地球磁场对带电赤道卫星的轨道半长轴和偏心率的摄动影响

本文利用摄动理论研究了带电的赤道卫星在地球磁场中做椭圆轨道运动时地磁摄动力对轨道半长径和偏心率的摄动影响。研究结果表明：地磁场对带电赤道卫星的轨道半长径没有摄动影响，既无周期摄动，也无长期摄动，但对轨道偏心率有摄动影响，且只有周期性摄动，而无长期摄动。当卫星自身带电量较大时，这种摄动影响必须予以考虑     

Decay of high eccentricity satellite orbits with air drag using uniformly regular KS canonical elements

A non-singular analytical theory for the motion of high eccentricity satellite orbits under the influence of air drag is developed in terms of the Uniformly Regular Kustaanheimo and Stiefel (URKS) canonical elements, by assuming the atmosphere to be oblate with variation of density scale height with altitude. The series expansions include up to fourth-order terms of an independent variable Δ=λ² (function of eccentric anomaly) and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically due to symmetry in the equations of motion. Comparison of the important orbital parameters semi-major axis and eccentricity up to 1000 revolutions, obtained with the present analytical solution and the KS theory, shows the superiority of the present solution over the KS elements analytical solution. The theory can be used effectively for the orbital decay of aero-assisted orbital transfer orbits during mission planning.     

SST-LL重力测量卫星轨道分析

论述了SST-LL重力测量卫星科学任务对轨道寿命、地面覆盖性能、轨道高度单圈波动、星间距离变化范围的需求。根据需求,计算了轨道的自然衰减情况,得出轨道初始高度为500km;综合考虑地面覆盖要求及运载火箭能力,得出了最佳轨道倾角为89°;得出了0.002 0偏心率下轨道高度波动范围不超过50km;分析得出星间距离的长周期变化主要受大气阻力影响,初步确定了轨道控制方案,即定期对受大气阻力较大的卫星进行轨道机动。     

动量轮卸载在改进GEO卫星东西轨道保持中的应用

空间外干扰力矩会使在轨GEO三轴卫星动量轮转速发生周期性变化,因此需要进行动量轮卸载。通过对卸载前后卫星轨道根数的比较,发现动量轮卸载可以延长卫星实际的东西轨道保持周期。以动量轮卸载有利卫星轨道保持为研究目的,通过计算和分析,推导出动量轮卸载时转速变化与卫星半长轴变化关系的数学模型,并以实际测量数据为基础,对模型进行了仿真验证,证明了动量轮卸载对改进GEO卫星东西轨道保持的可行性,提出了一种利用动量轮卸载改进GEO卫星东西轨道保持策略的新方法。     

分布式卫星轨道构形的大气摄动分析及修正方法

在低轨道运行的分布式卫星受大气摄动的影响,其轨道构形很快遭到破坏,环绕卫星的相对运动轨迹中心不断发生漂移。本研究的目的在于建立一种降低大气摄动对分布式卫星轨道构形影响的补偿方法,以使分布式卫星的轨道构形能够更好地自然维持。研究基于考虑高度变化和太阳周日变化的大气密度模型,得出分布式卫星不同初始相位环绕卫星的长半轴摄动方程。并提出一种补偿大气摄动影响的长半轴修正方法。仿真结果显示,采用此大气摄动补偿方法能够在给定时间内大大降低大气摄动的影响,从而显著提高分布式卫星轨道构形的自然维持能力。     

低轨卫星编队飞行的地面覆盖及轨道调整

通过施加冲量的方法消除J2项摄动和大气阻力摄动对编队飞行的影响,在编队的相对构型和整体绝对位置得到控制后,研究了低轨卫星编队飞行的地面覆盖问题,最后通过算例给出了卫星编队在南北纬86°之间全球覆盖所需的时间、周期、圈数和覆盖角。计算结果表明,对于偏心率较小的低轨编队飞行,根据本文所推导公式计算出的结果是比较可靠的。     

