate the entire capture braking process. Findings The three proposed braking strategies under the framework of PSO algorithm are very effective for solving the problem of lunar capture braking. The simulation results show that the orbit in the opposite direction of the trajectory has the most serious attenuation at perilune, and it should consume the least amount of fuel in theoretical analysis. The methods based on the fixed thrust direction braking and thrust uniform rotation braking can better ensure the final perilune control accuracy and fuel consumption. As for practice, the fixed thrust direction braking method is better realized among the three strategies. Research limitations/implications The process of lunar capture is a complicated process, involving effective coordination between multiple subsystems. In this article, the main focus is on the correctness of the algorithm, and a simplified dynamic model is adopted. At the same time, because the capture time is short, the lunar curvature can be omitted. Furthermore, to better compare the pros and cons of different braking modes, some influence factors and perturbative forces are not considered, such as the Earth’s flatness, light pressure and system noise and errors. Practical implications This paper presents three braking strategies that can satisfy all the constraints well and optimize the fuel consumption to make the lunar capture more effective. The results of comparative analysis demonstrate that the three strategies have their own superiority, and the fixed thrust direction braking is beneficial to engineering realization and has certain engineering practicability, which can also provide reference for lunar exploration orbit design. Originality/value The proposed capture braking strategies based on PSO enable effective capture of the lunar module. During the lunar exploration, the capture braking phase determines whether the mission will be successful or not, and it is essential to control fuel consumption on the premise of accuracy. The three methods in this paper can be used to provide a study reference for the optimization of lunar capture braking.

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Long-term capture orbits for low-energy space missions

Cited by 6 publications

References 38 publications

Characterization of Low-Energy Quasiperiodic Orbits in the Elliptic Restricted 4-Body Problem with Orbital Resonance

Characterization of Low-Energy Quasiperiodic Orbits in the Elliptic Restricted 4-Body Problem with Orbital Resonance

A Single-Launch Deployment Strategy for Lunar Constellations

Comparative analysis of lunar capture braking method based on particle swarm optimization

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