Finding multiple sun-earth saddle-point flybys for LISA Pathfinder

More than 70 years after its existence was postulated for the first time in order to explain the observed rotation curves of galaxies1, the nature of Dark Matter remains a complete mystery. After several decades of research, no particles have been detected to support this theory. Thus, other theories have been developed to explain Dark Matter problem. Rather than postulating the existence of a new matter, they tend to explain the observations by modifying the gravitational laws. TeVeS and its non-relativistic limit MOND2 is one of these theories. To date, proof to confirm it has not been provided either, but could be in a near future, thanks to ESA mission LISA Pathfinder. LISA Pathfinder is a mission due to be launched in the next few years. It carries on-board an extremely sensitive gradiometer which would be able to measure deviations from Newtonian gravity, hence demonstrating MOND theory. Doing so, however, requires that LISA Pathfinder spacecraft reaches a specific point in the solar system, called the Sun-Earth Saddle Point (SP). The SP is the point located between the Sun and the Earth where the gravity of the Sun exactly equals the gravity of the Earth. This point is very singular because of its very low gravity gradient, which recent studies have demonstrated would make MONDian effects measurable3. However, LISA Pathfinder spacecraft is to be injected in a halo orbit around the first Sun-Earth Lagrangian point (L1), at more than one million kilometres from the Saddle Point. Therefore, it has been suggested to fly the satellite by the SP in an extension to its nominal mission. The challenge issued by this additional trajectory lies in the ΔV budget. While a total ΔV of approximately 3 km/s will be used to reach L1 from a LEO orbit, a budget of only 4 to 5 m/s is supposed to be remaining at the end of the nominal mission. Despite this harsh constraint, this study shows that reaching the SP from a given L1 halo orbit is feasible. Furthermore, as it has been emphasized that flying by the SP more than once would be very profitable for the experiment’s reliability, trajectories reaching twice the SP have been created. Nevertheless, these trajectories have not been designed as coming from a given halo orbit around L1, as it would be necessary once the exact orbit known during the nominal mission. On the contrary the solutions found, although respecting the specifications on LISA Pathfinder mission trajectory, are not independent of the halo orbit part of the trajectory. Until now, it has not been possible to find orbits reaching twice the SP from a given halo orbit. Therefore, the final aim of this study is to assess the possibility of designing a trajectory flying twice by the Sun-Earth SP, once the actual orbit of LISA Pathfinder spacecraft is known. To do so, orbits like the ones designed by ESA/ESOC for the nominal mission are used. Conditions under which such double SP flybys could happen are evaluated, and methods to design interesting orbits are defined

Multiple Sun–Earth Saddle Point flybys for LISA Pathfinder

LISA Pathfinder is an ESA mission due to be launched in the next two years. The gravity gradiometer onboard has the sensitivity required to test predictions by gravitational theories proposed as alternatives to Dark Matter such as TeVeS. Within the Solar System measurable effects are predicted only in the vicinity of gravitational saddle points (SP). For this reason it has been proposed to fly LPF by the Earth–Sun SP, at some 259,000 km from Earth. This could be done in an extension to the nominal mission which uses a Lissajous orbit about the Earth–Sun L1 point. The responsibility for LPF mission design lies with ESA/ESOC, who have designed the transfer trajectories, orbits about L1, and station keeping strategies. This article describes an analysis performed by Astrium to support a suggestion for a possible mission extension to a saddle point crossing. With only very limited fuel availability, reaching the saddle point is a significant challenge. In this article, we present recent advances in the work on trajectory design. It is demonstrated that reaching the SP is feasible once the LPF mission is completed. Furthermore, in a significant enhancement, it is demonstrated that trajectories including more than one SP flyby are possible, thus improving the science return for this proposed mission extension

Guidance of magnetic space tug

Magnetic tugging of a target satellite without thrust capacity can be interesting in various contexts, as for example End-Of-Life management, or to complete launchers capabilities. The aim is to gradually modify the orbit of the target by constantly exerting on it a magnetic force. To do so, the chaser is assumed equipped with a steerable magnetic dipole, able to create both forces and torques on the magnetic torque rods carried by the target. The chaser is also supposed to carry electric thrusters, creating a continuous force which modifies the orbit of the whole formation composed of chaser and target. The relative motions of both satellites are derived, in order to assess the feasibility of such a concept. Relative configuration (attitudes and position) trajectories are derived, which are compliant with the dynamics, and enable the chaser to tug the target. Considering targets in Low Earth Orbit (LEO), the magnetic field of the Earth is taken into account, modelled by the International Geomagnetic Reference Field (IGRF). The position of the magnetic torque rod of the target may not be located at its center of mass. This lever-arm is taken into account in the dynamics. As for every Electro-Magnetic Formation Flight concept developed in the literature, satellites involved in magnetic tugging are constantly subjected to torques, created by the Earth magnetic field and by the magnetic fields created by the other satellites in the formation. In this study, the solution chosen to face this problem is to take into account the attitude equilibrium of the satellites early in the guidance phase, in order to avoid having to wave the dipole, as it is generally done. Promising results are presented for different types of orbit, showing that the concept could be feasible in many different scenarios

