Geostationary Ring Research Articles

Displaced geostationary orbits using hybrid low-thrust propulsion

In this paper, displaced geostationary orbits using hybrid low-thrust propulsion, a complementary combination of Solar Electric Propulsion (SEP) and solar sailing, are investigated to increase the capacity of the geostationary ring that is starting to become congested. The SEP propellant consumption is minimized in order to maximize the mission lifetime by deriving semi-analytical formulae for the optimal steering laws for the SEP and solar sail accelerations. By considering the spacecraft mass budget, the performance is also expressed in terms of payload mass capacity. The analyses are performed both for the use of pure SEP and hybrid low-thrust propulsion to allow for a comparison. It is found that hybrid low-thrust control outperforms the pure SEP case both in terms of payload mass capacity and mission lifetime for all displacements considered. Hybrid low-thrust propulsion enables payloads of 255–487 kg to be maintained in a 35 km displaced orbit for 10–15 years. Adding the influence of the J 2 and J 2 , 2 terms of the Earth's gravity field has a small effect on this lifetime, which becomes almost negligible for small values of the sail lightness number. Finally, two SEP transfers that allow for an improvement in the performance of hybrid low-thrust control are optimized for the propellant consumption by solving the accompanying optimal control problem using a direct pseudospectral method. The first type of transfer enables a transit between orbits displaced above and below the equatorial plane, while the second type of transfer enables customized service for which a spacecraft is transferred to a Keplerian parking orbit when geostationary coverage is not needed. While the latter requires a modest propellant budget, the first type of transfer comes at the cost of an almost negligible SEP propellant consumption.

Astrometric positioning and orbit determination of geostationary satellites

In the project titled “Astrometric Positioning of Geostationary Satellite” (PASAGE), carried out by the Real Instituto y Observatorio de la Armada (ROA), optical observation techniques were developed to allow satellites to be located in the geostationary ring with angular accuracies of up to a few tenths of an arcsec. These techniques do not necessarily require the use of large telescopes or especially dark areas, and furthermore, because optical observation is a passive method, they could be directly applicable to the detection and monitoring of passive objects such as space debris in the geostationary ring. By using single-station angular observations, geostationary satellite orbits with positional uncertainties below 350 m (2 sigma) were reconstructed using the Orbit Determination Tool Kit software, by Analytical Graphics, Inc. This software is used in collaboration with the Spanish Instituto Nacional de Técnica Aeroespacial. Orbit determination can be improved by taking into consideration the data from other stations, such as angular observations alone or together with ranging measurements to the satellite. Tests were carried out combining angular observations with the ranging measurements obtained from the Two-Way Satellite Time and Frequency Transfer technique that is used by ROA’s Time Section to carry out time transfer with other laboratories. Results show a reduction of the 2 sigma uncertainty to less than 100 m.

Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence

This paper provides a hamiltonian formulation of the equations of motion of an artificial satellite or space debris orbiting the geostationary ring. This theory of order 1 has been formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination. The theory accounts for the influence of the Earth gravity field expanded in spherical harmonics, paying a particular attention to the resonance occurring for geosynchronous objects. The luni-solar perturbations are also taken into account. We present the resonant motion and its main characteristics: equilibria, stability, fundamental frequencies and width of the resonant area by comparison with a basic analytical model. Finally, we show some results concerning the long term dynamics of a typical space debris under the influence of the gravitational field of the Earth and the luni-solar interactions.

Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios

This paper provides a Hamiltonian formulation of the averaged equations of motion with respect to short periods (1 day) of a space debris subjected to direct solar radiation pressure and orbiting near the geostationary ring. This theory is based on a semi-analytical theory of order 1 regarding the averaging process, formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination, truncated at an arbitrary high order. First, the dynamical evolution of space debris released near the geostationary ring, with area-to-mass ratios as high as 40 m 2/kg is analyzed within the framework of mid-term evolution (∼1 year) as well as long-term evolution (several decades). This study is carried out, using both simplified analytical models to clarify some properties, as well as our complete semi-analytical theory which leads to an accurate understanding of the mid-term and long-term evolution of the eccentricity and of the inclination. We also analyzed the coupling equations between the eccentricity and the inclination, considering a doubly averaged analytical model. Second, we also focused our attention on the comparison of various direct radiation pressure approximations in order to assess their consequences. Last, this paper claims to be the continuation and the counterpart of previous papers dealing with geosynchronous orbits and radiation pressure, that is Anselmo and Pardini (2005) [Anselmo, L., Pardini, C. Orbital evolution of geosynchronous objects with high area-to-mass ratios. In: Danesy, D. (Ed.), Proceedings of the Fourth European Conference on Space Debris, ESA SP-587. ESA Publications Division, Noordwijk, The Netherlands, pp. 279–284, 2005] and Valk et al. (submitted for publication) [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence, Advances in Space Research, submitted for publication].

