A method based on Jacobi Integral variational equation for computing Earth-Moon trajectories in the four-body problem

Filho, Luiz Arthur Gagg; Fernandes, Sandro da Silva

doi:10.1016/j.actaastro.2019.09.021

Cited by 5 publications

(1 citation statement)

References 11 publications

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“…To begin, the multi-body problem refers to the problem in the CRTBP that considers the gravity of other celestial bodies. 8 When the Sun is assumed to be the celestial body of interest, the problem can be further simplified to a restricted Earth–Moon–Sun bi-circular model. 9–11 Boudad et al, 12 in this model, calculated and analyzed the dynamics of synodic resonance NRHOs.…”

Section: Introductionmentioning

confidence: 99%

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Starinova

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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The near rectilinear halo orbit (NRHO) is a potential orbit for the establishment of lunar space station. This research is focused on the analysis of major orbital perturbations on NRHOs and the generation of nominal orbit using a low-thrust engine in the ephemeris model. First, the NRHO family is defined in the circular restricted three-body problem (CRTBP). Then, different perturbations are performed to integrate the spacecraft motion along the NRHOs; meanwhile, a modified momentum integral is employed to calculate the orbit deviation in the case of each perturbation examined independently. By this way, these perturbations are classified according to the magnitude of impact on NRHOs. Finally, combined with a fuel-optimal control, a target-point strategy generating the nominal-controlled NRHO in the real Earth–Moon system is proposed using low-thrust technology. By selecting a fixed point from the original NRHO, the spacecraft is forced to depart from this point and then return to it, thereby forming a controlled closed trajectory. This provides an alternative nominal orbit for the future application of the low-thrust engine to lunar exploration missions.

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Section: Introductionmentioning

confidence: 99%

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Starinova

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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Low-thrust transfer with Theory of Functional Connections: Application to 243 Ida with a solar sail

de Almeida,

Vaillant,

Santos

et al. 2024

Advances in Space Research

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Tangential velocity constraint for orbital maneuvers with Theory of Functional Connections

de Almeida,

Vaillant,

de Oliveira

et al. 2024

Sci Rep

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Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modeling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform gravity assist maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.

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A method based on Jacobi Integral variational equation for computing Earth-Moon trajectories in the four-body problem

Cited by 5 publications

References 11 publications

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Low-thrust transfer with Theory of Functional Connections: Application to 243 Ida with a solar sail

Tangential velocity constraint for orbital maneuvers with Theory of Functional Connections

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