Guidance and navigation for electromagnetic formation flight orbit modification

Electromagnetic formation flight (EMFF) is a recent concept, aiming to control relative motions of formation flying satellites using magnetic interactions. Each satellite is equipped with a magnetic dipole. The formation degree of cooperation,depending on the ability of each spacecraft to control its dipole and its attitude, has a great impact on the methods used to perform the formation GNC. This paper describes results obtained in the case of semi-cooperative EMFF composed of a chaser and a target, in the field of navigation and guidance. Preliminary studies indicate that the target relative position and attitude can be determined while measuring the magnetic field at the chaser location, and the acceleration of this chaser. Focus is also made on the guidance for the whole formation orbit transfer, if only the chaser has thrust capacity: theory shows that geometrical configurations exist for which the formation is in an equilibrium state

Guidance and Control of Magnetic Space Tug

Remorquer des satellites peut être utiles pour de nombreuses raisons : les désorbiter ou ré-orbiter, nécessaire dans le cas des satellites en fin de vie, ou pour finaliser les lancements par exemple. Dans ce cas, cette manœuvre augmenterait la capacité des étages supérieurs de lanceurs. Plusieurs moyens peuvent être envisagés pour modifier l’orbite d’un satellite cible grâce à un autre satellite. Parmi eux, les concepts sans contact sont intéressants, car ils fournissent un moyen d’éviter le besoin d’interfaces normalisées. Ils permettent ausside ne pas réaliser d’amarrages non coopératifs, qui représentent une grande difficulté. Enfin, ils contribuent à réduire le risque de créer de nouveaux débris par collision. Dans cette thèse, nous proposons d’utiliser les forces magnétiques pour remorquer le satellite cible. En effet, de nombreux satellites, en particulier en orbite terrestre basse, sont équipés de magnéto-coupleur, utilisés pour le contrôle d’attitude. Un satellite chasseur équipé d’un dipôle magnétique puissant pourrait donc générer des forces sur la cible. Cependant, la création d’une force entre deux dipôles magnétiques génère automatiquement des couples sur les deux dipôles. Par conséquent, la viabilité d’un remorqueur magnétique spatial n’est a priori pas assurée, étant donné qu’appliquer en permanence des couples sur les deux satellites ne serait pas acceptable.Satellite tugging can be undertaken for various reasons: de-orbiting or reorbiting,necessary in the case of satellites at the end-of-life, or for instance to finalise launches,in which case this manoeuvre would increase the capacity of launchers’ upper stages. Severalmeans can be considered to modify the orbit of a target satellite by tugging it with anothersatellite. Contact-less concepts are interesting, as they provide a way to avoid standardisedinterfaces and hazardous docking phases. They also help to prevent the creation of new debrisby reducing the risk of collision. In this thesis, we suggest using magnetic forces to tug the target. Indeed many satellites, especially in Low Earth Orbit, are equipped with Magnetic Torque Bars used for attitudecontrol. A chaser satellite equipped with a powerful magnetic dipole could hence generateforces on the target. However, creating a force between two magnetic dipoles automaticallycreates torque on both of them. Therefore, the feasibility of magnetic tugging is a priori notassured, considering that applying constant torques on both satellites would not be acceptable

Magnetic navigation for non-collaborative orbital rendezvous

Satellite servicing and active debris removal missions require an orbital rendezvous between a chaser satellite and a target satellite. If the considered target has not been designed to perform a rendezvous, the complexity of this manoeuvre is dramatically increased. In some of these non-cooperative rendezvous, the target satellite may not be able to stabilize itself or to communicate. It then falls to the chaser to determine the attitude and relative position of its target, in order to compute the manoeuvers it must undertake. This study shows that the chaser can use magnetic measurements to find the attitude and relative position of its target, as long as a fixed magnetic dipole is located in the target. As many satellites in LEO use magnetorquers to control their attitude, this assumption seems realistic. To obtain the pose, the measurements of the magnetic field and the magnetic field gradient produced by the dipole are combined with their analytical expression. This methodology gives the position of the dipole and the orientation of its axis, but does not give access to the orientation of the satellite around this axis. As the free motion of a body in the absence of a privileged rotation direction is determined by the tumbling equations, a Kalman filter is implemented in order to access this last degree of freedom. The performance of this navigation method is then evaluated studying the influence of several parameters, including the target’s distance and rotation speed. This shows that the estimated position and attitude of the target can be known with a good precision until a target-chaser distance of about 25 meters