Solar Sail Formation Flying Around Displaced Solar Orbits

R ECENTLY, attention has been focused on solar sail missions, such as the new artificial Lagrange points created by solar sails to be used to provide early warning of solar plasma storms, before they reach Earth [1,2]. There are several prior references with regard to such orbits in the literature. As early as 1929, Oberth mentioned in his study that solar radiation pressure would displace a reflector in an Earth polar orbit in the anti-sun direction, so that the orbit plane did not contain the center-of-mass of the Earth [3]. Later, in 1977, Austin et al. [4] noted that propulsive thrust can be used to displace the orbit of an artificial body, but only small displacements were considered for spacecraft proximity operations, and no analysis of the problem was provided. Similarly, Nock suggested a displaced orbit above Saturn’s rings for in situ observation, however, again no analysis was given [3]. In 1981, Forward [5] considered a displaced solar sail north or south of the geostationary ring. However, because he did not use an active control, subsequent analysis has criticized thiswork and claimed that such orbits were impossible. More recently, McInnes and Simmons have done work in which large families of displaced orbits were found by considering the dynamics of a solar sail in a rotating frame [6], and the dynamics, stability, and control of different families of displaced orbits were investigated in detail [7,8]. Based on McInnes’ and Simmons’ work [6], Molostov and Shvartsburg considered a more realistic solar sail model with nonperfect reflectivity and discussed the effect of finite absorption of the sail on the displaced orbits [9,10]. However, studies of the relative motion of solar sails are rare in the literature. The original idea of formation flying around a displaced orbit considered in this note comes from the concept of combining a displaced orbit with formation flying to achieve greater resolution than a single sail for science missions. This note outlines the characteristics of the relative motion around a displaced solar orbit and proposes some possible control strategies. Because the relative distance between the sails is very small compared with the distance from the sun to the sails, the relative equation of motion is linearized in the vicinity of a displaced solar orbit. Based on the linearized equation, two types of formations, seminatural and controlled formations, are discussed. The seminatural formations are performed with only sail attitude variations, but configurations of the relative orbits strongly depend on the orbit of the leader sail. Therefore, more complex controllers are adopted to build more sophisticated formations to meet special demands on the relative orbit configurations.

Properties of the high area-to-mass ratio space debris population at high altitudes

In the framework of its space debris research activities ESA established an optical survey program to study the space debris environment at high altitudes, in particular in the geostationary ring and in the geostationary transfer orbit region. The Astronomical Institute of the University of Bern (AIUB) performs these surveys on behalf of ESA using ESA’s 1-m telescope in Tenerife. Regular observations were started in 1999 and are continued during about 120–140 nights per year. Results from these surveys revealed a substantial amount of space debris at high altitudes in the size range from 0.1 to 1 m. Several space debris populations with different dynamical properties were identified in the geostationary ring. During the searches for debris in the geostationary transfer orbit region a new population of objects in unexpected orbits, where no potential progenitors exist, was found. The orbital periods of these objects are clustered around one revolution per day; the eccentricities, however, are scattered between 0 and 0.6. By following-up some of these objects using the ESA telescope and AIUB’s 1-m telescope in Zimmerwald, Switzerland, it was possible to study the properties of this new population. One spectacular finding from monitoring the orbits over time spans of days to months is the fact that these objects must have extreme area-to-mass ratios, which are by several orders of magnitudes higher than for ‘normal-type’ debris. This in turn supports the hypothesis that the new population actually is debris generated in or near the geostationary ring and which is in orbits with periodically varying eccentricity and inclination due to perturbations by solar radiation pressure. In order to further study the nature of these debris, multi-color and temporal photometry (light curves) were acquired with the Zimmerwald telescope. The light curves show strong variations over short time intervals, including signals typical for specular reflections. Some objects exhibit distinct periodic variations with periods ranging from 10 to several 100 s. All this is indicative for objects with complicated shapes and some highly reflective surfaces.

Estimating the number of debris in the geostationary ring

Two thousand seven hundred and ninety uncorrelated targets brighter than magnitude 18.5 were detected by the European Space Agency (ESA) 1-m space debris telescope at Tenerife during more than 1000 observation hours between February 2001 and December 2004. The number of detections can be approximated by a Gaussian distribution. Probabilities to detect individual objects during an observation campaign are determined by propagating 10 debris clouds of the ESA MASTER model and two other fictitious background populations. Based on these probabilities, a 95% confidence interval for the total number of unknown debris in the geostationary ring is derived. It is estimated that there are between 450 and 540 uncatalogued objects brighter than visual magnitude 18.5.

