Disposal Orbit Research Articles

Motion Control of Space Tug During Debris Removal by a Coulomb Force

One of the most promising methods of geosynchronous debris reorbiting is touchless actuation using electrostatic force. This paper investigates the dynamics and stability of two charged spacecraft formation when both spacecraft are charged with the same sign so that the active spacecraft (space tug) pushes the passive spacecraft (debris object) to a disposal orbit. A feedback control law is presented that uses thrusters of the space tug to control the distance between objects and aligns the line connecting the two objects along the orbital velocity vector of the space tug. The control law proposed requires measurements of the angle between the orbital velocity vector of the tug and the line connecting the tug and debris as well as the distance rate between the two craft. Stability criteria of the feedback control are developed in terms of inequalities for the parameters of the control. Numerical simulation shows how the parameters affect the stability of the system and propellant mass needed for the motion control to move the debris to a geosynchronous disposal orbit.

Flyby of large-size space debris objects and their transition to the disposal orbits in LEO

The article focuses on the flyby issue involving large-size space debris (LSSD) objects in low Earth orbits. The data on overall sizes of the known upper-stages and last stages of launch-vehicles make it possible to emphasize five compact groups of such objects from the Satellite catalogue in 600–2000km altitude interval. The flyby maneuvers are executed by a single space vehicle (SV) that transfers the current captured LSSD object to the specially selected circular or elliptical disposal orbit (DO) and after a period of time returns to capture a new one. The flight is always realized when a value of the Right Ascension of the Ascending Node (RAAN) is approximately the same for the current DO and for an orbit of the following LSSD object.Distinctive features of changes in mutual distribution of orbital planes of LSSD within a group are shown on the RAAN deviations’ evolution portrait. In case of the first three groups (inclinations 71°, 74° and 81°), the lines describing the relative orientation of orbital planes are quasi-parallel. Such configuration allows easy identification of the flyby order within a group, and calculation of the mission duration and the required total ΔV. In case of the 4th and the 5th groups the RAAN deviations’ evolution portrait represents a conjunction of lines chaotically intersecting. The article studies changes in mission duration and in the required ΔV depending on the catalogue number of the first object in the flyby order.The article also contains a comparative efficiency analysis of the two world-wide known schemes applicable to LSSD objects’ de-orbiting; the analysis is carried out for all 5 distinguished LSSD groups.

Risk to space sustainability from large constellations of satellites

The number of artificial objects in orbit continues to increase and, with it, a key threat to space sustainability. In response, space agencies have identified a set of mitigation guidelines aimed at enabling space users to reduce the generation of space debris by, for example, limiting the orbital lifetime of their spacecraft and launcher stages after the end of their mission. Planned, large constellations of satellites in low Earth orbit (LEO), though addressing the lack of basic internet coverage in some world regions, may disrupt the sustainability of the space environment enabled by these mitigation practices. We analyse the response of the space object population to the introduction of a large constellation conforming to the post-mission disposal guideline with differing levels of success and with different disposal orbit options. The results show that a high success rate of post-mission disposal by constellation satellites is a key driver for space sustainability.

Conjunction challenges of low-thrust geosynchronous debris removal maneuvers

The conjunction challenges of low-thrust engines for continuous thrust re-orbiting of geosynchronous (GEO) objects to super-synchronous disposal orbits are investigated, with applications to end-of-life mitigation and active debris removal (ADR) technologies. In particular, the low maneuverability of low-thrust systems renders collision avoidance a challenging task. This study investigates the number of conjunction events a low-thrust system could encounter with the current GEO debris population during a typical re-orbit to 300km above the GEO ring. Sensitivities to thrust level and initial longitude and inclination are evaluated, and the impact of delaying the start time for a re-orbiting maneuver is assessed. Results demonstrate that the mean number of conjunctions increases hyperbolically as thrust level decreases, but timing the start of the maneuver appropriately can reduce the average conjunction rate when lower thrust levels are applied.

A numerical investigation on the eccentricity growth of GNSS disposal orbits

We present the results of an extensive numerical exploration performed on the eccentricity growth in MEO associated with two possible end-of-life disposal strategies for GNSS satellites. The study calls attention to the existence of values of initial inclination, longitude of ascending node, and argument of perigee that are more advantageous in terms of long-term stability of the orbit. The important role of the initial epoch and a corresponding periodicity are also shown. The present investigation is influential in view of recent analytical and numerical developments on the chaotic nature of the region due to lunisolar perturbations, but also for the upcoming Galileo and BeiDou constellations.

