Single-Axis Solar Orientation of a Satellite of the Earth

The possibility of using the mode of single-axis solar orientation is considered for a satellite placed into a nearly circular orbit with an altitude of 900 km and bearing a solar sail. The satellite (together with the sail) has an axisymmetric structure, its symmetry axis being the principal central axis of the maximum moment of inertia. The center of the sail pressure lies on this axis and is displaced with respect to the satellite's center of mass. The symmetry axis of the satellite is set to the Sun so that its center of mass would be located between the Sun and the pressure center and would rotate around this axis with an angular velocity of a few degrees per second. The satellite's axis of symmetry makes a slow precession under the action of the gravitational moment and the moment of light pressure forces. Though the maximum magnitudes of these moments are comparable, the moment of the light pressure forces dominates and controls the precession in such a way that the symmetry axis orientation to the Sun remains unchanged.     

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.     

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.     

Modes of uncontrolled rotational motion of the <Emphasis Type="Italic">Progress M-29M</Emphasis> spacecraft

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3–7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft’s angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft’s motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth–Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1–0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.     

Station keeping of a solar sail around a Halo orbit

Solar sails are a concept of spacecraft propulsion that takes advantage of solar radiation pressure to propel a spacecraft. Although the thrust provided by a solar sail is small it is constant and unlimited. This offers the chance to deal with novel mission concept. In this work we want to discuss the controllability of a spacecraft around a Halo orbit by means of a solar sail. We will describe the natural dynamics for a solar sail around a Halo orbit. By natural dynamics we mean the behaviour of the trajectory of a solar sail when no control on the sail orientation is applied. We will then discuss how a sequence of changes on the sail orientation will affects the sail's trajectory, and we will use this information to derive efficient station keeping strategies. Finally we will check the robustness of these strategies including different sources of errors in our simulations.     

Estimation of residual microaccelerations on board an artificial earth satellite in the monoaxial solar orientation mode

The mode of monoaxial solar orientation of a designed artificial Earth satellite (AES), intended for microgravitational investigations, is studied. In this mode the normal line to the plane of satellite’s solar batteries is permanently directed at the Sun, the absolute angular velocity of a satellite is virtually equal to zero. The mode is implemented by means of an electromechanical system of powered flywheels or gyrodynes. The calculation of the level of microaccelerations arising on board in such a mode, was carried out by mathematical modeling of satellite motion with respect to the center of masses under an effect of gravitational and restoring aerodynamic moments, as well as of the moment produced by the gyrosystem. Two versions of a law for controlling the characteristic angular momentum of a gyrosystem are considered. The first version provides only attenuation of satellite’s perturbed motion in the vicinity of the position of rest with the required velocity. The second version restricts, in addition, the increase in the accumulated angular momentum of a gyrosystem by controlling the angle of rotation of the satellite around the normal to the light-sensitive side of the solar batteries. Both control law versions are shown to maintain the monoaxial orientation mode to a required accuracy and provide a very low level of quasistatic microaccelerations on board the satellite.     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

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°.     

条带式太阳帆航天器的热致结构动力学响应

本文研究条带式太阳帆在近地轨道运行进出地球阴影时的热致结构动力学响应，建立了在太阳热辐射和光压共同作用下的太阳帆结构动力学方程，采用分布传递函数法，给出了条带式太阳帆热致结构稳态振动幅频响应的计算方法。算例结果表明：热辐射冲击是引起近地轨道太阳帆结构动力学响应的主要原因，光压引起的结构响应可忽略不计；增加桅杆壁厚不能有效抑制太阳帆的热致结构动态响应；增大阻尼，减小结构的热膨胀系数能够明显减小太阳帆热致结构响应的振幅；热致结构动态响应是设计大尺寸近地轨道太阳帆必须解决的问题。本文提出的方法可为太阳帆结构设计、姿态和轨道控制提供有力的分析工具。     

The results of flight tests of an attitude control system for the Chibis-M microsatellite

The attitude control system of the Chibis-M microsatellite is described. Results of flight experiments on damping the initial angular velocity (made using magnetorquers) are considered, as well as stabilization in the orbital referece frame, and orientation of solar arrays toward the Sun using reaction wheels. The operation of algorithms of satellite attitude determination on sunlit and shadow segments of the orbit is also under study. The general logic of operation of the attitude control system in automatic mode is presented and discussed.     

倾角偏置太阳同步轨道的地面轨迹保持方法

为在倾角偏置条件下保持太阳同步轨道卫星的地面轨迹,在考虑地球扁率摄动、大气阻力摄动和太阳引力谐振等主要影响因素,以及卫星地面轨迹允许漂移范围的基础上,采用主动超调与被动控制结合的策略,提出了一种初始半长轴偏置后的卫星地面轨迹保持方法。分析了半长轴和倾角摄动变化率,以及初始半长轴和倾角偏置量对地面轨迹漂移的影响。仿真结果表明,该法可基本满足设计阶段的精度要求。     

NanoSail-D: A solar sail demonstration mission

In the early to mid-2000s, NASA made substantial progress in the development of solar sail propulsion systems. Solar sail propulsion uses the solar radiation pressure exerted by the momentum transfer of reflected photons to generate a net force on a spacecraft. To date, solar sail propulsion systems were designed for large robotic spacecraft. Recently, however, NASA has been investigating the application of solar sails for small satellite propulsion. The NanoSail-D is a subscale solar sail system designed for possible small spacecraft applications. The NanoSail-D mission flew on board the ill-fated Falcon Rocket launched August 2, 2008, and due to the failure of that rocket, never achieved orbit. The NanoSail-D flight spare is ready for flight and a suitable launch arrangement is being actively pursued. This paper will present an introduction solar sail propulsion systems and an overview of the NanoSail-D spacecraft.     

