Eccentricity Growth Research Articles

Secular dynamics and the lifetimes of lunar artificial satellites under natural force-driven orbital evolution

In this paper, we study the long-term (time scale of several years) orbital evolution of lunar satellites under the sole action of natural forces. In particular, we focus on secular resonances, caused either by the influence of the multipole moments of the lunar potential and/or by the Earth’s and Sun’s third-body effect on the satellite’s long-term orbital evolution. Our study is based on a simplified secular model obtained in ‘closed form’, i.e., without expansions in the satellite’s orbital eccentricity. Contrary to the case of artificial Earth satellites, in which many secular resonances compete in dynamical impact, we give numerical evidence that for lunar satellites only the 2g−resonance (ω̇=0) affects significantly the orbits at secular timescales. We interpret this as a consequence of the strong effect of lunar mascons. We show that the lifetime of lunar satellites is, in particular, nearly exclusively dictated by the 2g resonance. By deriving a simple analytic model, we propose a theoretical framework which allows for both qualitative and quantitative interpretation of the structures seen in numerically obtained lifetime maps. This involves explaining the main mechanisms driving eccentricity growth in the orbits of lunar satellites. In fact, we argue that the re-entry process for lunar satellites is not necessarily a chaotic process (as is the case for Earth satellites), but rather due to a sequence of bifurcations leading to a dramatic variation in the structure of the separatrices in the 2g resonance’s phase portrait, as we move from the lowest to the highest limit in inclination (at each altitude) where the 2g resonance is manifested.

Reducing reentry casualty risk for spacecraft on long-term reentering eccentric inclined geosynchronous (Tundra) disposal orbits

This paper considers disposal of spacecraft and upper stages on eccentric inclined geosynchronous orbits (eccentric IGSOs), specifically the class known as Tundra orbits. The U.S. Government Orbital Debris Mitigation Standard Practices (ODMSP) released in December 2019 include a disposal option to use orbital eccentricity growth for long-term reentry within 200 years that could be used for Tundra orbits. A condition of this disposal option is that reentry casualty risk be limited. An analysis was performed to assess reentry casualty risk for a generic Tundra spacecraft and typical upper stages on Tundra disposal orbits. From propagation sweeps accounting for eccentricity growth of Tundra disposal orbits, several Tundra disposal orbit cases were selected for reentry analysis. A reentry risk analysis for these cases assuming reentry from near-circular orbits was performed. Results show that predicted casualty risk for the generic Tundra spacecraft and typical upper stages well exceed allowable risk limits in the ODMSP. An analysis of reentry from the selected Tundra disposal orbits accounting for the high eccentricity due to eccentricity growth just before reentry was then performed. Results show that the distribution of reentry points on the Earth can be concentrated over ocean in the southern hemisphere where there is less human population. The generic Tundra spacecraft and one of the upper stages considered were then found to be compliant with the limit of 1 in 10,000 expected casualties in the ODMSP. These results indicate promise for wider usage of the long-term re-entry option in the ODMSP.

Orbital dynamics in the GG Tau A system: Investigating its enigmatic disc

Context. GG Tau is one of the most studied young multiple stellar systems: GG Tau A is a hierarchical triple surrounded by a massive disc and its companion, GG Tau B, is also a binary. Despite numerous observational attempts, a comprehensive understanding of the geometry of the GG Tau A system is still elusive. Given the significant role of dynamical interactions in shaping the evolution of these systems, it is relevant to characterise the stellar orbits and the discs’ properties. Aims. To determine the best orbital configuration of the GG Tau A system and its circumtriple disc, we provide new astrometric measures of the system and we run a set of hydrodynamical simulations with two representative orbits to test how they impact a disc composed of dust and gas. Methods. We tested the dynamical evolution of the two scenarios on short and long timescales. We obtained synthetic flux emission from our simulations at different timescales and we compared them with multi-wavelength observations of 1300 µm ALMA dust continuum emission and 1.67 µm SPHERE dust scattering to infer the most likely orbital arrangement. Results. We extend the analysis of the binary orbital parameters using six new epochs from archival data, showing that the current measurements alone (and future observations coming in the next 5–10 yr) are not capable of fully breaking the degeneracy between families of coplanar and misaligned orbits, but finding that a modest misalignment is probable. We find that the timescale for the onset of the disc eccentricity growth, τecc, is a fundamental timescale for the morphology of the system. Results from the numerical simulations obtained using the representative coplanar and misaligned (∆θ = 30°) orbits show that the best match between the position of the stars, the cavity size, and the dust ring size of GG Tau A is obtained with the misaligned configuration on timescales shorter than τecc. The results exhibit an almost circular cavity and dust ring, favouring slightly misaligned (∆θ ~ 10–30°) low-eccentricity (e ~ 0.2–0.4) orbits. However, for both scenarios, the cavity size and its eccentricity quickly grow for timescales longer than τecc and the models do not reproduce the observed morphology anymore. This implies that either the age of the system is shorter than τecc or that the disc eccentricity growth is not triggered or dissipated in the system. This finding raises questions about the future evolution of the GG Tau A system and, more generally, the time evolution of eccentric binaries and their circumbinary discs.