Bi-objective optimization of a multiple-target active debris removal mission

The increasing number of space debris in Low-Earth Orbit (LEO) raises the question of future Active Debris Removal (ADR) operations. Typical ADR scenarios rely on an Orbital Transfer Vehicle (OTV) using one of the two following disposal strategies: the first one consists in attaching a deorbiting kit, such as a solid rocket booster, to the debris after rendezvous; with the second one, the OTV captures the debris and moves it to a low-perigee disposal orbit. For multiple-target ADR scenarios, the design of such a mission is very complex, as it involves two optimization levels: one for the space debris sequence, and a second one for the “elementary” orbit transfer strategy from a released debris to the next one in the sequence. This problem can be seen as a Time-Dependant Traveling Salesman Problem (TDTSP) with two objective functions to minimize: the total mission duration and the total propellant consumption.In order to efficiently solve this problem, ONERA has designed, under CNES contract, TOPAS (Tool for Optimal Planning of ADR Sequence), a tool that implements a Branch & Bound method developed in previous work together with a dedicated algorithm for optimizing the “elementary” orbit transfer. A single run of this tool yields an estimation of the Pareto front of the problem, which exhibits the trade-off between mission duration and propellant consumption. We first detail our solution to cope with the combinatorial explosion of complex ADR scenarios with 10 debris. The key point of this approach is to define the orbit transfer strategy through a small set of parameters, allowing an acceptable compromise between the quality of the optimum solution and the calculation cost. Then we present optimization results obtained for various 10 debris removal scenarios involving a 15-ton OTV, using either the deorbiting kit or the disposal orbit strategy.We show that the advantage of one strategy upon the other depends on the propellant margin, the maximum duration allowed for the mission and the orbit inclination domain. For high inclination orbits near 98 deg, the disposal orbit strategy is more appropriate for short duration missions, while the deorbiting kit strategy ensures a better propellant margin. Conversely, for lower inclination orbits near 65 deg, the deorbiting kit strategy appears to be the only possible with a 10 debris set. We eventually explain the consistency of these results with regards to astrodynamics.

Impacts of Hot Space Plasma and Ion Beam Emission on Electrostatic Tractor Performance

A recent proposed technique for geostationary debris mitigation is the electrostatic tractor. The tug vehicle approaches a debris object to within 20 m and emits a focused electron beam onto it. This results in a negative charge on the debris and a positive charge on the tug vehicle. Used in conjunction with low thrust, the electrostatic force is used to tow a debris object into a disposal orbit. In this paper, the impacts of geomagnetic storm activity on the charging of tug and debris are considered. The influence of electrons emitted from the debris (photoelectrons and secondary electrons) on tug charging is also considered. Both of these phenomena yield improved electrostatic tractor performance. The simultaneous emission of an electron and ion beam by the tug is also considered to improve tractor performance and enable charge transfer for scenarios where it fails when only an electron beam is used. The theoretical maximum electrostatic force that is possible with simultaneous emission is computed, and the results indicate that emitting both an electron and ion beam enables smaller tug vehicles to tow larger objects that could not otherwise be towed with only an electron beam.

Выбор низковысотных орбит захоронения и перевод на них выработавших свой ресурс космических аппаратов

Выбор низковысотных орбит захоронения и перевод на них выработавших свой ресурс космических аппаратов

Solar electric propulsion orbital debris ferry, vehicle concept and reference mission

The hazards of orbital debris in Low Earth Orbit (LEO) are well understood and concepts for Active Debris Removal (ADR) have been proposed in the literature, yet no mission has been launched to date. This is in part due to the lack of baseline space vehicle concepts. To give a point of departure design, a Solar Electric Propulsion (SEP) orbital debris ferry concept and operations approach has been developed. This concept provides a feasible solution to ADR that is currently ready for a demonstration mission. This approach uses a single space vehicle to independently and autonomously rendezvous with multiple LEO debris objects, secure, and ferry them to a sufficiently low disposal orbit. This mission architecture is enabled by flight-proven, relatively high-power SEP technologies and Autonomous Rendezvous and Docking (AR&D) algorithms and systems. The high Specific Impulse (Isp) of SEP enables low propellant requirements for removal of many debris objects with a single vehicle, and results in a low cost per target removed. Results from system sizing, low-thrust trajectory analysis, AR&D simulation, conceptual vehicle design, a concept of operations, and an implementation approach are provided. Results show that the SEP orbital debris ferry is a relatively low-cost and low-risk solution to mitigate the threat of orbital debris.