The Orbital Perturbation Environment for the COBRA and COBRA Teardrop Elliptical Constellations

Elliptical, non-geostationary satellite orbit (NGSO) satellite constellations have been proposed as a solution to the problem of the shortage of slots in the Geostationary Ring for new communications satellites. These elliptical constellations have the potential to greatly multiply the available space real estate without interfering with the existing GEO satellites. These constellations employ eight-hour “leaning” elliptical orbits, operating at approximately the critical inclination of 63.4 degrees. The three active arcs of a single satellite have a ground trace that resembles a coiled cobra, hence the acronym name COBRA. Due to the exact repeat ground-track, with three orbital revolutions for each rotation of the Earth, these COBRA orbits experience deep tesseral resonance perturbations with the 3rd, 6th, and other (multiples of three) order geopotential harmonic coefficient pairs. These resonant perturbations are dependent on the RAAN of the particular ground-track. These orbits also experience strong perturbations due to the lunar-solar point masses. The semi-analytical satellite theory DSST is used to explore both the tesseral resonance and lunar-solar point mass perturbations.

The situation in the geostationary ring

For more than 25 years, the practice of reorbiting of a geostationary satellite at the end of its mission in order to protect the geostationary orbit (GEO) environment has been recommended and performed by a number of operators. In recent years, an internationally recognised re-orbiting altitude has been defined by the Inter-Agency Space Debris Coordination Committee (IADC). Based on orbital data contained in the DISCOS database, the situation on the geostationary ring is analysed. In January 2004, from 1036 catalogued objects passing through the geostationary region, 340 are controlled within their allocated longitude slots, 395 are drifting above, below or through GEO, and 140 are in a libration orbit. In the periods 1997–2003, 103 spacecraft reached their end of life; 34 were reorbited in compliance with the IADC recommendation, 35 were reorbited below the minimum recommended altitude, and 34 were abandoned without any end-of-life disposal manoeuvre. Apart from these catalogued objects, the ESA 1-m telescope has observed many smaller debris (down to 10–15 cm) in this orbital region representing a collision risk for GEO spacecraft which is difficult to quantify.

Orbit improvement for GTO objects using follow-up observations

The Astronomical Institute of the University of Bern was and is conducting several search campaigns for space debris in the geostationary ring (GEO) and the geostationary transfer orbit (GTO). First tests to build up a catalogue of satellites and space debris were performed recently. As the discovery observations of an object usually cover a time interval of a few minutes only, the first orbits determined are assumed to be circular. For GEO objects a circular orbit is a rather good approximation. This is certainly not the case for GTO objects. Nevertheless, a circular orbit seems to be an acceptable approximation for a short time interval around the observations. The first orbits can be used to acquire follow-up observations, which allow the determination of elliptical orbits. The maximum allowed time span between the detection and the follow-up for a successful recovery is found using simulated GTO orbits and observations. Further follow-up observations are simulated in order to study the orbit improvement process and the required force model. The accuracy of orbits needed to build up a catalogue is studied. The simulations are compared to the results achieved with observations acquired by the 1 m telescope on Tenerife.

Performance estimation for GEO space surveillance

For space surveillance Europe is currently strongly depending on external sources. Although some European radar and optical facilities for space object tracking exist, there is no operational European space surveillance system. An ESA-funded feasibility study for a future independent European space surveillance capability was performed recently. Some of the main conclusions are presented here. We discuss the surveillance of the geostationary ring (GEO) by evaluating existing and newly designed optical ground-based sensors in terms of their performance. The main performance-related issues – the coverage of the GEO ring and the minimum detectable objects size – are discussed. In order to perform detailed simulations, an observation strategy was defined and algorithms for the correlation of objects with a catalogue and for the maintenance of that catalogue were developed. We used the ESA PROOF software to estimate the sensor performance and AIUB tools to simulate the catalogue correlation. The performance was validated using data from campaigns performed with the ESA Space Debris Telescope at Tenerife, Spain.