Runaway Eccentricity Growth: A Pathway for Binary Black Hole Mergers in AGN Disks

Binary black holes (BBHs) embedded within the accretion disks that fuel active galactic nuclei (AGN) are promising progenitors for the source of gravitational wave (GW) events detected by LIGO/VIRGO. Several recent studies have shown that when these binaries form, they are likely to be highly eccentric and retrograde. However, many uncertainties remain concerning the orbital evolution of these binaries as they either inspiral toward merger or disassociate. Previous hydrodynamical simulations exploring their orbital evolution have been predominantly two-dimensional or have been restricted to binaries on nearly circular orbits. We present the first high-resolution, three-dimensional local shearing-box simulations of both prograde and retrograde eccentric BBHs embedded in AGN disks. We find that retrograde binaries shrink several times faster than their prograde counterparts and exhibit significant orbital eccentricity growth, the rate of which monotonically increases with binary eccentricity. Our results suggest that retrograde binaries may experience runaway orbital eccentricity growth, which may bring them close enough together at pericenter for GW emission to drive them to coalescence. Although their eccentricity is damped, prograde binaries shrink much faster than their orbital eccentricity decays, suggesting they should remain modestly eccentric as they contract toward merger. Finally, binary precession driven by the AGN disk may dominate over precession induced by the supermassive black hole depending on the binary accretion rate and its location in the AGN disk, which can subdue the evection resonance and von Ziepel–Lidov–Kozai cycles.

Eccentricity and inclination of massive planets inside low-density cavities: results of 3D simulations

ABSTRACT We study the evolution of eccentricity and inclination of massive planets in low-density cavities of protoplanetary discs using three-dimensional (3D) simulations. When the planet’s orbit is aligned with the equatorial plane of the disc, the eccentricity increases to high values of 0.7–0.9 due to the resonant interaction with the inner parts of the disc. For planets on inclined orbits, the eccentricity increases due to the Kozai–Lidov mechanism, where the disc acts as an external massive body, which perturbs the planet’s orbit. At small inclination angles, ${\lesssim}30^\circ$, the resonant interaction with the inner disc strongly contributes to the eccentricity growth, while at larger angles, eccentricity growth is mainly due to the Kozai–Lidov mechanism. We conclude that planets inside low-density cavities tend to acquire high eccentricity if favourable conditions give sufficient time for growth. The final value of the planet’s eccentricity after the disc dispersal depends on the planet’s mass and the properties of the cavity and protoplanetary disc.

Extreme Resonant Eccentricity Excitation of Stars around Merging Black-Hole Binary.

We study the dynamics of a star orbiting a merging black-hole binary (BHB) in a coplanar triple configuration. During the BHB's orbital decay, the system can be driven across the apsidal precession resonance, where the apsidal precession rate of the stellar orbit matches that of the inner BHB. As a result, the system gets captured into a state of resonance advection until the merger of the BHB, leading to extreme eccentricity growth of the stellar orbit. This resonance advection occurs when the inner binary has a nonzero eccentricity and unequal masses. The resonant driving of the stellar eccentricity can significantly alter the hardening rate of the inner BHB and produce observational signatures to uncover the presence of nearby merging or merged BHBs.