Analysis on the long-term dynamical evolution of the inclined geosynchronous orbits in the Chinese BeiDou navigation system

Five inclined geosynchronous orbit (IGSO) satellites with the inclination of about 55° in the Chinese BeiDou navigation system have been put in orbit until now. The Inter-Agency Space Debris Coordination Committee (IADC) has defined a geosynchronous orbit (GEO) protected region and recommended that the GEO satellite should be maneuvered to a disposal orbit high enough at end-of-mission to remain above the GEO protected region. The recommended disposal altitude is at least 235km+(1000·CR·A/M) higher than the perigee altitude of the GEO satellite, where CR and A/M are radiation pressure coefficient and area-to-mass ratio respectively. Whether this recommendation is also adequate for the disposal of these IGSO satellites in the Chinese BeiDou navigation system at end-of-mission? And if not, is there any other possible strategy to do? In view of these considerations, the long-term dynamical evolution of these IGSO satellites is investigated by both theoretical analysis and numerical computation methods in this paper. Some qualitative orbital evolution characteristics and quantitative result of variation ranges of the semi-major axis a, the inclination i and the eccentricity e are presented respectively. Based on these results, a possible mitigation strategy to reduce the orbital lifetime of the IGSO satellites after end-of-mission is proposed.

Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration points L1 and L2 are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth–Moon system. This isomorphic mapping of trajectories allows the identification and intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first at L1, and the second at L2, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit at L1 and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining suitable, convenient end-of-life strategies for spacecraft orbiting the Earth. Seven distinct options are identified, and lead to placing the spacecraft into the final disposal orbit, which is either (a) a lunar capture orbit, (b) a lunar impact trajectory, (c) a stable lunar periodic orbit, or (d) an outer orbit, never approaching the Earth or the Moon. Two remarkable properties that relate the velocity variations with the spacecraft energy are employed for the purpose of identifying the optimal locations, magnitudes, and directions of the velocity impulses needed to perform the seven transfer trajectories. The overall performance of each end-of-life strategy is evaluated in terms of time of flight and propellant budget.

Cylindrical isomorphic mapping applied to invariant manifold dynamics for Earth–Moon Missions

Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\).

The classical Laplace plane as a stable disposal orbit for geostationary satellites

The classical Laplace plane is a frozen orbit, or equilibrium solution for the averaged dynamics arising from Earth oblateness and lunisolar gravitational perturbations. The pole of the orbital plane of uncontrolled GEO satellites regress around the pole of the Laplace plane at nearly constant inclination and rate. In accordance with Friesen et al. (1993), we show how this stable plane can be used as a robust long-term disposal orbit. The current graveyard regions for end-of-life retirement of GEO payloads, which is several hundred kilometers above GEO depending on the spacecraft characteristics, cannot contain the newly discovered high area-to-mass ratio debris population. Such objects are highly susceptible to the effects of solar radiation pressure exhibiting dramatic variations in eccentricity and inclination over short periods of time. The Laplace plane graveyard, on the contrary, would trap this debris and would not allow these objects to rain down through GEO. Since placing a satellite in this inclined orbit can be expensive, we discuss some alternative disposal schemes that have acceptable cost-to-benefit ratios.

Long-term evolution of Galileo operational orbits by canonical perturbation theory

Galileo operational orbits are slightly affected by the 3 to 5 tesseral resonance, an effect that can be much more important in the case of disposal orbits. Proceeding by canonical perturbation theory we show that the part of the long-term Hamiltonian corresponding to the non-centralities of the Earth's gravitational potential can be replaced by an intermediary that shows the pendulum dynamics of the 3 to 5 tesseral resonance problem. Inclusion of lunisolar perturbations requires a semi-analytical integration, which is compared with the corresponding results from the well-established Draper Semi-analytical Satellite Theory.

