Christian Circi

On the Dynamics of Weak Stability Boundary Lunar Transfers

Recent studies demonstrate that lunar and solar gravitational assists can offer a good reduction of total variation of velocity ΔVneeded in lunar transfer trajectories. In particular the spacecraft, crossing regions of unstable equilibrium in the Earth—Moon—Sun system, can be guided by the Sun towards the lunar orbit with the energy needed to be captured ballistically by the Moon. The dynamics of these transfers, called weak stability boundary (WSB) transfers, will be studied here in some detail. The crucial Earth—Moon—Sun configurations allowing such transfers will be defined. The Suns gravitational effect and lunar gravitational capture will be analyzed in terms of variations of the Jacobi ‘constants’ in the Earth—Sun and Earth—Moon systems. Many examples will be presented, supporting the understanding of the dynamical mechanism of WSB transfers and analytical formulas will be obtained in the case of ‘quasi ballistic captures’.

Refined Solar Sail Force Model with Mission Application

The aim of this paper is to propose a refined mathematical model for describing the acceleration experienced by a solar sail. Unlike the conventional model characterized by constant coefficients, the force coefficients of the sail are now assumed to depend on the light incidence angle, the sail surface roughness, and the sun–sail distance. The new model is elaborated with the support of experimental data that show how the main variable affecting the force coefficients is the light incidence angle. To emphasize the differences between the refined force model with respect to the conventional one, a comparison is established through the analysis of a circle-to-circle interplanetary rendezvous 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 results obtained are discussed as a function of the dimensionless sail loading parameter and the sail surface roughness.

Simple strategy for geostationary stationkeeping maneuvers using solar sail

This study deals with solar-sail applications to geostationary satellites and the analysis of stationkeeping maneuvers. A thrust strategy for north‐south maneuvers is found as a function of the lunar inclination and the solar-sail’s characteristic acceleration. The characteristic acceleration obtained for north‐south maneuvers is used for the east‐west maneuvers thrust strategy. The dependence with respect to the Earth’s position around the sun and the sun-Earth-spacecraft relative position are analyzed for both types of maneuvers. The solar-sail stationkeeping performances are presented as a function of the geostationary satellite longitude, and the results are given for a one-year simulation. A comparison with chemical propulsion systems, from the total mass point of view, is presented. The reorbiting maneuver at the end of the operational life is also considered, and the extra propellant necessary for a chemical engine is evaluated.

Minimum-Time Reconfiguration Maneuvers of Satellite Formations Using Perturbation Forces

A novel approach for minimum-time reconfiguration of satellite formations is proposed considering the perturbation forces as control variables. Planning appropriate attitude maneuvers for each satellite, the atmospheric drag and of the solar radiation pressure are properly controlled, and the formation is given the appropriate inputs to achieve the imposed reconfiguration. Limits and advantages of the presented maneuvers are examined considering low Earth orbits, medium Earth orbits, and geostationary orbits. The recent inverse dynamics particle swarm optimization is involved; the integration of the attitude dynamics is avoided, thus reducing the computational effort, and satisfied attitude constraints at the initial and final time instants are guaranteed. B-spline curves approximate the attitude kinematics, variable time mesh points are introduced, and adaptive decreasing tolerances are considered for the imposed constraints. The evolution of the configuration is simulated with a high-fidelity orbital si...

Dynamic and structural performances of a new sailcraft concept for interplanetary missions

Typical square solar-sail design is characterised by a central hub with four-quadrant sails, conferring to the spacecraft the classical X-configuration. One of the critical aspects related to this architecture is due to the large deformations of both membrane and booms, which leads to a reduction of the performance of the sailcraft in terms of thrust efficiency. As a consequence, stiffer sail architecture would be desirable, taking into account that the rigidity of the system strongly affects the orbital dynamics. In this paper, we propose a new solar-sail architecture, which is more rigid than the classical X-configuration. Among the main pros and cons that the proposed configuration presents, this paper aims to show the general concept, investigating the performances from the perspectives of both structural response and attitude control. Membrane deformations, structural offset, and sail vibration frequencies are determined through finite element method, adopting a variable pretensioning scheme. In order to evaluate the manoeuvring performances of this new solar-sail concept, a 35-degree manoeuvre is studied using a feedforward and feedback controller.

Use of weak stability boundary trajectories for planetary capture

The consideration of transfers to the Weak Stability Boundary region represents one of the most advanced concepts when trying to reduce the propellant requirements to obtain an interplanetary goal. Deimos Space, under ESA contract, has developed a tool to simulate such transfers to inner planets, giant planets and natural moons of giant planets. The method is based on a three-step approach consisting on: selection of strategy, generation of initial solutions and numerical optimisation. The feasibility of building WSB transfer trajectories to Mercury, Venus and Mars has been proven. Instead of ∆V saving, the greatest advantage results from the increased flexibility in the selection of the final orbit with no ∆V penalty in most cases. The use of the Sun/Planet WSB region for the problem of giant planets capture does not introduce significant profit since the penalty in transfer time makes the mission unrealistic. Feasible missions to Jupiter and Saturn are obtained when using a double flyby strategy in Ganymede and Titan respectively. The capture by a natural moon of a giant planet incorporates a phase of energy reduction by moon flybys using resonant orbits linking at the end with the WSB region of the moon to achieve a ballistic capture.

Optimal Strategy for Geostationary Orbit Acquisition Using Ion Propulsion

The geostationary satellite for telecommunication, Artemis, is equipped with a chemical propulsion system and an ion propulsion system. Because of the third-stage ignition failure of the Ariane V launcher, the low-thrust propulsion system is used to complete the transfer orbit to geostationary Earth orbit. The optimal trajectory is determined using Pontryagins principle. All constraints for the thrust direction, due to the initial design and onboard breakdown, are considered in the optimization process, and the minimum-time problem is solved. The effect of perturbations, namely, the gravitational force of the sun and the moon, the oblateness and triaxiality of the Earth, and the solar radiation pressure, are considered. The performances of the transfer orbit and the optimal thrust strategy are presented for every case. The transfer time, considering the perturbations, increases by 20 days with respect to the Keplerian case, but this does not imply an increase in propellant mass consumption. Finally a comparison with a solution obtained using a parametric optimization process is given. The parametric optimization results are close to those of the Pontryagin solution, but do not allow the satellite to obtain the best transfer time. In fact, the control strategy efficiency depends on the number of variables used in the process, and a time-variable strategy is possible only with an enormous increase of the computational effort, although it is natural when the Pontryagin principle is applied.

On the Accessibility of the Moon

The large mass fraction of the Moon with respect to the Earth implies an extended sphere of influence which can be exploited in planning exploration missions either directed to our satellite or to other solar system bodies. The dynamical systems approach to mission design has shown the existence of novel trajectories in the Earth-Moon system, which can respond to widely different exploration goals such as low-energy lunar orbit insertion, reaching Mars from the Moon or bringing lunar resources to Earth. Within this framework the general topic of the accessibility of our satellite is discussed and examples of actual mission profiles are given.

Low ΔV Orbit Insertion in Interplanetary Missions

A key issue in interplanetary missions is the attempt to reduce as much as possible the on board propellant, which has a direct inpact on the payload weight and eventually on the cost of the mission. Then in the mission analysis one tries to to minimize the variation of velocity ΔV f needed for the spacecraft orbit insertion, and it is of interest to look for arrival conditions close to (temporary) ballistic capture of the spacecraft by the target planet (ΔV f ~ 0).