Differences between Stable and Unstable Architectures of Compact Planetary Systems

We present a stability analysis of a large set of simulated planetary systems of three or more planets based on architectures of multiplanet systems discovered by Kepler and K2. We propagated 21,400 simulated planetary systems up to 5 billion orbits of the innermost planet; approximately 13% of these simulations ended in a planet–planet collision within that time span. We examined trends in dynamical stability based on dynamical spacings, orbital period ratios, and mass ratios of nearest-neighbor planets as well as the system-wide planet mass distribution and the spectral fraction describing the system’s short-term evolution. We find that instability is more likely in planetary systems with adjacent planet pairs that have period ratios less than 2 and in systems of greater variance of planet masses. Systems with planet pairs at very small dynamical spacings (less than ∼10–12 mutual Hill radii) are also prone to instabilities, but instabilities also occur at much larger planetary separations. We find that a large spectral fraction (calculated from short integrations) is a reasonable predictor of longer-term dynamical instability; systems that have a large number of Fourier components in their eccentricity vectors are prone to secular chaos and subsequent eccentricity growth and instabilities.

Growth and evolution of low-mass planets in pressure bumps

Observations of protoplanetary disks have revealed dust rings that are likely due to the presence of pressure bumps in the disk. Because these structures tend to trap drifting pebbles, it has been proposed that pressure bumps may play an important role in the planet formation process. In this paper, we investigate the orbital evolution of a 0.1 M⊕ protoplanet embedded in a pressure bump using 2D hydrodynamical simulations of protoplanetary disks consisting of gas and pebbles. We examine the role of thermal forces generated by the pebble accretion-induced heat release, taking into account the feedback between the luminosity and the eccentricity. We also study the effect of the pebble-scattered flow on the planet’s orbital evolution. Due to the accumulation of pebbles at the pressure bump, the planet’s accretion luminosity is high enough to induce significant eccentricity growth through thermal forces. Accretion luminosity is also responsible for vortex formation at the planet’s position through baroclinic effects, which cause the planet to escape from the dust ring if dust feedback on the gas is neglected. Including the effect of the dust feedback leads to weaker vortices, which enable the planet to remain close to the pressure maximum on an eccentric orbit. Simulations in which the planet mass is allowed to increase as a consequence of pebble accretion result in the formation of giant planet cores with masses in the range of 5–20 M⊕ over ~2 × 104 yr. This occurs for moderate values of the Stokes number, St ≈ 0.01, such that the pebble drift velocity is not too high and the dust ring mass not too small. Our results suggest that pressure bumps mays be preferred locations for the formation of giant planets, but this requires a moderate level of grain growth within the disk.

The eccentricity growth phenomenon for MEO navigation satellites

Lunisolar resonances shape the dynamics in the MEO region and have the effect of increasing an object’s eccentricity possibly up to a value so high that the orbit’s perigee reaches the atmosphere and friction determines the re-entry. The focus of this paper is the eccentricity growth phenomenon observed for navigation satellites. In particular, starting from a secular Hamiltonian model, analytical estimates for the maximum eccentricity reachable along an inclination-only dependent lunisolar resonance are derived as a function of the initial inclination. Also, trajectories that minimize an object’s lifetime are studied, and analytical estimates for such a minimum lifetime are provided as a function of the initial eccentricity of the object. In addition, lifetime cartography maps are presented in the plane of the argument of perigee and the longitude of the ascending node.

Gravitational wave mergers of accreting binary black holes in AGN discs

ABSTRACT Binary black hole (BBH) evolution in the discs of active galactic nuclei (AGNs) is a promising channel for gravitational wave (GW)-driven mergers. It is, however, unclear whether binaries interacting with the surrounding disc undergo orbital contraction or expansion. We develop a simple analytical model of accreting BBHs in AGN discs to follow the orbital evolution from the disc-dominated regime at large separations into the GW-driven regime at small separations (the coupled ‘disc + GW’-driven evolution). We obtain that accreting binaries expand in thick discs with aspect ratio greater than a critical value (>hcrit); whereas accreting binaries contract and eventually merge in thin discs (<hcrit). Interestingly, accreting BBHs can experience faster mergers compared to non-accreting counterparts, with a non-monotonic dependence on the disc aspect ratio. The orbital contraction is usually coupled with eccentricity growth in the disc-dominated regime, which lead to accelerated inspirals in the GW-driven regime. We quantify the resulting BBH merger time-scales in AGN discs (τmerger ∼ 105–107 yr) and estimate the associated GW merger rates ($\mathcal {R} \sim (0.2 {\small --} 5) \, \text{Gpc}^{-3} \text{yr}^{-1}$). Overall, accreting binaries may efficiently contract and merge in thin discs, hence this particular BBH-in-AGN channel may provide a non-negligible contribution to the observed GW merger event rate.