A reorbiter for large GEO debris objects using ion beam irradiation

In recent years, space debris problems have become very serious. The worst case occurs in the low Earth orbit (LEO) region, where debris-to-debris collisions generate new debris. The situation in the geostationary orbit (GEO) region is not as bad as that in the LEO. The debris problem in the GEO region, however, should not be left as it is because the GEO is unique and has few debris-cleansing modes. Thus, we proposed a concept for a reorbiter to reorbit large GEO debris objects such as satellites and rocket upper stages left in orbit after the ends of their missions. This concept is based on the idea of thrusting a debris object by irradiating it with an ion beam. The reorbiter, equipped with two ion engines, approaches a debris object, and the ion beam exhausted from one of the ion engines irradiates and thrusts it to change its orbit. The other engine on the opposite side is operated so that the reorbiter follows the debris object. Their orbits are raised in a spiral to a disposal orbit approximately 300km higher. After that, the reorbiter returns to GEO to approach another debris object. This system can operate without catching debris objects; thus, it can be applied to a wide range of debris objects without regard to their shapes or rotations. A mission scenario was made to conduct efficient maneuvers. In the GEO region, a number of debris objects are distributed on orbit planes close to each other, and they can be reorbited one after another using a single reorbiter. For a typical model mission, the mission time and the total impulse of the ion engines were calculated. The results show that six debris objects can be reorbited in 170 days. The reorbiter has a targeted launch mass of 2500kg and 6.9kW of total power. The ion beam convergence, the effects of ion beam irradiation, and non-cooperative rendezvous were recognized as the critical issues of this system. A highly converged beam is required to make efficient debris irradiation. Numerical calculations and basic experiments gave a feasibility of the required irradiation efficiency of over 25%. The irradiation of debris objects may cause sputtering of their surfaces and depositions of the back-sputtered materials on the reorbiter surface. The data were obtained experimentally to evaluate the effects of the depositions, especially on solar cells. The results indicated no serious contamination problems. Preliminary studies were conducted on the approach to an uncollaborative object and the maintenance of the separation distance.

Utilization of Residual Helium to Extend Satellite Lifetimes and Mitigate Space Debris

A new electric propulsion device concept takes advantage of residual helium gas that is trapped in the chemical propellant feed system and currently unused at end of life. The helium ion thruster provides additional propellant resources to extend satellite lifetimes and transfer geostationary orbit space assets to ultrasafe disposal orbits. The predicted capability, if fully allotted to the disposal, allows for perigee heights above the geostationary altitude that are one order of magnitude greater than existing international guidelines of 250 km. Furthermore, the proposed helium ion thruster concept makes the classic propellant gauge uncertainty problem moot, as satellite operators could use all of their conventional propellant for nominal station-keeping operations. The helium ion thruster concept therefore mitigates future space debris arising from depleted assets in the geostationary orbit belt through both aggressive orbit raising and depressurization of satellites at end of life. An analysis of the helium ion thruster theoretical performance shows that the device could raise the altitude of an end-of-life 2500 kg, 5 kW spacecraft by 2200 km in two months using 2 kg of residual helium.

The effect of secular resonances on the long-term orbital evolution of uncontrollable objects on satellite radio navigation systems in the MEO region

We present the results of the study of long-term orbital evolution of space debris objects, formed from end-of-life space vehicles (SV) of satellite radio navigation systems in the medium Earth orbit (MEO) region. Dynamical features of the evolution of objects in this region have been studied on the basis of 20-year laser surveillance with the Etalon-1 and Etalon-2 satellites and the results of numerical simulation of the long-term evolution of operating and disposal orbits of uncontrolled GLONASS and GPS SVs. It is shown that perturbations from secular lunisolar resonances produce an eccentricity growth for orbits with inclinations chosen for navigation constellations; this significantly changes the positions of these orbits in space and results in the ingress of end-of-life objects into the area of operating SVs.

