63rd International Astronautical Congress, Naples, Italy. Copyright ©2012 by the International Astronautical Federation. All rights reserved. IAC-12-D9.2.8 ORBITAL DEBRIS MITIGATION THROUGH DEORBITING WITH PASSIVE ELECTRODYNAMIC DRAG Denis Zanutto, CISAS – “G. Colombo” Center of Studies and Activities for Space, University of Padova, Italy, [email protected] Enrico C. Lorenzini, Department of Industrial Engineering, University of Padova, Italy. Also member of CISAS “G. Colombo”. [email protected] Riccardo Mantellato, CISAS – “G. Colombo” Center of Studies and Activities for Space, University of Padova, Italy, [email protected] Giacomo Colombatti, CISAS – “G. Colombo” Center of Studies and Activities for Space, University of Padova, Italy, [email protected] Antonio Sanchez-Torres, Universidad Politécnica de Madrid, Spain, [email protected] The increase of orbital debris and the consequent proliferation of smaller objects through fragmentation are driving the need for mitigation strategies. The issue is how to deorbit the satellite with an efficient system that does not impair drastically the propellant budget of the satellite and, consequently, reduces its operating life. We have been investigating, in the framework of a European-Community-funded project, a passive system that makes use of an electrodynamics tether to deorbit a satellite through Lorentz forces. The deorbiting system will be carried by the satellite itself at launch and deployed from the satellite at the end of its life. From that moment onward the system operates passively without requiring any intervention from the satellite itself. The paper summarizes the results of the analysis carried out to show the deorbiting performance of the system starting from different orbital altitudes and inclinations for a reference satellite mass. Results can be easily scaled to other satellite masses. The results have been obtained by using a high-fidelity computer model that uses the latest environmental routines for magnetic field, ionospheric density, atmospheric density and a gravity field model. The tether dynamics is modelled by considering all the main aspects of a real system as the tether flexibility and its temperature-dependent electrical conductivity. Temperature variations are computed by including all the major external and internal input fluxes and the thermal flux emitted from the tether. The results shows that a relatively compact and light system can carry out the complete deorbit of a relatively large satellite in a time ranging from a month to less than a year starting from high LEO with the best performance occurring at low orbital inclinations. I. INTRODUCTION (1) the motion of the conducting tether with respect to The continuous growth of orbital debris constitutes a the planet’s magnetic field and (2) the presence of the serious and dangerous risk for space missions around plasma that allows an electrical current to flow in the the Earth and, if not mitigated, in the next future it could tether. The system collects electrons from the compromise the launch of new satellites. To help solve ionosphere at its anodic end (the conductive tether itself this problem and guarantee the safety of key regions of left bare in our case [9]) and emits electrons through a space the Inter-Agency Debris Coordination Committee plasma contactor at the cathodic end. The current that (IADC) has defined guidelines [1] to follow after the circulates in the tether produces the Lorentz drag force end of life of a satellite in order to mitigate the growth through the interaction with the Earth’s magnetic field. of orbital debris. The guidelines call for spacecraft to be Power can also be tapped from the tether for running the either moved to a “disposal orbit” if in GEO or cathode and other ancillary on-board equipment. deorbited within 25 years if in LEO. Such a system can carry out a propellantless and For satellites in LEO a very interesting concept for relatively quick reentry of satellites in LEO because the deorbiting is represented by the electrodynamic tethered Earth's environment is particularly favourable to (EDT) system (see among others Refs. [2-8]). In fact operating an EDT. In fact the high electron density one of the most significant features of these systems is surrounding the planet at LEO orbits and the magnetic their ability to extract electric power from the field generate a non-negligible induced potential, which plasmasphere of a planet and to produce a sizeable enables the collection of ionospheric electrons at the electrodynamic drag. This outstanding characteristic is anodic end of the tether. Consequently, when the due to the interaction of the tether with the environment: electric circuit is closed the interaction between the IAC-12-D9.2.8 Page 1 of 9 63rd International Astronautical Congress, Naples, Italy. Copyright ©2012 by the International Astronautical Federation. All rights reserved. charged particles and the magnetic field generates a massless elastic springs and dampers. The model spatial considerable Lorentz force that progressively lowers the resolution improves with the number of nodes orbit of the satellite. discretizing the wire, but this increases rapidly the The dynamics of EDTs depends on several factors: computational time required for the solution. So the gravity gradients forces, electrodynamics interaction number of lumped masses is a trade-off between and to a lesser extent thermal variations [10]. The adequate spatial resolution [16] and the minimization of Earth's gravitational attraction tends to stabilize the the integration time without loss of fundamental satellite keeping the wire taught and aligned with the information about the critical aspects of the system. local vertical, while perturbations (mainly due to The instantaneous state J of each node is defined by Lorentz force, aerodynamic drag, and solar pressure) seven degree of freedom: the position and velocity change its orbit. Specifically, the electrodynamic force vectors and the temperature. pumps continuously energy into the system attitude motion, increases the libration dynamics, and bends the r tether exciting the natural modes of the lateral motion forcing an uncontrolled EDT to go into instability [11]. Ji v [1] At last the temperature changes the electric properties of T the wire and, consequently, affects the current intensity. In this paper we presents some results obtained with a new orbital simulator built to investigate in details the The motion followed by every lump mass, dynamical behaviour of an EDT during deorbiting. The discretizing the wire, depends on all the forces acting on code uses a lump-mass approach to model the deflection the system as shown in Eqn. (2). In a detailed analysis of the wire to simulate the overall dynamics that is the contributions are several because the dynamics is strongly influenced by the tether lateral motion. affected by various interactions with the surrounding Parametric analyses have been carried out to study the environment. We can define three main external system performance for different scenarios, in particular contributions (gravitational, electrodynamic and by varying the orbital parameters and the tether size. aerodynamic forces) and one internal due to the visco- Moreover, a passive control technique has been utilized elastic properties of the tether that connects contiguous to provide stability to the system to assure a complete lumps. The temperature variation of each tether segment deorbiting. depends on all the input and output thermal fluxes affecting it. II. TETHERED SYSTEM MODEL There are two main models to describe the dynamics v of a tethered system: the first is simplified and models the satellite as a rigid dumbbell [12] with an 1 J F F F Y inextensible wire; the second is more accurate and i m gr el a [2] i considers the wire as flexible and extensible [13,14]. 1 The dumbbell model is very useful during preliminary Q studies to obtain quickly information about the system, cmi investigate its performance and identify operative orbital scenarios. On the other hand, the flexible wire In Eqn. (2) c is the specific heat capacity of the wire model gives a more detailed description of the and mi the mass of each element used to discretize the dynamics, modelling also the lateral bending caused by tethered system. electrodynamic and aerodynamic forces acting on the tether. The model provides a complete representation of Gravitational Force the tether instantaneous shape and includes a number of Each element of tether is subjected to the modes (and modal frequencies) as high as the number of gravitational attraction. To investigate the gravitational mass lumps for both the lateral and longitudinal effects accurately we adopt a reference model that dynamics of the tether. For these reasons in the includes also the higher harmonics of the gravitational following we will treat the tether as flexible in order to potential, which are mostly important at low altitudes. A include the lateral dynamics that plays an important role 4x4 gravity field model [17] provides enough accuracy in the stability analysis [15]. for describing the orbital dynamics of the whole system. In summary the gravitational force will have two main II.I Mathematical Model contributions: one to model the homogenous Earth An effective strategy to model the system dynamics, gravity attraction and the other representing the uneven avoiding mathematical