The Aligned Orbit of the Eccentric Proto Hot Jupiter TOI-3362b* *Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under program ID 110.23Y8.004.

High-eccentricity tidal migration predicts the existence of highly eccentric proto hot Jupiters on the “tidal circularization track,” meaning that they might eventually become hot Jupiters, but that their migratory journey remains incomplete. Having experienced moderate amounts of tidal evolution of their orbital elements, proto hot Jupiter systems can be powerful test beds for the underlying mechanisms of eccentricity growth. Notably, they may be used for discriminating between variants of high-eccentricity migration, each predicting a distinct evolution of misalignment between the star and the planet’s orbit. We constrain the spin–orbit misalignment of the proto hot Jupiter TOI-3362b with high-precision radial-velocity observations using ESPRESSO at Very Large Telescope. The observations reveal a sky-projected obliquity ° and constrain the orbital eccentricity to e = 0.720 ± 0.016, making it one of the most eccentric gas giants for which the obliquity has been measured. Although the large eccentricity and the striking orbit alignment of the planet are puzzling, we suggest that ongoing coplanar high-eccentricity migration driven by a distant companion is a possible explanation for the system's architecture. This distant companion would need to reside beyond 5 au at 95% confidence to be compatible with the available radial-velocity observations.

Eccentricity growth of massive planets inside cavities of protoplanetary discs

ABSTRACT We carry out hydrodynamical simulations to study the eccentricity growth of a 1–30 Jupiter mass planet located inside the fixed cavity of a protoplanetary disc. The planet exchanges energy and angular momentum with the disc at resonant locations, and its eccentricity grows due to Lindblad resonances. We observe several phases of eccentricity growth where different eccentric Lindblad resonances dominate from 1:3 up to 3:5. The maximum values of eccentricity reached in our simulations are 0.65–0.75. We calculate the eccentricity growth rate for different planet masses and disc parameters and derive analytical dependencies on these parameters. We observe that the growth rate is proportional to both the planet’s mass and the characteristic disc mass for a wide range of parameters. In a separate set of simulations, we derived the width of the 1:3 Lindblad resonance.

A Single-Averaged Model for the Solar Radiation Pressure Applied to Space Debris Mitigation Using a Solar Sail

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is the most relevant perturbation for objects in orbit around the Earth with a high area-to-mass ratio (A/m). We consider the single-averaged SRP model with the Sun in an elliptical and inclined orbit. In addition to the SRP effect, the orbital evolution of space debris is analyzed considering the perturbations due to the Earth’s flattening and third-body perturbations in the dynamical system. The idea is to use the solar sail as a propulsion system using the Sun itself as a clean and abundant energy source so that it can remove space debris from the geostationary orbit and also contribute to the sustainability of space exploration. Using averaged dynamical maps as a tool, the numerical simulations show that the solar sail contributes strongly to exciting the eccentricity of the space debris, causing its reentry into Earth’s atmosphere. To perform the numerical simulations, we consider data from real space debris. We also show that the solar sail can be used to remove space debris for a graveyard orbit. In this way, the solar sail can work as a clean and sustainable space-debris-removal mechanism. Finally, we show that the convenient choice of the argument of perigee and the longitude of the ascending node might contribute to amplify the growth of eccentricity. It is also shown that solar radiation pressure destroys the symmetry of the orbits that can be observed in keplerian orbits, so all the orbits will be asymmetric when considering the presence of this force.

Exciting spiral arms in protoplanetary discs from flybys

ABSTRACT Spiral arms are observed in numerous protoplanetary discs. These spiral arms can be excited by companions, either on bound or unbound orbits. We simulate a scenario where an unbound perturber, i.e. a flyby, excites spiral arms during a periastron passage. We run three-dimensional hydrodynamical simulations of a parabolic flyby encountering a gaseous protoplanetary disc. The perturber mass ranges from $10\, \rm M_J$ to $1\, \rm {\rm M}_{\odot }$. The perturber excites a two-armed spiral structure, with a more prominent spiral feature for higher mass perturbers. The two arms evolve over time, eventually winding up, consistent with previous works. We focus on analysing the pattern speed and pitch angle of these spirals during the whole process. The initial pattern speed of the two arms are close to the angular velocity of the perturber at periastron, and then it decreases over time. The pitch angle also decreases over time as the spiral winds up. The spirals disappear after several local orbital times. An inclined prograde orbit flyby induces similar disc substructures as a coplanar flyby. A solar-mass flyby event causes increased eccentricity growth in the protoplanetary disc, leading to an eccentric disc structure which dampens over time. The spirals’ morphology and the disc eccentricity can be used to search for potential unbound stars or planets around discs where a flyby is suspected. Future disc observations at high resolution and dedicated surveys will help to constrain the frequency of such stellar encounters in nearby star-forming regions.