太阳同步回归轨道的长期演变与控制

近地轨道的遥感卫星绝大部分都采用太阳同步回归轨道。这类轨道由于受到大气阻力的影响,半长轴将不断地衰变并导致地面轨迹的东漂,为保持回归特性需周期性地对半长轴进行调整。另一类长期变化是太阳引力引起的倾角变化,这是太阳同步轨道特有的。倾角长期的变化又进一步导致回归轨道的标称半长轴和降交点地方时的相应变化。文章给出了这些变化的解析模型以及轨道控制的策略。     

地磁扰动期间低轨目标轨道预报的误差修正

针对地磁扰动期间大气密度变化造成的低轨目标较大的轨道预报误差,提出一种根据POES卫星观测的极光能量注入数据改进短期轨道预报的方法。分析表明CHAMP卫星的沿迹大气密度及轨道衰减与极光能量注入具有较好的相关性。通过线性回归方法,建立轨道半长轴衰减及阻力调制系数的修正公式,并使用修正后的阻力调制系数取代两行元(TLE)中的该系数带入SGP4模型进行位置预报。该方案考虑了外推过程中地磁扰动引起的大气密度响应,能更准确地反映外推过程中大气阻力对轨道的影响。将其应用到2008年CHAMP卫星和国际空间站的轨道预报中,结果表明,半长轴和位置的预报误差可分别降低50%和30%左右。进一步对不同年份、不同轨道高度的目标进行了预报误差修正的分析,验证了该方法的普适性。     

用于对地观测定位的编队飞行卫星群轨道构形设计

编队飞行卫星群是一组小卫星,它们具有短的相对距离、相等的轨道半长轴和微小差别的其它轨道要素,它们形成相互伴随运动,并且具有一定的构形。提出将编队飞行卫星群的轨道设计技术应用于对地观测定位卫星系统中。根据设想的要求,针对由四颗伴随卫星围绕基准卫星(或一个虚拟的中心)飞行的轨道设计案例,初步分析了编队飞行卫星群的构形保持,地球引力和大气阻力的摄动影响等问题。     

大气阻力摄动对卫星编队飞行队形的影响分析

为了分析大气阻力摄动对卫星编队队形的影响,利用相对轨道根数法推导了包含大气阻力摄动的卫星编队相对运动的状态转移方程。仿真结果表明当几何形状和质量不同的两颗卫星在低轨道做编队飞行时,大气阻力摄动对编队队形的影响很大而不能忽略;当主卫星的半长轴相等时,主卫星轨道的偏心率越大编队飞行受大气阻力摄动的影响也越大;大气阻力摄动主要影响编队飞行迹向相对距离。     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

空间摄动对InSAR卫星编队的影响研究

针对干涉合成孔径雷达(InSAR)编队卫星的特点,分析了地球形状、大气阻力、第三体引力和太阳光压等空间摄动力对卫星轨道的影响,并仿真讨论其对编队构型的影响。结果表明:地球形状摄动和大气阻力摄动是引起InSAR编队构型变化的主要摄动因素,在这些摄动力的作用下,编队构型的变化主要是沿航迹向的累积变化和编队椭圆的空间指向变化两种,并给出了编队构型随时间的变化量。研究为编队保持控制提供了参考。     

Elimination of relative secular drift of orbits of two satellites caused by polar oblateness of the Earth

A method of elimination of relative secular drifts in satellite formations is suggested for the case of influence of a perturbation due to polar oblateness of the Earth. The method is applied to eliminate relative secular drifts in the case when a satellite is controlled using an engine mounted along its orientation axis (the satellite is supplied with a passive magnetic attitude control system) and with the help of a solar sail installed on one of the satellites. Analytical results are confirmed by numerical simulation.     

