On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T  . Therefore, for a pre-fixed minimum contribution, for instance 1×10^-8$1\times {10}^{-8}$ m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500 km of altitude (like the GRACE satellites at the beginning of their mission) we found 35?M?198$35?M?198$ for T=1$T=1$ day. We analyzed the individual contribution of the second order harmonic (_J2$J_2$) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.     

高精度重力场下回归轨道半解析优化设计

为解决太阳同步回归轨道的标称设计问题,提出一种基于高精度重力场的半解析优化方法。建立地球非球形引力摄动阶数为J15 的高精度重力场解析模型,并分离出引力摄动的长期项和长周期项。构建回归轨道从半长轴到平交点周期的对应关系,平交点周期变化随引力摄动阶数的提高而逐渐收敛。通过微分修正迭代算法所确定的半长轴相对于传统J2摄动模型的半长轴确定值具有更高的精度和更好的稳定性。考察摄动短周期项影响下的密切交点周期,结果表明其受初始位置(平近点角)影响较大,变化范围为0.015s,并由此给出精确回归轨道优化设计的基准：不同的初始位置上满足星下点轨迹严格回归的半长轴期望值。     

精密进近阶段的多系统GNSS组合RAIM可用性算法及分析

给出了多系统全球卫星导航系统（GNSS）组合接收机自主完好性监测（ReceiverAutonomousIntegrityMonitoring,RAIM）可用性计算方法,在此基础上利用GPS、GLONASS实测数据与BDS、Galileo全星座仿真数据,分析了BDS、GPS、GLONASS和Galileo不同组合在精密进近阶段的RAIM可用性。通过试验分析发现,BDS的5颗地球同步轨道卫星和3颗倾斜地球同步轨道卫星对亚洲、非洲和欧洲大部分地区的RAIM可用性有很大的贡献。这些地区站星间几何观测结构得到改善,使得RAIM可用性相对于其他地区有很大幅度的提升。在亚太地区APV-I阶段单系统导航情况下,北斗导航系统RAIM可用性达到99.5%,高于其他三个导航系统。在精密进近阶段（APV-I、APV-II和CAT-I）,BDS与其他导航系统（GPS、GLONASS和Galileo）的组合导航可以满足全球大部分区域的RAIM可用性需求,大多可达到100%。     

用于深空探测任务的先进通信与导航体制

介绍了一套用于深空探测的先进通信与导航体制.在综述美国国家航空航天局相关研究进展、讨论这套体制中的关键特征技术的同时,文章利用飞行在地月平动点L3/L4/L5的晕轨道上的中继通信和跟踪卫星,建议了一种超长距离干涉测量(ELBI)技术.探讨了ELBI技术对先进通信与导航体制进行增强的可能性和应用潜力.     

地球同步轨道SAR曲线轨迹模型和成像算法研究

由于地球同步轨道合成孔径雷达(GEO SAR)轨道高度高,地球自转对其影响较为严重,其相对地球的运动变得更为复杂,低轨SAR中的直线轨迹模型已不能精确逼近其真实成像几何,基于该模型推导的成像算法也不再适用。针对这一问题,本文首先根据GEO SAR平台的运动特点,使用高阶逼近模型建立了适用于GEO SAR长合成孔径时间的斜距方程,并结合级数反演法,推导出该斜距方程下的二维频谱高阶近似表达式。在此基础上提出了一种二维频域成像算法并分析了其运算量。该算法所有操作都由快速傅里叶变换和相位点乘完成,具有较高的效率。点目标仿真结果表明本文斜距方程精度较高,该算法能实现GEO SAR全孔径高精度成像。     

Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.     

Gravity field models from kinematic orbits of CHAMP,GRACE and GOCE satellites

The aim of our work is to generate Earth’s gravity field models from GPS positions of low Earth orbiters. Our inversion method is based on Newton’s second law, which relates the observed acceleration of the satellite with forces acting on it. The observed acceleration is obtained as numerical second derivative of kinematic positions. Observation equations are formulated using the gradient of the spherical harmonic expansion of the geopotential. Other forces are either modelled (lunisolar perturbations, tides) or provided by onboard measurements (nongravitational perturbations). From this linear regression model the geopotential harmonic coefficients are obtained.     

Space debris mitigation in geosynchronous orbit

In order to preserve the geosynchronous region, the Inter-Agency Space Debris Coordination Committee (IADC) proposed and endorsed a re-orbiting strategy for spacecraft at the end-of-life: they should be disposed above the synchronous altitude and passivated, to reduce the risk of inadvertent explosions. The recommended perigee altitude of the disposal orbit took into account all relevant perturbations and was a function of the expected perturbing acceleration induced by solar radiation pressure. It was intended to prevent any further interference with a properly defined geostationary protected region.     

Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L₂ southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.     

The Investigation of Possible Approaches of Cataloged Space Objects to Manned Spacecraft

Initial orbital parameter errors are used to examine the miss distance between a spacecraft and an ensemble of tracked objects by a Monte Carlo-type analysis. The radial separation between orbits is evaluated and a keep-out zone is determined, which reduces the risk of collision to an acceptable level.An operational prediction methodology is suggested based on a catalog database, which identifies potentially hazardous approaches and computes the probability of collision for selected spacecraft. An example for the Mir Space Station is presented, which estimates the collision probability and the cross-sectional flux of cataloged objects for the time frame of interest. The results appear to be in good agreement with those of other space debris models.