Geostationary Transfer Orbits Research Articles

Expanding Interplanetary Transfer Opportunities from Geostationary Transfer Orbits via Earth Synchronous Orbits

Geostationary transfer orbits (GTOs) are geocentric orbits widely considered for kick-stage operations of satellites for deep space missions. A piggyback spacecraft departing from GTOs requires a low transfer cost. The type of GTO and launch timings of piggyback missions, on the other hand, are typically determined by the primary mission that carried the piggyback spacecraft. This research introduces a new transfer strategy that coordinates piggyback spacecraft’s departure timing from Earth to deep space via an Earth synchronous orbit (ESO) after departure from a GTO. It also enables the spacecraft to change its velocity direction by introducing Earth gravity assists. Connecting several GTOs and interplanetary trajectories via ESOs reduces the required for the transfers. It leads to using transfer opportunities previously considered unsuitable for missions or miniaturizing the kick motor. As a result, ESOs allow for a broader launch opportunity for deep space piggyback probes. In addition, the feasibility of ESOs is shown numerically by comparing direct and ESO-assisted transfers from GTOs to Mars with the required .

Long-term evolution and lifetime analysis of geostationary transfer orbits with solar radiation pressure

The dynamical evolution of geostationary transfer orbits (GTOs) is a fundamental issue for the space debris mitigation in this orbit region. In this paper, the long-term dynamical evolution and orbital lifetime of low-inclination GTOs are investigated based on the Semi-analytic Tool for End of Life Analysis software (STELA) with the solar radiation pressure (SRP) and Earth's shadow taken into account. We carry out numerical investigations of long-term orbital evolution of objects with area-to-mass ratio (A/m) between 0.02 m2/kg and 1 m2/kg in the GTO region. Their dynamical orbital lifetime is recorded and presented in the Ω–ω (right ascension of ascending node–argument of perigee) plane to investigate its dependence on the initial conditions and physical parameters, particularly the initial azimuth of the Sun with respect to the apsidal line and the value of A/m. Based on these results, we further analyze the effect of SRP on the long-term dynamical evolution, as well as the solar apsidal resonances. The results are helpful to enrich the knowledge about long-term evolution and orbital lifetimes of GTO objects with relatively high A/m as well as to promote uncatalogued objects observation and identification.

Luni-solar resonances and effect on long-term evolution of inclined geostationary transfer orbits

In this paper, a singly-averaged, semi-analytical orbital dynamic model in terms of Milankovitch elements is given for geostationary transfer orbits (GTOs), which includes the Earth's oblateness, luni-solar perturbations, atmospheric drag and solar radiation pressure (SRP). The orbital dynamic model is verified through a numerical simulation compared with the Semi-analytic Tool for End of Life Analysis software (STELA) by CNES. We find that if the area-to-mass ratio of the object is relatively large, the SRP will have a significant impact on the long-term evolution of GTOs. Then, the long-term dynamical evolution and orbital resonances of rocket upper stages in inclined geostationary transfer orbits (IGTOs) are studied. It has been found that the luni-solar secular resonances, which are inclination-dependent-only, play a leading role in the long-term evolution of IGTOs. By comparing and analyzing long-term dynamical evolution of orbits with different initial inclinations, the effects of luni-solar secular resonances are studied in details. Finally, a mitigation method for IGTO objects by utilizing luni-solar secular resonances is proposed, in which the eccentricity growth caused by the resonances is used for an early atmospheric re-entry.

Dynamical lifetime survey of geostationary transfer orbits

In this paper, we study the long-term dynamical evolution of highly-elliptical orbits (HEOs) in the medium-Earth orbit (MEO) region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A/m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A/m, and drag coefficient. We find that the majority of small debris (> 70%, depending on the inclination) can naturally reenter within 25-90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A/m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) "ReDSHIFT" project.