Population evolution in the GEO vicinity

The geostationary orbit is now in use for nearly 40 years. Due to the absence of major energy dissipating mechanisms, the object population in the GEO environment steadily grew during this time. Currently, a total of 934 known objects permanently resides within the GEO region, if GEO objects are defined by a mean motion between 0.9 and 1.1 (corresponding to GEO ± 2800 km) and an inclination below 20°. Additionally, two explosion events are confirmed within the geostationary ring, which further enlarge the already existing population consisting of payloads and upper stages. Recent observation results obtained by the ESA Space Debris Telescope (SDT) at Tenerife show strong indications for even more fragment clouds. Since the geostationary ring can be seen as a unique resource, which is not protected by any significant self-cleaning effect, a monitoring of the object environment in the vicinity of this orbit is mandatory. In a first step, this paper characterizes the history and current state of the GEO environment. Besides to explosion prevention, the transfer of satellites to a graveyard orbit about 300 km above the geostationary altitude is the most effective means to preserve GEO. Although this procedure is internationally recommended, only about 20% of the retiring spacecraft is currently brought to a sufficiently high orbit. Another 40% performs a re-orbiting, but is ending up in an orbit in the direct vicinity of the GEO ring or even touching or crossing it. In the future, one possibility to mitigate the population growth could be a dedicated vehicle transferring several large objects to the graveyard area at end of mission. Assuming a future traffic model and different scenarios for re-orbiting and removal, the future evolution of the large object population in and near GEO is assessed.

Optical observations of space debris in GEO and in highly-eccentric orbits

The space debris population in low Earth orbits (LEO) has been extensively studied during the last decade and reasonable models covering all size ranges were produced. Information on the distribution of objects in the geostationary ring (GEO), however, is still comparatively sparse. Until quite recently the population of man-made objects in GEO had to be inferred solely from the about 900 continuously tracked objects and the modeling of the two explosions known to have occurred in GEO. Optical observations from the last two years performed with ESA's 1-m telescope at the Teide observatory in Tenerife changed the situation substantially. A hitherto unknown but significant population of small-size objects with diameters as small as ten centimeters has been detected in GEO. Objects in highly-eccentric orbits crossing the GEO region, in particular objects in geostationary transfer orbits (GTO), also contribute to the density of space debris in GEO. This family is even less well known than the GEO population, although many explosion events were reported in this orbital region. The paper will summarize recent results from the ESA GEO survey and describe the techniques and first results of a trial GTO survey.

Orbit improvement for GEO objects using follow-up observations

During the preceding years, the Astronomical Institute of the University of Bern (AIUB) was conducting several search campaigns for space debris in the geostationary ring (GEO). The optical observations were performed with a 1-m Ritchey–Chrétien telescope on Tenerife. A substantial population of unknown, small-sized objects was found in these surveys. For all objects a circular orbit was determined using the discovery observations. In order to test the hypothesis of circular orbits – which most likely is not valid for all detected objects – it is necessary to determine eccentricities for at least a part of the population. This in turn requires follow-up observations of the detected objects. The improved orbits resulting from follow-up observations also increase the probability for a successful recovery of the object in subsequent nights. Eventually, follow-up observations over several nights yield “secure” orbits allowing to build up a catalogue. In this paper we present the results of the determination of circular orbits and the orbit improvement process yielding elliptical orbits. The accuracy of the determined orbits is discussed, and the orbit quality is tested with follow-up observations after a few nights. The orbital elements are compared with those based on the assumption of circular orbits.

The end-of-life disposal of the Italian geostationary satellites

To date, four Italian satellites have been launched in geostationary orbit: SIRIO, Italsat 1, Italsat 2, and SICRAL. Of these, only the latter is still operational: SIRIO was abandoned close to the geopotential equilibrium point at 75°E in 1985; Italsat 1 was re-orbited above the geosynchronous altitude at the beginning of 2001; and Italsat 2 was moved, due to a malfunction, in July 2002, below the geosynchronous altitude. This paper reviews how the strategy for the end-of-life disposal has evolved over the last 20 years, due to the growing concern regarding the possible overcrowding of the geostationary ring. The Italian experience is revisited, in order to show the lessons learned in the context of the new international awareness of the space debris problem at the geosynchronous altitude, which has led to the endorsement of a specific disposal strategy by the Inter-Agency Space Debris Coordination Committee (IADC). Long-term orbital propagation is used to assess the impact and relative effectiveness of different disposal scenarios, employing the Italian geostationary satellites as test cases.

Space science. Space junk--protecting space for future generations.

