Evolution of the Orbit of an Earth Satellite with a Solar Sail

The efficiency of using the light pressure of solar radiation for increasing the semimajor axis of the orbit of an Earth Satellite carrying a solar sail is estimated. The orbit is nearly circular and has an altitude of about 900 km. The satellite is in the mode of single-axis solar orientation: it rotates at an angular velocity of 1 deg/s around the axis of symmetry, which traces the direction to the Sun. This mode is maintained by the solar sail, which serves in this case as a solar stabilizer. The following method of increasing the semimajor axis of the orbit (which is equivalent to increasing the total energy of the satellite's orbital motion) is considered. On those sections of the orbit, where the angle between the light pressure force acting upon the sail and the vector of geocentric velocity of the satellite does not exceed a specified limit, the sail is functioning as a solar stabilizer. On those sections of the orbit, where the above-indicated angle exceeds this limit, the sail is furled by way of turning the edges of the petals towards the Sun. Such a control increases the semimajor axis by more than 150 km for three months of flight. In this case, the accuracy of solar orientation decreases insignificantly.     

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.     

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.     

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.     

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.     

Uncontrolled Attitude Motion of the Foton-12 Satellite and Quasi-Steady Microaccelerations onboard It

The results of determination of the uncontrolled attitude motion of the Foton-12 satellite (placed in orbit on September 9, 1999, terminated its flight on September 24, 1999) are presented. The determination was carried out by the onboard measurement data of the Earth's magnetic field strength vector. Intervals with a duration of several hours were selected from data covering almost the entire flight. On each such interval the data were processed simultaneously using the least squares method by integrating the satellite's equations of motion with respect to the center of mass. The initial conditions of motion and the parameters of the mathematical model employed were estimated in processing. The results obtained provided for a complete representation of the satellite's motion during the flight. This motion, beginning with a small angular velocity, gradually sped up. The growth of the component of the angular velocity with respect to the longitudinal axis of the satellite was particularly strong. During the first several days of the flight this component increased virtually after every passage through the orbit's perigee. As the satellite's angular velocity increased, its motion became more and more similar to the regular Euler precession of an axisymmetric rigid body. In the last several days of flight the satellite's angular velocity with respect to its longitudinal axis was about 1 deg/s and the projection of the angular velocity onto the plane perpendicular to this axis had a magnitude of approximately 0.15 deg/s. The deviation of the longitudinal axis from the normal to the orbit plane did not exceed 60°. The knowledge of the attitude motion of the satellite allowed us to determine the quasi-steady microacceleration component onboard it at the locations of the technological and scientific equipment.     

Can solar sails be used to test fundamental physics?

The relative importance of certain general relativistic effects is enhanced by solar radiation pressure (SRP). The observation and study of the trajectories of a solar sail could potentially provide tests of various effects of general relativity. In particular, we study Keplerian and non-Keplerian orbits near the sun as well as escape trajectories for a solar sail, for which general relativistic effects and the solar radiation pressure are considered simultaneously. In contrast with the conventional solar mission, a solar sail allows for non-Keplerian orbits, for which the orbital plane lies above the sun. It is predicted that there is an analog of the Lense–Thirring effect for non-Keplerian orbits. Also the SRP increases the amount of precession per orbit due to the Lense–Thirring effect for polar heliocentric orbits. A solar sail would also enhance the relative importance of effects associated with a possible net charge on the sun and during many rotations this effect may be measurable.     

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.     

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.     

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.     

Extrasolar solar-sail trajectories and dark matter

Hyper-thin, high-speed solar-photon sail space probes exploring the Sun?s Oort comet cloud could also be used to set an upper bound to the concentration of WIMPS (weakly interacting massive particles), one of the suggested (but unconfirmed) forms of dark matter within the vicinity of the solar system. Newton?s Shell Theorem would be applied to determine variations in apparent solar mass as the probe moves further out from the Sun. Application of this technique to the trajectories of Pioneer 10/11 reveals that the upper limit to WIMP concentration within ~60 AU of the Sun is ~0.2 Earth masses, as revealed in studies of the Pioneer Anomaly. If the published accuracy of the Pioneer acceleration measurements can be increased by an order of magnitude, probe trajectory measurements out to ~10,000 AU may confirm or falsify the hypothesis that WIMP mass within the solar vicinity is ~3X star mass. It is shown that a space-manufactured ~40-nm thick beryllium hollow-body solar sail deployed from a ~0.07 AU perihelion is a candidate spacecraft for such a mission. Possible science-team organization strategy for a ~100-year mission to ~10,000 AU is discussed.     

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.     

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.     