FY-2C星发射轨道计算与分析

根据卫星发射窗口的一般性和风云二号(FY-2)C气象卫星特定限制条件,计算了2004年10月19日符合要求的发射窗口.在比较上午和晚上发射窗口的基础上,确定C星选择上午发射窗口.给出了影响卫星定点捕获所需速度增量的入轨轨道参数和点火姿态等因素,并仿真计算了轨道半长轴、近地点高度、倾角和近地点幅角与速度增量的关系.分析结果表明,卫星发射窗口的确定与星、地、日间的位置密切相关.入轨偏差越小,定点捕获所需肼燃料消耗也越少.     

太阳帆绕地球周期轨道研究

  地球同步和太阳同步卫星在各个领域有着广泛的应用。静止轨道是一种特殊的地球同步轨道,轨道资源有限。利用化学推进或电推进可以实现轨道高度不同的同步轨道,如悬挂轨道,但需要消耗较多的燃料,工程上无法承受。本文考虑利用太阳帆实现地球同步和太阳同步轨道。太阳光压力在轨道平面内沿拱线方向,选择光压力与平面的夹角使得轨道平面的旋转速率与太阳光同步。研究表明,设计合适的半长轴和偏心率可以使得轨道旋转速率与地球自转速率一致。假设太阳光与赤道平面平行,可以得到准静止轨道,太阳帆将在传统静止轨道的附近运动,星下点的经度将在一个固定值附近振动。实际上太阳光是与黄道面平行,黄道面与赤道面之间存在夹角。考虑黄赤交角的情况下,太阳帆将在一定纬度和经度范围内运动。适合于对某个区域进行长期观测任务。     

卫星热设计中β角在不同轨道下的变化规律分析

阳光矢量与卫星轨道平面之间夹角是卫星热控设计中至关重要的一个设计参数,其不仅与到达卫星表面的阳光热流密度密切相关,也与到达卫星表面的地球反射热流密度密切相关。文章根据β角的变化规律将传统意义上的轨道分为了同步轨道和非同步轨道两种,并结合升黄赤经夹角的变化规律分析了不同轨道下β角的变化规律,以及相应的热设计特点。     

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     

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.     

太阳帆日心定点悬浮转移轨道设计

研究了太阳帆航天器日心定点悬浮轨道(HFDO)的转移轨道设计问题,以球坐标形式建立了太阳帆的动力学模型,基于该模型给出在日心悬浮轨道基础上实现定点悬浮的条件,提出了一种实现日心定点悬浮的转移轨道设计方法。首先,确定定点悬浮的位置;然后,设计经过该位置的绕日极轨轨道;最后,实施轨道减速实现定点悬浮,并给出了解析形式的轨道控制律。结合太阳极地观测任务,设计了定点悬浮在太阳北极1AU处的太阳帆转移轨道。仿真结果表明:该轨道转移方案总耗时3.5年,太阳帆定点到黄北极距日心1AU处,此后只要保持太阳光垂直照射帆面,即可维持稳定的悬浮状态。     

Control of an orbiting flexible square platform in the presence of solar radiation

A mathematical model for the solar radiation forces and moments acting on a square plate (platform) in orbit is obtained by considering the plate mode shapes as combinations of free-free beam shape functions. The moment expressions for a plate of arbitrary reflectivity coefficient are obtained as a function of the solar incidence angle. It is seen that only the first three flexible modes of the plate generate a first order net moment about the center of mass, and that the solar radiation pressure does not influence the flexible modes of the plate for small amplitude vibrations. The solar radiation disturbance model is then included in the dynamic model of a square plate nominally oriented along the local vertical and having the major surface of the plate normal to the orbital plane. The roll angle of the plate is seen to increase steadily due to the solar radiation pressure whereas the pitch and yaw motions oscillate with an amplitude of approximately 0.2° for a 100 m square thin aluminum plate in synchronous orbit. To control the shape and orientation of the plate two point actuators are assumed—one whose force axis is normal to the plane of the plate, the second with a force axis in the plane of the plate. The control law and the feedback gain values are obtained based on linear quadratic Gaussian methods. Transient responses and control requirements are simulated for local vertical and horizontal orientations.     

Calculation of resultant vector and principal moment of light pressure forces acting upon the spacecraft with a solar sail

Two methods of calculating the resultant vector and principal moment of light pressure forces, having an effect on a spacecraft with a composite solar sail, are compared. The first method is based on analytical formulas obtained without regard to shading of some parts of the sail by others. The second method uses a detailed geometrical model of the sail, which allows one to take such shading into account. Some part of photons falling on a sail is supposed to be reflected from it in a mirror manner, while the others are completely absorbed. The range of variation of sail orientation parameters with respect to incident solar light streams, where the first method turns out to be accurate enough, is found.