Long-term capture orbits for low-energy space missions
Celestial mechanics & dynamical astronomy
In the framework of the space debris problem, in order to mitigate the already critical situation in the Low Earth Orbit (LEO) region, and, more generally, to preserve the circumterrestrial environment, the scientific community is now aware of the need of designing feasible and effective solutions for the satellites' end-of-life. To this end, it is mandatory to obtain a deep understanding of the dynamics at stake. Within the H2020 ReDSHIFT project, we mapped the whole LEO region in terms of
... ial semi-major axis, eccentricity and inclination, for 16 combinations of longitude of ascending node and argument of pericenter, and 2 initial epochs. The dynamical model considered includes the geopotential of order and degree 5, lunisolar perturbations, solar radiation pressure (SRP) effects and atmospheric drag. The numerical simulations and specific analytical developments revealed the role of resonant inclinations associated with the just mentioned main perturbations. In particular, the resonances corresponding to the gravitational attraction of Moon and Sun and the SRP induce preferential paths which can be exploited to decrease the lifetime of the satellite, either in combination with the effect of the drag, or, if possible, using a SRP enhanced device. Besides the extension of the numerical results, the novelty of our findings consists in the theoretical understanding of the important role of lunisolar and SRP perturbations also in LEO. Concerning the SRP, resonances which were so far considered as secondary can play instead a fundamental role, and for values of area-to-mass ratio which can be achieved with the present technology. Abstract. Hitherto unprecedented detections of exoplanets have been triggered by missions and ground based telescopes. The quest of "exo-Earths" has become intriguing and the long-term stability of planetary orbits is a crucial factor for the biosphere to evolve. Planets in mean-motion resonances (MMR) prompt the investigation of the dynamics in the framework of the three-body problem (TBP), where the families of stable periodic orbits constitute the backbone of stability domains in phase space. Here, we address the question of the possible co-existence of terrestrial planets with a giant companion on circular or eccentric orbit and explore the extent of the stability regions, when both the eccentricity of the outer giant planet and the semi-major axis of the inner terrestrial one vary, i.e. both non-resonant and resonant configurations. Our study exploits the restricted three-body problem (RTBP). Starting from the circular family and its bifurcation points, the families of periodic orbits in the circular and elliptic RTBP are computed for the 3/2, 2/1, 5/2, 3/1, 4/1 and 5/1 MMRs. We construct maps of dynamical stability to identify the boundaries of the stability domains where such a co-existence is allowed. We also compute the vertical critical periodic orbits (i.e. bifurcation points that can generate spatial families of periodic orbits) and provide hints with respect to vertically stable planetary orbits, as islands in their neighbourhood can host resonant mutually inclined exoplanets. Finally, the maximum mutual inclination of stably evolving planets that can be attained by spatial families of periodic orbits is also discussed. Joint work with A.-S. Libert. Abstract. We consider the motion of an infinitesimal mass under the gravitational influence of two masses moving in parabolic orbits and in the same plane. The main features of the problem are the gradient-like character, the Hill's regions, and the invariant manifolds associated to the equilibrium points. From them, we describe the final evolutions of the solutions, forward and backward in time. This model can be used to understand, at a basic level, the effect of a close encounter of two galaxies. Such a close encounter may cause a significant modification in the mass distribution. Taking into account just one particle within one galaxy, after the close encounter, the particle may jump to the other galaxy or escape. We study in the frame of the planar parabolic problem, the mechanisms that allow to explain the different behaviors. Furthermore, after a close encounter of two galaxies, brigdes and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. We use the model to a mechanism that explain the formation of bridges and tails. Joint work with Josep M. Cors, Mercé Ollé and Laura Garcia. Abstract. Index Theory can be used in Celestial Mechanics both to study linear stability of some classes of periodic orbits and to compute the Morse Index of a huge classes of solutions. In this talk we will focus on some recent results, that give a necessary and sufficient condition for the finiteness of the Morse index of trajectories interacting with the singular set and provide an Index Theorem to link the Morse index to a finite dimensional symplectic invariant, the Maslov Index. Joint work with Title: "Notes on logarithmic spiral trajectories generated by solar sails" Abstract. A solar sail represents a very promising option in the set of low-thrust propulsion systems. It exploits the solar radiation pressure that acts on a large reflective surface to generate a propulsive acceleration. The recent successful missions of IKAROS, Nanosail-D2 and LightSail-1 have confirmed the potentialities of such a propulsive concept and laid the foundation for future space missions. The trajectory design for a solar sail-based spacecraft within a heliocentric mission is usually addressed by numerically integrating the spacecraft equations of motion, since in general no closed-form analytical solution exists. In this respect an exception is offered by the special case of logarithmic spiral. The latter is characterized by a constant flight path angle and a thrust vector direction that remains fixed in an orbital reference frame. Therefore, the Sun-spacecraft distance exponentially grows (or reduces) with respect to an angular coordinate measured from a given heliocentric direction. Even though the logarithmic spiral has some intrinsic limitations (such as the inability of generating a circle-to-circle orbit transfer), it may represent an useful tool for the preliminary analysis of some mission scenarios. The aim of this paper is to provide a systematic study about the possibility of inserting a solar sail spacecraft into a heliocentric logarithmic spiral trajectory. The required conditions in terms of solar sail (fixed) attitude, performance, and initial position are discussed. It is shown that the spiral trajectory is required to start from a specific point that depends on the solar sail performance and the parking orbit characteristics. Moreover, the evolution of the osculating orbital parameters are presented, and some potential mission scenarios involving logarithmic spirals are analyzed, including the rotation of the apse line and the phasing trajectories of a spacecraft placed along an elliptic orbit. Joint work with Abstract. About half of the Sun-like stars are part of multiple star systems. Many of them have an orbital period of a few days only. Our work focuses on the Lidov-Kozai tidal migration mechanism and aims to understand which dynamical effects are the most active in the accumulation of stellar companions with short orbital periods in binary star systems. Our framework is the hierarchical three-body problem (octupole), with the effects of tides, stellar oblateness, general relativity and spin down for the host star. Both the orbital evolution and the spin evolution are considered. Using orbital and physical parameters for the stars consistent with current observations, we perform 100 000 numerical simulations of well diversified triple star systems, and compare our results to Fabrycky & Tremaine (2007) and Naoz & Fabrycky (2014). We show that the final distribution of the final systems is very dependent on the initial parameters of the simulations. A similar study is finally realized for Hot Jupiters in binary systems, where the debate about the possible formation mechanisms (disc-planet interactions, planet-planet scattering and Lidov-Kozai migration) of such planets is very intense. Joint work with A.Abstract. We present a topological mechanism of diffusion in a priori chaotic systems. The method leads to a proof of diffusion for an explicit range of perturbation parameters. The assumptions of our theorem can be verified using interval arithmetic numerics, leading to computer assisted proofs. As an example of application we prove diffusion in the Neptune-Triton planar elliptic restricted three body problem. Joint work with Title: "Coorbital quasi-periodic motion in the three-body problem" Abstract. We consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 3-tori. The study is based on a combination of normal form and symplectic reduction theories and the application of a KAM theorem for high-order degenerate systems. We approach the problem as a perturbation of decoupled Kepler. This approximation is valid in the region of phase space where coorbital solutions occur. A joint work with J.F. Palacián and P. Yanguas. References J.M. Cors and G.R. Hall. Coorbital periodic orbits in the three body problem. SIAM J. Appl. Dyn. Syst. (2003), no. 2, 219-237. J. M. Cors, J.F. Palacián and P. Yanguas. Asymptotic stability estimates near an equilibrium point. In preparation.