HEOSAT: a mean elements orbit propagator program for highly elliptical orbits

The algorithms used in the construction of a semi-analytical propagator for the long-term propagation of Highly Elliptical Orbits (HEO) are described. The software propagates mean elements and include the main gravitational and non-gravitational effects that may affect common HEO orbits, as, for instance, geostationary transfer orbits or Molniya orbits. Comparisons with numerical integration show that it provides good results even in extreme orbital configurations, as the case of SymbolX.

The role of solar apsidal resonance in the evolution of geostationary transfer orbits

Subjected to multiple perturbations and their complex interplay, the dynamical evolution of geostationary transfer orbits (GTOs) is sensitive to initial conditions and model parameters. As one of the most remarkable outcomes of multiple perturbations, the solar apsidal resonance, i.e., the 1:1 resonance between the solar orbital motion and the rotation of the orbital apsidal line caused by Earth’s oblateness, is an important feature of the GTO evolution. It occurs when the semi-major axis is reduced by the atmospheric drag to the critical value, with which the rotation of the orbital apsidal line is commensurate with the solar orbital motion. In the present paper, we show that the solar apsidal resonance plays an important role in the evolution and decay of GTOs. To do so, we first explain the underlying dynamical mechanism of the solar apsidal resonance, which is the U-turn of the solar azimuth with respect to the orbital apsidal line and the resulting monotonic increase or decrease of the eccentricity. The resonance is then classified into three kinds, and their causes and effects are analyzed. Previous studies have regarded the solar apsidal resonance as a mechanism extending the orbital lifetime. However, we find that in most cases the GTO will re-enter Earth’s atmosphere soon or only several years after the resonance, and so the solar apsidal resonance can be regarded as the prelude to the GTO final re-entry. Finally, the sensitivity of orbital dynamics is studied through numerical simulations. It is shown that the high sensitivity of the dynamics can be attributed to the resonance, which is difficult to predict or manage. With the initial state, it is possible to predict the orbit evolution of GTO only before the solar apsidal resonance. To predict the lifetime of GTO, new measurements on the orbit after the resonance are required.

Optimal Design and Deorbiting Performance of Thermionic Tethers in Geostationary Transfer Orbits

The application of a recent concept, a thermionic bare tether (that is, a long conductor coated with a thermionic material), to a practical engineering problem (deorbit space debris from geostationary transfer orbit) is presented. Lorentz drag on a thermionic bare tether, during each pass through an arc close to the perigee, lowers the apogee progressively and produces the object reentry. The performance of a spacecraft equipped with a thermionic bare tether is studied at two different levels, using models that couple thermal and electrical effects. In first place, a simple formula for the eccentricity decrement produced during each perigee pass as a function of TBT properties is derived and used to select TBT optimal dimensions. For a given tether mass, the formula shows that long tethers with small cross-section areas, but large enough to accomplish mechanical constraints, yield the best performance. Second, full numerical simulations of the deorbit maneuver including Lorentz force, air drag, and perturbations are carried out. A spinning thermionic bare tether with a mass of about 16 kg, as well as a length, width, and thickness equal to 6 km, 2 cm, and , respectively, passively deorbits a half-ton spacecraft (with a natural deorbit time of about 50 years) in less than six months, without using propellant, expellant, or power supply. The important roles played by the eclipses and the Earth’s oblateness on thermionic bare tether performance are highlighted.

Dynamical modeling and lifetime analysis of geostationary transfer orbits

The dynamics and lifetime reduction of geostationary transfer orbits (GTOs) are of great importance to space debris mitigation. The orbital dynamics, subjected to a complex interplay of multiple perturbations, are complicated and sensitive to the initial conditions and model parameters. In this paper, a simple but effective non-singular orbital dynamics model in terms of Milankovitch elements is derived. The orbital dynamics, which include the Earth oblateness, luni-solar perturbations, and atmospheric drag, are averaged over the orbital motion of the GTO object, or, as needed, also over the orbital motions of the Moon and Sun, to eliminate the short-period terms. After the averaging process, the effect of the atmospheric drag assumes a simple analytical form. The averaged orbital model is verified through a numerical simulation compared with commercial orbit propagators. GTO lifetime reduction by using the luni-solar perturbations is studied. It is shown that the long-period luni-solar perturbation is induced by the precession of the GTO orbital plane and apsidal line, whereas the short-period perturbation is induced by the periodic luni-solar orbital motions. The long- and short-period perturbations are isolated and studied separately, and their global distribution with respect to the orbital geometry is given. The desired initial orbital geometry with a short orbital lifetime is found and verified by a numerical simulation.