Nonlinear Evolution of a Balloon Satellite Orbit

The motion of a spherically symmetric balloon satellite near the equatorial plane is considered. Taking the Earth's oblateness and solar light pressure into account, the integral of motion can be obtained under certain simplifications. The eccentricity is related to the solar angle which represents an angle between pericenter and the Sun. This analytical approximation describes a large and complicated evolution of the eccentricity in corresponding areas of the phase space and the space of parameters. Phase portraits contain fixed saddle points and separatrices that divide different types of oscillations of the eccentricity. In the unsimplified problem, separatrices break down, and specific stochastic motions arise. The aims of the present study are (1) evaluation of the accuracy of analytical approximation with the help of numerical integration using a sufficiently complete model of motion and (2) numerical investigation of stochastic motions and dimensions of stochastic zones in the region of broken separatrices for an adequate model of motion. For a balloon satellite with a semimajor axis of 2.15 Earth's radii and a windage of 30 cm²/g the dimensions of a stochastic zone in eccentricity and solar angle are 10^–5and 0.1°, respectively. The analytical approximation describes the orbit evolution in the right way, except for the cases of large eccentricities, e> 0.4, which corresponds to a pericenter height of less than 1400 km, where the atmospheric drag is already significant.     

Variation of the Satellite Orbit Altitude by the Light Pressure Force

The possibility of the uncontrolled increase of the altitude of an almost circular satellite orbit by the force of the light pressure is investigated. The satellite is equipped with a damper and a system of mirrors (solar batteries can serve as such a system). The flight of the satellite takes place in the mode of a single-axis gravitational orientation, the axis of its minimum principal central moment of inertia makes a small angle with the local vertical and the motion of the satellite around this axis constitutes forced oscillations under the impact of the moment of force of the light pressure. The form of the oscillations and the initial orbit are chosen so that the transverse component of the force of the light pressure acting upon the satellite be positive and the semimajor axis of the orbit would continuously increase. As this takes place, the orbit remains almost circular. We investigate the evolution of the orbit over an extended time interval by the method which employs separate integration of the equations of the orbital and rotational motions of the satellite. The method includes outer and inner cycles. The outer cycle involves the numerical integration of the averaged equations of motion of the satellite center of mass. The inner cycle serves to calculate the right-hand sides of these equations. It amounts to constructing an asymptotically stable periodic motion of the satellite in the mode of a single-axis gravitational orientation for current values of the orbit elements and to averaging the equations of the orbital motion along it. It is demonstrated that the monotone increase of the semimajor axis takes place during the first 15 years of motion. In actuality, the semimajor axis oscillates with a period of about 60 years. The eccentricity and inclination of the orbit remain close to their initial values.     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

Orbit design for the Spektr-R spacecraft of the ground-space interferometer

In order to carry out tasks of the RadioAstron mission, a high-apogee orbit was designed. On average, the period of its satellite’s orbit around the Earth is 8.5 days with evolution due to gravitational perturbations produced by the Moon and the Sun. The perigee and apogee of this orbit vary within the limits 7500–70000 km and 270000–333000 km, respectively. The basic evolution of the orbit represents a rotation of its plane around the line of apsides. Over 3 years, the plane normal to the orbit draws on the celestial sphere an oval with a semi-major axis of about 150° and semi-minor axis of about 45°.     

Fourth-order theories for orbit predictions for low- and high-eccentricity orbits in an oblate atmosphere with scale height dependent on altitude

Two new fourth-order non-singular analytical theories for the motion of near-Earth satellite orbits with air drag are developed for low- and high-eccentricity orbits in an oblate atmosphere with variation of density scale height with altitude. Uniformly regular Kustaanheimo–Stiefel (KS) canonical elements are utilized for low-eccentricity orbits and KS element equations are employed for high-eccentricity orbits. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The analytical solutions are compared with the numerically integrated values up to 100 revolutions, and found to be quite accurate over a wide range of eccentricity, perigee height and inclination.     

J2摄动作用下近地轨道卫星编队构形长期演化机理分析

研究近地轨道卫星编队构形在引力摄动作用下的长期演化机理。把用转移矩阵法得出的相对运动分析解表达成一般轨道根数形式，为研究摄动影响而进一步表达成无奇点轨道根数形式；根据各轨道根数的J2摄动解分别研究编队构形在轨道坐标系三个方向上的振幅与相位的长期变化情况，揭示了构形引力摄动的长期演化机理；给出编队构形的摄动表达式，并以仿真实例验证其可信性；最后给出构形长期引力摄动的相关结论，并对编队构形设计提出建议，这将为研究编队构形的规划技术带来方便。