Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure perturbations. A two-dimensional differential system is derived by considering the classical theory, supported by the existence of an integral of motion comprising semi-major axis, eccentricity and inclination. Under the single resonance hypothesis, the analytical expressions for the equilibrium points in the eccentricity-resonant angle space are provided, together with the corresponding linear stability. The Hamiltonian formulation is also given. The model is applied considering, as example, the Earth as major oblate body, and a simple tool to visualize the structure of the phase space is presented. Finally, some considerations on the possible use and development of the proposed model are drawn

Gravitational capture opportunites for asteroid retrieval missions

Asteroids and comets are of strategic importance for science in an effort to uncover the formation, evolution and composition of the Solar System. Near-Earth objects (NEOs) are of particular interest because of its accessibility from Earth, but also because of their speculated wealth of resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we analyze the possibility of retrieving entire objects from accessible heliocentric orbits and moving them into the Earth’s neighbourhood. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroidal material. With the objective to minimise transfer costs, a global search of impulsive transfers connecting the unperturbed asteroid’s orbit with the stable manifold phase of the transfer is performed. A catalogue of asteroid retrieval opportunities of currently known NEOs is presented here. Despite the highly incomplete census of very small asteroids, the catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. All, but one, of these objects have an expected size and transfer requirements that can be met by current propulsion technologies. Moreover, the methodology proposed represents a robust search for future retrieval candidates that can be automatically applied to a growing survey of NEOs

Editorial: The earth–moon system as a dynamical laboratory

Postprint (published version

The dynamical structure of the MEO region: long-term stability, chaos, and transport

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.Comment: Submitted to Celestial Mechanics and Dynamical Astronomy. Comments are greatly appreciated. 28 pages, 15 figure

Analytical and semi-analytical approaches to the third-body perturbation in nearly co-orbital regimes

Since the beginning of space exploration, close encounters with celestial bodies in the Solar System have been exploited to change the motion of a spacecraft. Gravity assists are such an example; since they take place inside the planet’s sphere of influence, their most used modelling framework is the patched- conics approximation. This, however, simplifies the spacecraft’s motion as to be affected by only one celestial body at a time. Higher accuracy approaches, such as the circular-restricted three-body problem (CR3BP) models a simultaneous attraction of two bodies (primary and secondary: for example, Sun and Earth) and its application domain extends beyond the classical sphere of influence. In between these approaches, perturbation techniques exist to account for the influence of the sec- ondary, well outside the sphere of influence, in addition to the main attractive body. This paper presents two twin formulations for the variation of the spacecraft’s orbital elements due to the third-body effect in the CR3BP, i.e. the regime of distant encounters outside the secondary’s sphere of influence. These are based on the disturbing function of the previously studied Keplerian Map, derived from the Hamiltonian of the CR3BP in a barycentric coordinate system; additionally, they can be used in any kind of system of small gravitational parameter, such as the Sun-Earth one. The first formulation is a partially analytical solution to the Lagrange planetary equations of motion. This strategy unites fully analytical equations for the evolution of the semi-major axis of the motion, which are obtained via a Taylor expansion on the eccentricity, with the use of the Euler method for the remaining unsolvable differential equations. This strategy allows the prediction of the orbital shape, making it potentially useful for fast online computations and application in GNC algorithms. The second formulation is a mapping model for long time propagation, in which the orbital elements are updated at every periapsis and apoapsis to minimise the inherent numerical errors. This strategy is called the EK-PAP (Euler-Keplerian Periapsis to Apoapsis) map. It shows to be several orders of magnitude faster than the CR3BP, remaining accurate for motion durations up to several synodic periods. Particularly, the application to end-of-life disposal strategies is envisioned, in which the EK-PAP map can ensure that the long-term propagation of the disposed spacecraft follows the guidelines for clean space missions

Transfer orbits in the Earth-Moon system and tefinement to JPL ephemerides

We describe how to determine transfers between libration point orbits and either the surface of the Moon or a Low Earth Orbit within the Circular Restricted Three – Body Problem (CR3BP) assumptions. Moreover, we explain how to refine such trajectories to ones verifing more comprehensive equations of motion. We are interested in seeing how the geometry of the nominal target orbits and of the associated stable manifolds drives the connections and also how much reliable the CR3BP is. The main tools we take advantage of are the Lindstedt–Poincaré semi-analytical method, differential correction procedures and an optimizer.Postprint (published version

Semi-analytical perturbative approaches to third body resonant trajectories

In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by past missions such as SMART-1, as well as are proposed to benefit future missions to Jupiter, Saturn or Neptune, and disposal strategies from Earth’s High Eccentric or Libration Point Orbits. This paper revises three totally different descriptions of the effects of the third body gravitational perturbation. These are the averaged dynamics of the classical third body perturbing function, the Öpik’s close encounter theory and the Keplerian map approach. The first two techniques have respectively been applied to the cases of a spacecraft either always remaining very far or occasionally experiencing extremely close approaches to the third body. However, the paper also seeks solutions for trajectories that undergo one or more close approaches at distances in the order of the sphere of influence of the third body. The paper attempts to gain insight into the accuracy of these different perturbative techniques into each of these scenarios, as compared with the motion in the Circular Restricted Three Body Problem