多枝柽柳年轮生长速率测量及TRGR指标优势分析

PDF HTML阅读 XML下载 导出引用 引用提醒 多枝柽柳年轮生长速率测量及TRGR指标优势分析 DOI: 10.5846/stxb202202080312 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 欧盟Erasmus+项目（598838-EPP-1-2018-EL-EPPKA2-CBHE-JP） Tree-ring growth rate measurement of Tamarix ramosissima and tree-ring growth rate index superiority analysis Author: Affiliation: Fund Project: This work was supported by the GIS and RS for Sustainable Forestry and Ecology（598838-EPP-1-2018-EL-EPPKA2-CBHE-JP） 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:灌木对生境和气候变化具有高度敏感性，其年轮资料在认识区域环境演变过程、全球气候变化和环境保护中具有重要作用。灌木植株在生长过程中受遗传和极端环境的影响，年轮常出现偏心和不规则生长，这使得专业年轮分析软件测量的年轮宽度数据难以准确反映其整体径向生长信息。为探讨适合于寒旱区灌木年轮学研究的年轮测量指标和测量方法，研究以该区域荒漠常见植物多枝柽柳（Tamarix ramosissima Ledeb.）为研究对象，通过U-net深度学习方法，获得年轮提取训练模型，自动获取扫描轮盘各年早材区域。轮盘扫描及语义分割后的图像经GIS配准赋坐标、ENVI图像处理后，借助GIS编辑和测量工具，完成多枝柽柳各年年轮生长速率（Tree-ring growth rate，TRGR）、年轮宽度（Tree-ring width，TRW）和树木基部断面积生长增量（Basal area increment，BAI）的测量；研究基于Timesat Savitzky-Golay （S-G）滤波时间序列拟合，获取点样尺度归一化植被指数（Normalized difference vegetation index，NDVI）季节曲线峰值、季节开始时的增长速率、大季节积分和季节结束时的值等7个关键参数。将多枝柽柳TRGR、TRW和BAI测量结果与NDVI季节曲线关键参数进行相关性分析，检验TRGR指标的合理性，分析指标优势。结果表明：测量的多枝柽柳TRGR指标与点样尺度NDVI关键参数间存在高度正相关，最高相关系数达0.98。TRGR指标不仅能够反映多枝柽柳年轮整体径向生长情况，而且可以有效去除年轮指标中的胸径趋势，突显指标环境趋势，有利于解决树木年轮学中指标去趋势难的问题。TRGR与TRW和BAI指标相比优势明显，可以作为灌木年轮学研究的新代用指标。研究结果为多枝柽柳年轮信息重构NDVI或反之提供了有利证据。研究构建的年轮测量方法相比于专业年轮分析系统具有更为多样的测量手段。研究结果可推动寒旱区灌木年轮学发展。 Abstract:Shrubs are highly sensitive to habitat and climate change, and its tree-ring data plays an important role in understanding regional environmental evolution, global climate change and environmental protection. Due to the influence of heredity and extreme environment during shrub growth, the growth rings often have serious eccentricity and irregular growth, which makes it difficult for the tree-ring width measurement by professional tree-ring analysis software to accurately reflect the overall radial growth information. In order to explore the measuring indexes and methods of tree-ring, which are suitable for study on shrub dendrochronology in cold and arid regions, this study takes Tamarix ramosissima Ledeb., a common desert plant in this region, as the study object. Based on U-net deep learning method, we created the training model of Tamarix ramosissima tree-ring extraction, which would automatically obtain each year tree-ring springwood area of scanning disc. After tree-ring scanning image and semantic segmentation image were processed by GIS assigning measurement coordinates and ENVI image processing, tree-ring growth rate (TRGR), tree-ring width (TRW), and basal area increment (BAI) of tamarix ramosissima were measured by using GIS editing and measurement tools. Based on Timesat Savitzky-Golay (S-G) filtering time series fitting, seven key parameters of seasonal curve of normalized difference vegetation index (NDVI) were obtained at point-scale, including peak value, rate of increase at the beginning of the season, large seasonal integral and value for the end of the season etc. The correlation between TRGR, TRW, BAI and the key parameters of NDVI seasonal curve were analyzed to test the rationality and to analyze the advantages of TRGR index. The results show that there are high positive correlations between TRGR index of Tamarix ramosissima and the key parameters of point-scale NDVI seasonal curve. The highest correlation coefficient is 0.98.TRGR index can not only reflect the overall radial growth of tree-ring, but also effectively remove trend of diameter at breast height (DBH) in tree-ring index and highlight the index's environmental trend, which is helpful to solve the problem of index detrending in dendrochronology. Compared with TRW and BAI, TRGR index has obvious advantages and it can be used as a new index for shrub dendrochronology. The results provide evidence for NDVI reconstruction from tree-ring information of tamarix ramosissima or vice versa. Research methods have more diverse means than the professional tree-ring analysis system measurement. The results can promote the development of shrub dendrochronology in cold and arid regions. 参考文献 相似文献 引证文献