Man-made space debris comes from launch and orbital operations and includes fragmentation debris from past explosions and collisions in orbit. Although 99% of the mass of debris in orbit is cataloged (objects >10 cm), smaller objects cannot be tracked and cataloged; those objects >1 cm, of which there are more than 100,000 in orbit, can cause catastrophic damage to satellites and spacecraft. Hypervelocity collisions in space threaten future space ventures and communication and navigation systems. In particular, the geostationary ring (for satellites orbiting in synchrony with Earth9s rotation) is crowded with objects that will remain in orbit for hundreds or thousands of years. In this Policy Forum, Crowther discusses the sources of debris and short-term and longer term international cooperation among space-faring nations to mitigate space debris in near-Earth space for generations to come.

Feasibility of using statellites in non-equatorial 24-hour circular orbits for communications

The early sixties witnessed the debate among competing candidate orbits that led to the emergence of perfect geostationary systems as virtually the sole “instruments” for satellite communication. The subsequent problem of overcrowding of geostationary ring on one hand and explosive growth in demand on communication capacity on the other led comsat experts to focus on the alternate routes through various near-earth and medium attitude satellite constellations later proposed for uninterrupted communication. However, the opportunities thrown up by quasi-stationary orbits for augmentation of the space communication capacity have gone abegging. This paper attempts to draw attention of communication satellite designers/planners to the immense potential for utilization of the non-equatorial, 24-hour circular orbits for communication. For the proposed quasi-stationary orbits, the change and/or control of the inclination of the plane is not envisaged in the launch and/or operational phase. The resulting significant payload weight advantage is associated with the problem of periodic as well as secular apparent angular satellite drift relative to the ground terminal. However, the problem may be largely overcome through controlled satellite tilting using solar radiation pressure or through the use of tethered auxiliary mass attachment. Alternatively, it may be possible to overcome the attitude control problem by the use of systems such as on-bard electronically steerable phased array antenna capable of following the line-of-sight to the co-operative ground station.

Influence of the spacecraft end-of-life re-orbiting altitude on the long-term collision risk in the geostationary ring

A novel approach was developed to assess the contribution of satellite explosions to the object density in the geostationary ring. A low intensity explosion of a typical operational spacecraft was simulated at eight different altitudes, in between 0 and 2000 km above the geostationary orbit (GEO). The fragments produced were propagated for 72 years, taking into account all the relevant perturbations, and their contribution to the average object density in the GEO ring, both short and long-term, was analyzed as a function of the end-of-life re-orbiting altitude. The explosions in geostationary orbit are the most detrimental for the GEO ring environment. However, the average fragment density in the ring is never higher than 1 5 of the current background, decreasing to less than 1 100 of the existent environment after 4 years, apart for the density rebound, about five decades later, due to the luni-solar perturbations. The spacecraft end-of-life re-orbiting is a possible mitigation solution, but the long-term situation improves quite slowly, as a function of the altitude above GEO, if the explosions continue to occur. A re-orbiting 300 km above the geostationary altitude seems adequate to guarantee, after 2 – 4 years, a long-term average density of fragments in the GEO ring at least two orders of magnitude below the present-day background, even during the density rebound observed after 54 years. However, at least 1000 km of re-orbiting are needed to stay below that 1 100 threshold also in the short-term.

Long-term evolution of disposal orbits beyond the geostationary ring

The effect of long term gravitational influence of the Earth, Moon and Sun, together with the Sun radiation pressure was studied for a randomly generated population of 10000 orbits with the perigees taken from the interval 50–3000 km above the geostationary ring. The evolution of each orbit on a time span of 200 years was studied by means of an explicit sixth-order symplectic integrator of the Wisdom-Holman type. 389 orbits crossed the ‘security zone’ of 35 km above the geostationary orbit, most of them during the first 10 years. The simulation indicates a strong correlation between the semi-major axes and the eccentricities of ‘unsafe orbits’. Some less significant effects in the distribution of elements for such orbits are also discussed.

Distinguishing the populations of natural meteoroids and space debris by GORID in geostationary orbit

The Geostationary Orbit Impact Detector, GORID, is a dust impact plasma detector flying aboard the Russian Express-2 telecommunications spacecraft in geostationary orbit. The detector is the flight spare instrument of the successful Ulysses interplanetary dust detector which has contributed major results such as the detection of interstellar dust within our solar system. GORID is an active sensor, returning time resolved impact data, with approximate mass and direction information, from a rather different environment to interplanetary space. The geostationary ring is likely to be populated by a significant component of orbital debris, and data returned so far have shown some unusual characteristics, interpreted as relatively slow, large, highly charged debris particles. The data also appear to show diurnal and seasonal effects probably correlated with natural meteoroids and the detector's time dependent exposure geometry. This paper investigates the orbits of debris and meteoroids that the detector can sample as a function of time of day and time of year, in order to help the analysis of the GORID data.