In this work, we introduce a modified double-averaging approach by considering the shortterm effects and formulate a more accurate double-averaged Hamiltonian (in comparison to the classical octupole-level Hamiltonian) for hierarchial triple systems. The Hamiltonian is expressed as a power series in the ratio of the semi-major axes of the inner and outer binaries. Both the Delaunay's elements and the classical orbit elements are adopted to describe the motion. To derive the secular Hamiltonian, the short-term oscillations in the Hamiltonian are averaged out by means of a double-averaging approach. In particular, during the average over the orbital period of the outer binary, the periodic corrections to the secular motion are taken into account. Based on the double-averaged Hamiltonian, we provide two versions of equations of secular motion, given in the form of canonic relations and Lagrange planetary equations. The resulting secular evolution equations can be utilized to reproduce the long-term behaviours for those physical systems where the perturbations coming from the disturbing bodies are relatively strong. To test the approach, we use the averaged Hamiltonian to predict the longterm motions of a planet in a stellar binary system and natural satellites in Sun-planet systems. Simulation results show that the modified Hamiltonian can reproduce secular behaviours with high accuracy. Additionally, the comparison of dynamical models truncated at different orders indicates that the secular Hamiltonian with inclusion of higher order terms has better accuracy in predicting long-term evolution.
This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally, the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach stable capture, which allows orbit circularization using low-thrust propulsion systems.
The aim of this paper is to propose a refined mathematical model for describing the acceleration experienced by a\ud\ud solar sail. Unlike the conventional model characterized by constant coefficients, the force coefficients of the sail are\ud\ud now assumed to depend on the light incidence angle, the sail surface roughness, and the sun–sail distance. The new\ud\ud model is elaborated with the support of experimental data that show how the main variable affecting the force\ud\ud coefficients is the light incidence angle. To emphasize the differences between the refined force model with respect to\ud\ud the conventional one, a comparison is established through the analysis of a circle-to-circle interplanetary rendezvous\ud\ud problem between coplanar orbits. The problem is solved using an indirect approach and the optimal steering law is approximated in polynomial form. A number of optimal trajectories toward Mars and Venus are simulated and the\ud\ud results obtained are discussed as a function of the dimensionless sail loading parameter and the sail surface\ud\ud roughness
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.