Low-Thrust Geostationary Transfer Orbit (LT2GEO) Radiation Environment and Associated Solar Array Degradation Modeling and Ground Testing

Low-thrust geostationary transfer orbits (LT2GEO) are found to offer significant low cost options thus making them very attractive for GEO missions. However, LT2GEOs increase the transfer orbit time from days to months, thereby causing a significant increase in the time that satellites traverse the most intense trapped particle radiation belts. This paper describes the LT2GEO radiation environment and provides some practical implications using new solar cell technologies and materials. New solar cell and coverglass testing protocols are established using Monte Carlo transport modeling and experimental results are given for Qioptiq CMG borosilicate coverglass.

On-Orbit Operational Range Computation Using Gauss’s Variational Equations with Perturbations

Aircraft operational range, the distance an aircraft can travel with a fixed quantity of fuel, is an intuitive measure that provides strategic and tactical insight to the end user. Currently, there is no rigorously defined and derived operational range measure for on-orbit spacecraft operations with which to inform strategic decisions and planning. This paper illustrates how operational range may be computed in the context of orbital motion using optimal control theory and how existing results in reachability set computation may be leveraged. The solution method presented incidentally solves the free-time minimum-impulse full orbit-element transfer problem under perturbations. The derived optimal control policy reproduces known optimal free-time minimum basis maneuvers. The methodology presented is shown to have the capability to exactly capture the minimum-fuel free-time operational range volumes, although numerical solution algorithm errors persist. The approach is validated using known minimum-fuel optimal maneuvers, and numerical examples of on-orbit operational range for low Earth orbits, geostationary transfer orbits, and geostationary Earth orbits are given. Applications to spacecraft operations are detailed.

On Lambert’s problem and the elliptic time of flight equation: A simple semi-analytical inversion method

In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180° transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.

Evolution of the orbital elements for objects with high area-to-mass ratios in geostationary transfer orbits

A new population of uncatalogued objects in geosynchronous Earth orbits (GEO), with a mean motion of about 1 rev/day and eccentricities up to 0.6, has been identified recently. The first observations of this new type of objects were acquired in the framework of the European Space Agency’s (ESA) search for space debris in GEO and the geostationary transfer orbit (GTO) using the ESA 1-m telescope on Tenerife. Earlier studies have postulated that the perturbations due to the solar radiation pressure can lead to such large eccentricities for GEO objects with a high area-to-mass ratio ( A/ M). The simulations showed that the eccentricities of GEO objects with large A/ M exhibit periodic variations with periods of about one year and amplitudes depending on the value of A/ M. The findings of these studies could be confirmed by observations from the ESA 1-m telescope on Tenerife. As opposed to GEO objects, only one GTO object with high A/ M has been identified so far. Nevertheless, more such objects probably exist. Simulations were performed in order to study the orbital evolution of GTO objects with high A/ M. The objective was on the one hand to find a possible explanation why only one GTO object with a high A/ M has been observed so far, and on the other hand to propose suitable search patterns. The A/ M values were assumed to vary from 1 to 20 m 2/kg in our simulations. The semi-major axis a and the eccentricity e of GTO objects have a correlated decrease (in the sense that a(1 − e) ≈ const.) with time caused by the air drag, leading to a characteristic line in the ( a, e)-diagram. Thus, the initial values of the semi-major axis and the eccentricity were randomly selected along this line. In addition to the evolution of the orbital elements, the dependency of the lifetime on the A/ M value was also studied.