Experimental investigation of the modes of operation of uncontrolled attitude motion of the Progress spacecraft

Results of in-flight tests of three modes of uncontrolled attitude motion of the Progress spacecraft are described. These proposed modes of experiments related to microgravity are as follows: (1) triaxial gravitational orientation, (2) gravitational orientation of the rotating satellite, and (3) spin-up in the plane of the orbit around the axis of the maximum moment of inertia. The tests were carried out from May 24 to June 1, 2004 onboard the spacecraft Progress M1-11. The actual motion of this spacecraft with respect to its center of mass, in the above-mentioned modes, was determined by telemetric information about an electric current tapped off from solar batteries. The values of the current obtained during a time interval of several hours were processed jointly using the least squares method by integration of the equations of the spacecraft’s attitude motion. The processing resulted in estimation of the initial conditions of motion and of the parameters of mathematical models used. For the obtained motions the quasi-static component of microaccelerations was computed at a point onboard, where installation of experimental equipment is possible.     

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.     

Superlight rotating reflectors in space

There is a general possibility of creation in space of large controlled mirror reflectors for solar and electromagnetic radiation with specific mass order of 1 g m^?2 or less. Such reflectors may be used in space energetics for concentration of solar energy for its further conversion into microwave beam and transmission to the Earth. They can also be used to illuminate the Earth surface in a dark period with reflected sunlight, to control the weather, for research work and some other purposes. Such reflector is a good solar sail. The control of its orientation and position in space is performed using solar energy and light pressure without spending fuel delivered from the Earth. Its form is maintained by centrifugal forces and light pressure. The film strength permits concentrators with radii of several kilometres and nearly flat reflectors for lighting applications with radii of hundreds of metres. Large series of identical reflectors can be built in space using superthin film tape at assembly station. For a year more than a hundred reflectors with a diameter of 600 m can be assembled at such a station. The assembly station can be placed at the height of 1000 km. The reflectors transfer to synchronous or other orbit is performed using their sail-likeness. For realization of such reflectors one should solve a very difficult problem of superthin film mass production as well as assembly technology problems. Careful study and experimental checks of their lifetime should be also made.     

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.     

一种海洋测高卫星质心在轨估计算法

为了满足海洋测高卫星在轨质心位置精度的要求,提出了一种使用陀螺仪测量数据在轨估算卫星质心位置的算法。该算法利用推力器工作产生外力矩,采用总体最小二乘法,综合考虑了实际推力器推力的误差及陀螺仪的测量误差,由卫星的姿态动力学方程估算得到卫星质心位置。数值仿真证明了该算法的有效性,结果表明质心位置的估计精度在毫米量级,可以满足海洋测高卫星对质心位置精度的需求。     

European Sail Tower SPS concept

Based on a DLR-study in 1998/99 on behalf of ESA/ESTEC called “System Concepts, Architectures and Technologies for Space Exploration and Utilization (SE&U)” a new design for an Earth-orbiting Solar Power Satellite (SPS) has been developed. The design is called “European Sail Tower SPS” and consists mainly of deployable sail-like structures derived from the ongoing DLR/ESA solar sail technology development activity. Such a SPS satellite features an extremely light-weight and large tower-like orbital system and could supply Europe with significant amounts of electrical power generated by photovoltaic cells and subsequently transmitted to Earth via microwaves. In order to build up the sail tower, 60 units - each consisting of a pair of square-shaped sails - are moved from LEO to GEO with electric propulsion and successively assembled in GEO robotically on a central strut. Each single sail has dimensions of 150m × 150 m and is automatically deployed, using four diagonal light-weight carbon fiber (CFRP) booms which are initially rolled up on a central hub. The electric thrusters for the transport to GEO could also be used for orbit and attitude control of the assembled tower which has a total length of about 15 km and would be mainly gravity gradient stabilized. Employing thin film solar cell technology, each sail is used as a solar array and produces an electric power in orbit of about 3.7 MW_e. A microwave antenna with a diameter of 1 km transmits the power to a 10 km rectenna on the ground. The total mass of this 450 MW SPS is about 2100 tons. First estimates indicate that the costs for one kWh delivered in this way could compete with present day energy costs, if launch costs would decrease by two orders of magnitude. Furthermore, mass production and large numbers of installed SPS systems must be assumed in order to lower significantly the production costs and to reduce the influence of the expensive technology development. The paper presents the technical concept and an economic assessment as well as results of a recent solar sail deployment ground demonstration at DLR's facilities in Cologne.     

电动帆轨迹优化及其性能分析

电动帆是一种新兴的无推进剂损耗的推进方式,利用太阳风的动能冲力飞行。电动帆由数百根长而细的金属链所组成,这些金属链通过空间飞行器自旋展开,太阳能电子枪向外喷射电子,使金属链始终保持在高度的正电位,这些带电的金属链会排斥太阳风质子,利用太阳风的动能冲力推动空间飞行器驶向目标方向。针对电动帆轨迹优化问题,提出采用Gauss伪谱法进行轨迹优化,克服了间接法对协态变量初值敏感的缺点。考虑在太阳风暴等原因造成特征加速度改变的情况,基于Gauss伪谱法实现电动帆在线轨迹重新规划,提高电动帆对太阳风不确定性的适应能力。最后以太阳系外探测任务为例,对电动帆和太阳帆的性能进行对比,仿真结果表明电动帆在星际远航任务中所用时间较短。