A detailed dynamical model for inclination-only dependent lunisolar resonances. Effect on the “eccentricity growth” mechanism

The focus of this paper is on inclination-only dependent lunisolar resonances, which shape the dynamics of a MEO (Medium Earth Orbit) object over secular time scales (i.e. several decades). Following the formalism of Daquin et al. (2022), we discuss an analytical model yielding the correct form of the separatrices of each one of the major lunisolar resonances in the “action” space (i,e) (inclination, eccentricity) for any given semi-major axis a. We then highlight how our method is able to predict and explain the main structures found numerically in Fast Lyapunov Indicator (FLI) cartography. We focus on explaining the dependence of the FLI maps from the initial phase of the argument of perigee ω and of the longitude of the ascending node Ω of the object and of the moon ΩL. In addition, on the basis of our model, we discuss the role played by the Ω-ΩL and the 2Ω-ΩL resonances, which overlap with the inclination-only dependent ones as they sweep the region for increasing values of a, generating large domains of chaotic motion. Our results provide a framework useful in designing low-cost satellite deployment or space debris mitigation strategies, exploiting the natural dynamics of lunisolar resonances that increase an object’s eccentricity up until it reaches a domain where friction leads to atmospheric re-entry.

Structural optimization of ball bearings with three-point contact at high-speed

Three-point contact state is a common state for four-point contact ball bearings (FPCBB), significantly improving the performance in high-speed and light-load conditions. However, in this case, the internal contact state is in a dynamic transition between two-point and three-point contact, with substantial frictional losses. To this end, a nonlinear dynamic model of FPCBB, considering the lubrication traction and the bearing assemblies’ dynamic features, is proposed to optimize the FPCBB's performance for three-point contact state. The dynamic changes of contact states under high-speed and light-load conditions are revealed, and four sets of conditions are picked as optimization conditions. Beside, groove curvature coefficient and curvature center eccentricity, depending on outer ring structure, are selected as optimized structural parameters. On this basis, the behavior performance in three-point contact state is optimized for specific operating conditions. The results show that with the gradual growth of eccentricity, the bearing fatigue life first extends slowly and then reduces rapidly, where an optimum value exists; for bearings possibly serving in skidding condition, it is better to prefer a larger eccentricity or a smaller curvature coefficient to reduce sliding damage.

Analysis of ODMSP-compliant near-circular GPS disposal orbits and resulting long-term collision risk

The U.S. Government Orbital Debris Mitigation Standard Practices (ODMSP) released in December 2019 include several disposal options that are applicable to GPS satellites. One option is to leave a satellite on a near-circular disposal orbit with limited long-term eccentricity growth. Many currently operational GPS satellites are planned to move to near-circular disposal orbits above the GPS operational constellation and below the BeiDou Satellite System (BDS). The conditions in the ODMSP specify that GPS disposal orbits avoid crossing the semi-synchronous zone (altitude range 20,182 +/- 300 km, occupied by GPS) or the BDS operational altitude for 100 years. An analysis was performed to determine ways to achieve ODMSP-compliance of near-circular GPS disposal orbits and limit associated collision risk. Disposal orbit propagations over 100 years were used to determine the available initial semi-major axis (SMA) range for compliant disposal orbits. Next, the GPS constellation and satellite disposals were simulated over a 200-year time frame. The disposal orbits were propagated and the collision probability between disposed satellites was then evaluated. Results show an available initial SMA range of 363 km for an initial eccentricity of 0.0003 and a range of only 3 km for an initial eccentricity of 0.001, which cover worst-case eccentricity growth scenarios. Results also show that a disposal strategy with initial eccentricity of 0.0003 and initial SMA uniformly spread over 363 km has the lowest collision probability for future disposed GPS satellites.

