Analytic estimates and topological properties of the weak stability boundary

The weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3 body problem (PCR3BP), 1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; 2) a precise description of the topology of the WSB; 3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB

On Optimal Two-Impulse Earth-Moon Transfers in a Four-Body Model

In this paper two-impulse Earth-Moon transfers are treated in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. The problem is formulated with mathematical means and solved through direct transcription and multiple shooting strategy. Thousands of solutions are found, which make it possible to frame known cases as special points of a more general picture. Families of solutions are defined and characterized, and their features are discussed. The methodology described in this paper is useful to perform trade-off analyses, where many solutions have to be produced and assessed

A study of low-energy transfer orbits to the Moon: towards an operational optimization technique

In the Earth-Moon system, low-energy orbits are transfer trajectories from the earth to a circumlunar orbit that require less propellant consumption when compared to the traditional methods. In this work we use a Monte Carlo approach to study a great number of such transfer orbits over a wide range of initial conditions. We make statistical and operational considerations on the resulting data, leading to the description of a reliable way of finding "optimal" mission orbits with the tools of multi-objective optimization

Transfers to distant periodic orbits around the Moon via their invariant manifolds

This paper presents two ways to transfer a spacecraft to distant periodic orbits in the Earth–Moon system. These unstable periodic orbits of the restricted three-body problem reveal a rich phase-portrait structure that can be used by space missions. Through the perspective of dynamical system theory, distant periodic orbits’ invariant manifolds can be exploited to design novel low-energy trajectories in the Earth–Moon framework. Interior and exterior transfers are presented. The latter use impulsive, high-thrust propulsion to target the stable manifold from the exterior. Interior transfers are instead formulated with continuous, low-thrust propulsion. The attainable sets are used in both cases to handle families of either coast arcs or low-thrust orbits. First guess solutions are optimized in the framework of the Sun–Earth-Moon–Spacecraft restricted four-body problem through direct transcription and multiple shooting. The novelty of the presented solutions, as well as their efficiency, is demonstrated through examples

Hybrid Propulsion Transfers for Mars Science Missions

Special Earth-Mars transfers that exploit both chemical and solar electric propulsion are investigated in this work. A dedicated launch strategy via Soyuz is considered. Firstly, a high-thrust, low-Isp impulse is used to place the spacecraft onto an Earth-escape trajectory, possibly performing a lunar swingby. Then, an heliocentric rendezvous with Mars is achieved via low-thrust, high-Isp propulsion, followed by a ballistic capture leading to a final, low-altitude orbit around Mars. Hybrid propulsion transfers outperform chemical transfers (Hohmann) in terms of propellant consumption. Furthermore, a few considerations at system level are also proposed

Alternative Hybrid Propulsion Transfers for Marco Polo NEOs Sample Return Mission

In this paper the new concept of hybrid propulsion transfers is applied to the trajectory design for the ESA Marco Polo mission, a NEO sample return mission. The concept of hybrid propulsion transfers combine the features of low-energy transfer, which implies impulsive maneuver accomplished using chemical propulsion, and low-thrust transfer. The optimization is performed with a direct transcription procedure. The problem is formulated as a nonlinear programming problem and solved for a finite set of variables, maximizing the final spacecraft mass. The designed hybrid propulsion transfers have been in-depth compared with the baseline trajectories obtained for Marco Polo mission

Numerical Methods to Design Low-Energy, Low-Thrust Sun-Perturbed Transfers to the Moon

In this work we merge together the low-thrust propulsion and the invariant manifold technique to design transfer trajectories from GTO to equatorial orbits around the Moon. The dynamical framework is the Sun-perturbed Earth-Moon-spacecraft restricted three-body problem. The problem is formulated in an optimal control fashion, and it is solved using a direct transcription approach. Two different direct methods have been investigated: multiple shooting and collocation; in the latter the dynamics is discretized over an uniform time grid using a 6th-order linear multi-point method. Optimal transfers are made up by three different phases: a spiral arc, hyperbolic transit orbit shadowing the invariant manifolds associated to L 1, and a low-thrust arc that places the spacecraft on its final orbit around the Moon. Results show the feasibility of this kind of transfers requiring both moderate propellant mass fractions and reasonable times of flight. Considerations are made on the solutions found with respect to numerical methods adopted