Geosynchronous Large Debris Reorbiter: Challenges and Prospects

An elegant solution is proposed to an old problem of how to remove expired or malfunctioning satellites from the geosynchronous belt. Previous “space-tug” concepts describe a scenario where one craft (the tug) docks with another (debris) and then boosts that object to a super-synchronous orbit. The most challenging aspect of these concepts is the very complex proximity operations to an aging, possibly rotating and, probably, non-cooperative satellite. Instead, the proposed method uses an elegant blend of electrostatic charge control and low-thrust propulsion to avoid any contact requirement. The Geosynchronous Large Debris Reorbiter (GLiDeR) uses active charge emission to raise its own absolute potential to 10’s of kilovolts and, in addition, directs a stream of charged particles at the debris to increase its absolute potential. In a puller configuration the opposite polarity of the debris creates an attractive force between the GLiDeR and the debris. Pusher configurations are feasible as well. Next, fuel-efficient micro-thrusters are employed to gently move the reorbiter relative to the debris, and then accelerate the debris out of its geosynchronous slot and deposit it in a disposal orbit. Preliminary analysis shows that a 1000 kg debris object can be re-orbited over two-four months. During the reorbit phase the separation distance is held nominally fixed without physical contact, even if the debris is tumbling, by actively controlling the charge transfer between the reorbiter and the debris. Numerical simulations are presented illustrating the expected performance, taking into account also the solar radiation pressure.

Post-disposal orbital evolution of satellites and upper stages used by the GPS and GLONASS navigation constellations: The long-term impact on the Medium Earth Orbit environment

The long-term evolution and environmental impact in MEO of all the abandoned spacecraft and upper stages associated with the GPS and GLONASS navigation constellations were analyzed. The orbits of the disposed objects, as of 1 May 2011, were propagated for 200 years and snapshots of their evolving distribution were obtained, together with an estimation of the changing collision probability with the spacecraft of the operational navigation systems existing or planned in MEO, i.e., GLONASS, GPS, Beidou and Galileo. The probability that the abandoned objects considered will collide with the operational spacecraft of the navigation constellations is very low, even taking into account the intrinsic eccentricity instability of the disposal orbits. Assuming the present or envisaged configuration of the constellations in MEO, the probability of collision, integrated over 200 years, would be <1/300 with a GLONASS spacecraft, <1/15,000 with a GPS or Beidou spacecraft, and <1/250,000 with a Galileo spacecraft. The worst disposal strategy consists in abandoning satellites and upper stages close to the altitude of the operational constellation (GLONASS), while a re-orbiting a few hundredkm away (GPS) is able to guarantee an effective long-term dilution of the collision risk, irrespective of the eccentricity instability due to geopotential and luni-solar perturbations. The disposal strategies applied so far to the GPS satellites should be able to guarantee for at least a few centuries a sustainable MEO environment free of collisions among intact objects. Consequently, there would be no need to adopt disposal schemes targeting also the optimal value of the eccentricity vector. However, it should be pointed out that the GPS disposal strategy was devised well in advance of the Beidou constellation announcement, so most of the abandoned satellites were re-orbited fairly close to the altitude of the new Chinese system. A new re-orbiting approach will be therefore needed in the future.

Orbital evolution of the first upper stages used for the new European and Chinese navigation satellite systems

The solutions adopted for the disposal of the upper stages used to put in orbit the first satellites of the new European (Galileo) and Chinese (Beidou) navigation constellations were analyzed. The orbit evolution of the rocket bodies was modeled for 200 years, taking into account all relevant perturbations, and the chosen disposal options were evaluated in terms of their long-term consequences for the debris environment. The results obtained, when applicable, were also discussed in the context of the eccentricity instability problem, pointed out in previous studies. In addition, the long-term evolution of the fragments resulting from a Beidou rocket body breakup, and of simulated high area-to-mass ratio objects released in the disposal orbits of the first two Galileo upper stages, was investigated. Eight out of ten Beidou upper stages were found to have an orbital lifetime <25 years and the other two resulted in a dwell time of approximately 6 years below 2000 km. It was also found that the perigee heights of the two upper stages used to deploy the first Galileo test spacecraft will remain more than 169 km above the constellation nominal altitude, never crossing the existing or planned navigation systems. In spite of an inclination resonance possibly leading to the exponential growth of the eccentricity over several decades, the optimal choice of the disposal orbital elements was able to prevent such an outcome, by maintaining the orbit nearly circular. Therefore, the upper stage disposal strategies used so far for Beidou and Galileo have generally been quite successful in averting the long-term interference of such rocket bodies with the navigation constellations, provided that accidental breakups are prevented.