Two-dimensional phase plane structure and the stability of the orbital motion for space debris in the geosynchronous ring

Based on the orbital resonance model, we study the two-dimensional phase plane structure of the motion of space debris orbiting the geosynchronous ring under the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ of the Earth’s gravitational field. We present the main characteristic parameters of the two-dimensional phase plane structure. We also analyze the stability of the two-dimensional phase plane structure with numerical method. Our main findings indicate that the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ fully determine the two-dimensional phase plane structure of the space debris, and it remains robust under the effect of the Earth’s actual gravitational field, the luni-solar perturbations and the solar radiation pressure with the normal area-to-mass ratios.     

Ariane 5 GTO debris mitigation using natural perturbations

GTO objects can potentially collide with operative satellites in LEO and GEO protected regions. Internationally accepted debris mitigation guidelines require that these objects exit these protected regions within 25?years, e.g. by re-entering and burning up in Earth’s atmosphere. In this paper, an inventory of the GTO debris generated from Ariane 5 launches in the period 2012–2017 is provided, and it is expected that none of these objects will re-enter within 25?years. For future launches, natural perturbations can be exploited to increase compliance with mitigation guidelines without the use of extra propellant or complex de-orbiting systems, which is attractive from an economic point of view. The lifetime of GTO objects is very sensitive to initial conditions and some environmental and body-related parameters, mainly due to the effect of solar gravity on the perigee altitude. As a consequence, the lifetime of a specific GTO object cannot be predicted accurately, but its probability of re-entering in less than 25?years can be estimated with proper accuracy by following a statistical approach. By propagating the orbits of over 800,000 simulated Ariane 5 GTO objects, it was found that the launch time leading to the highest probability of compliance with debris mitigation guidelines for GEO launches from Kourou corresponds to about 2 PM local time, regardless of the date of launch, which leads to compliance rates ranging from 60 to 100%. Current practice is to launch at around 5–9?PM, so a change in procedures would be required in order to reach a higher degree of compliance with debris mitigation guidelines, which was predicted to be on average below 20% for the objects generated in the period 2012–2017.     

DebrisWatch I: A survey of faint geosynchronous debris

Recent anomalies exhibited by satellites and rocket bodies have highlighted that a population of faint debris exists at geosynchronous (GEO) altitudes, where there are no natural removal mechanisms. Despite previous optical surveys probing to around 10–20 cm in size, regular monitoring of faint sources at GEO is challenging, thus our knowledge remains sparse. It is essential that we continue to explore the faint debris population using large telescopes to better understand the risk posed to active GEO satellites. To this end, we present photometric results from a survey of the GEO region carried out with the 2.54 m Isaac Newton Telescope in La Palma, Canary Islands. We probe to 21st visual magnitude (around 10 cm, assuming Lambertian spheres with an albedo of 0.1), uncovering 129 orbital tracks with GEO-like motion across the eight nights of dark-grey time comprising the survey. The faint end of our brightness distribution continues to rise until the sensitivity limit of the sensor is reached, suggesting that the modal brightness could be even fainter. We uncover a number of faint, uncatalogued objects that show photometric signatures of rapid tumbling, many of which straddle the limiting magnitude of our survey over the course of a single exposure, posing a complex issue when estimating object size. This work presents the first instalment of DebrisWatch, an ongoing collaboration between the University of Warwick and the Defence Science and Technology Laboratory (UK) investigating the faint population of GEO debris.     

Local orbital debris flux study in the geostationary ring

A local orbital debris flux analysis is performed in the geostationary (GEO) ring to investigate how frequently near-miss events occur for each longitude slot in the GEO ring. The current resident space object (RSO) environment at GEO is evaluated, and publicly-available two-line element (TLE) data are utilized in tandem with a geostationary torus configuration to simulate near-miss events incurred by the trackable RSO population at GEO. Methodology for determining near-miss events with this formulation is introduced, and the results of the analysis for a one-year time frame are provided to illustrate the need for active GEO remediation.     

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.     

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.     

Practical method to identify orbital anomaly as spacecraft breakup in the geostationary region

Identifying spacecraft breakup events is an essential issue for better understanding of the current orbital debris environment. This paper proposes an observation planning approach to identify an orbital anomaly, which appears as a significant discontinuity in archived orbital history, as a spacecraft breakup. The proposed approach is applicable to orbital anomalies in the geostationary region. The proposed approach selects a spacecraft that experienced an orbital anomaly, and then predicts trajectories of possible fragments of the spacecraft at an observation epoch. This paper theoretically demonstrates that observation planning for the possible fragments can be conducted. To do this, long-term behaviors of the possible fragments are evaluated. It is concluded that intersections of their trajectories will converge into several corresponding regions in the celestial sphere even if the breakup epoch is not specified and it has uncertainty of the order of several weeks.     

On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

基于驻留时间比的近地空间碎片环境建模

为分析近地空间碎片的分布规律,提出了一种以碎片在空间网格内驻留时间为基础的碎片环境统计建模方法.该方法利用多项式拟合和求根方法统计碎片在空间网格内的停留时间,获取模型基础数据,并据此采用多项式预测、插值和时间序列分析等技术,综合分析空间碎片的分布与演化规律.给出了一个基于双行根数(TLE,Two Line Elements)数据的建模实例,该实例通过了ORDEM2000模型的对比验证,并获得了一些更精细的近地空间碎片环境特征.所得建模方法和分析结论可为长期运行的近地航天器轨道设计、碰撞风险评估及防护等提供技术支撑.     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.