Long-Term Orbit Prediction and Deorbit Disposal Investigation of MEO Navigation Satellites

With the increase in satellites in the medium Earth orbit (MEO) region, there should be a focus on orbit safety in the MEO region. A safe orbit disposal strategy is necessary to maintain the sustainability of the MEO region. This paper focuses on long-term evolution modeling, safety analysis of MEO objects, and different disposal techniques for end-of-life BDS-2 MEO satellites. On the one hand, a long-term numerical evolution model is established, and mean equinoctial elements are adopted to propagate a long-term orbit. Long-term evolution for the MEO region over 100 years is carried out, including the Galileo, BDS, GPS, and GLONASS constellations. The earliest orbit intersection time with other global navigation satellite system (GNSS) constellations is put forward. On the other hand, a dynamic model and an optimization model for disposal orbit are established, which minimize the eccentricity growth within 200 years and the fuel consumption for maneuvering to the disposal orbit. The bounds for the disposal region of BDS MEO satellites are also proposed, which consider the measurement and control error of BDS MEO satellites and the eccentricity bounds for end-of-life BDS MEO satellites. A genetic algorithm is adopted to optimize the orbital elements for end-of-life BDS MEO satellites. In addition, two disposal cases, namely, upraising and reducing the orbit, for end-of-life BDS MEO satellites are simulated. The long-term evolutions for the disposal of orbital elements within 200 years are implemented, and the fuel consumption is calculated. The results show that the current MEO region is relatively safe and that the eccentricity is the most important factor that influences the long-term evolution of safety analysis for BDS MEO disposal orbits. Upraising the orbit is safe for end-of-life BDS MEO satellites. This investigation provides the theoretical foundation for investigating the long-term evolutionary mechanisms of the MEO region and references disposal strategy analysis for decommissioned navigation satellites, and the spent upper stages for other GNSS constellations.

Analysis of the orbital evolution of space debris using a solar sail and natural forces

Since the launch of the first artificial satellite around the Earth up to the present date, various non-functional objects are orbiting the Earth, such as deactivated satellites, satellite components, rocket bodies, among others. These objects can collide with operational satellites or other debris, generating a cloud of smaller particles. Space agencies are concerned about the current scenario of the space environment. If we continue as we are the number of objects in orbit will make it difficult to operate safely in the space environment. So space exploration may become unsustainable (ESA (2020)). In this work, the orbital evolution of these objects that are located in the geostationary orbit (GEO) is analyzed. In the mathematical model we consider the main disturbing forces, such as the direct solar radiation pressure (SRP), the perturbation of the third body (Sun and Moon) and the Earth oblateness. The SRP is the most relevant perturbation for objects with larger area-mass ratio. Knowing this, the possibility of using a solar sail is considered to help to clean the space environment. The main natural environmental perturbations that act in the orbit of the debris are considered in the dynamics. Such forces acting in the solar sail can force the growth of the eccentricity of these objects in the GEO orbit. Several authors have presented models of the solar radiation pressure considering the single-averaged model. But, doing a literature research, we found that the authors consider the Earth around the Sun in a circular and inclined orbit. Our contribution to the SRP model is in developing a different approach from other authors, where we consider the Sun in an elliptical and inclined orbit, which is valid for other bodies in the solar system when the eccentricity cannot be neglected. The expression of the SRP is developed up to the second order. We found that the first-order term is much superior to the second-order term, so the quadrupole term can be neglected. Another contribution is the approach to identify the initial conditions of the perigee argument (g) and the longitude of the ascending node (h), where some values of the (g,h) plane contribute to amplify the eccentricity growth. In the numerical simulations we consider real data from space debris removed from the site Stuff in Space. The solar sail helps to clean up the space environment using a propulsion system that uses the Sun itself, a clean and abundant energy source, unlike chemical propellants, to contribute to the sustainability of space exploration.