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.

Model improvement for low-velocity collision possible in space

We have conducted research related to space debris issues, including impact experiments associated with visualization of fragment creation processes. However, we aim at those phenomena in the geosynchronous regime where the impact velocity is far lower than hypervelocity. The research purpose is to understand dispersion properties of newly created fragments to be used in the eventual orbital dispersion and debris population models. At Kyushu University, the experiments had been carried out up to velocity of 300m/s so far. However, if debris in geostationary transfer orbits should be taken into consideration, the maximum impact velocity on geostationary satellites will become up to 1500 m/s. Therefore, the experiment in 300-1500 m/s is planed to be conducted using the Two-Stage Light Gas Gun at Kyushu Institute of Technology. The similarities and differences in the experimental results from Kyushu University and Kyushu Institute of Technology are discussed.

Contraction of high eccentricity satellite orbits using KS elements in an oblate atmosphere

A non-singular analytical theory for the contraction of high eccentricity orbits (eccentricity e > 0.5) under the influence of air drag is developed in terms of the KS elements, using an oblate exponential atmospheric model. With the help of MACSYMA software, the series expansions include up to the sixth power in terms of an independent variable λ, introduced by Sterne as cos E =1 − H λ 2 a e , where E and a are the eccentric anomaly and semi-major axis of the orbit and H, the density scale height, is assumed constant. The solution is tested numerically over a wide range of orbital parameters: perigee height (H p), e and inclination (i) up to 100 revolutions and is found to be quite accurate. The % error in the semi-major axis computation when compared with numerically integrated values, for test cases whose perigee heights vary from 150 to 300 km and eccentricities increase from 0.6 to 0.8, is found to be less than one. The decay rates of a and e are found to be lower than those obtained with spherically symmetrical atmospheric models and increasing with increase in inclination. The theory can be effectively used for the orbital decay of Molniya type of communication satellites, decay of geostationary transfer orbits and during mission planning of aeroassisted orbital transfer orbits.

Contraction of high eccentricity satellite orbits using K-S elements with air drag

A new non–singular analytical theory for the contraction of high eccentricity satellite orbits under the influence of air drag is developed in terms of the K–S elements, utilizing a spherically symmetrical atmospheric model. The series expansions include up to sixth power in terms of an independent variable λ, used by King–Hele in his theory. Numerical experimentation establishes a supremacy of the present theory over that of King–Hele over a wide range of the involved orbital parameters. The theory can be used effectively for the orbital decay of geostationary transfer orbits and during the mission planning of aeroassisted orbital transfer orbits.

Decay of debris in geostationary transfer orbit

This paper reports on some current difficulties encountered in the prediction of the re-entry of objects on highly eccentric orbits. Concerned here are uncontrolled objects usually called debris. After recalling the importance of following the orbital evolution of space debris, the particular case of debris on Geostationary Transfer Orbits is treated. Although third body perturbation is the main perturbation in this type of orbit, it will be shown how the atmospheric drag, acting at perigee, may considerably change the evolution of the orbit. The prediction of re-entry date of a debris on a high eccentricity orbit is usually rather accurate. For GTO however, the effect of the drag at perigee may render the prediction totally uncertain. This is illustrated in an example taken from the recent re-entry of the first Ariane launch payload.

Attitude determination covariance analysis for geostationary transfer orbits

Fundamental biases in V-slit sun and pencil-beam infrared Earth sensor measurements are identified and modeled in terms of representative covariances. Their effects on attitude determination accuracy are assessed by means of covariance transformations following the calculations involved in a realistic attitude estimation process. The results are useful in identifying the best attitude determination intervals and for providing quantitative estimates of the expected error for selected launch configurations. On this basis the most favorable sensor settings can be selected for a given launch window. This is of particular interest for present-day communication satellites equipped with variable sensor mountings which can be adjusted before launch.