Drag force on solar sails due to absorption of solar radiation

We consider a special relativistic effect, known as the Poynting–Robertson effect, on various types of trajectories of solar sails. Since this effect occurs at order v^?/c, where v^? is the transversal speed relative to the sun, it can dominate over other special relativistic effects, which occur at order v²/c². While solar radiation can be used to propel the solar sail, the absorbed portion of it also gives rise to a drag force in the transversal direction. For escape trajectories, this diminishes the cruising velocity, which can have a cumulative effect on the heliocentric distance. For a solar sail directly facing the sun in a bound orbit, the Poynting–Robertson effect decreases its orbital speed, thereby causing it to slowly spiral towards the sun. We also consider this effect for non-Keplerian orbits in which the solar sail is tilted in the azimuthal direction. While in principle the drag force could be counter-balanced by an extremely small tilt of the solar sail in the polar direction, periodic adjustments are more feasible.     

On the stabilizing effect of Solar Radiation Pressure in the Earth-Moon system

Solar sails change the natural dynamics of systems: Trajectories that are driven by gravitational forces can be displaced and changed because of the effect of Solar Radiation Pressure (SRP). Moreover, if the lightness number of the sail is large enough, the instability of certain orbits can be diminished and even removed. In this paper we modify two models for the motion of a probe in the Earth-Moon system that include the effect of Sun’s gravity to take also into account the effect of SRP. These models, the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP), are periodic perturbations of the Earth-Moon Restricted Three Body Problem (RTBP). The models are modified to consider the effect of the SRP upon a solar sail. We provide examples of periodic orbits that are stabilized (or made less unstable) due to the effect of SRP.     

An empirical solar radiation pressure model for satellites moving in the orbit-normal mode

We present a family of empirical solar radiation pressure (SRP) models suited for satellites orbiting the Earth in the orbit normal (ON) mode. The proposed ECOM-TB model describes the SRP accelerations in the so-called terminator coordinate system. The choice of the coordinate system and the SRP parametrization is based on theoretical assumptions and on simulation results with a QZS-1-like box-wing model, where the SRP accelerations acting on the solar panels and on the box are assessed separately. The new SRP model takes into account that in ON-mode the incident angle of the solar radiation on the solar panels is not constant like in the yaw-steering (YS) attitude mode. It depends on the elevation angle of the Sun above the satellite’s orbital plane. The resulting SRP vector acts, therefore, not only in the Sun-satellite direction, but has also a component normal to it. Both components are changing as a function of the incident angle. ECOM-TB has been used for precise orbit determination (POD) for QZS-1 and BeiDou2 (BDS2) satellites in medium (MEO) and inclined geosynchronous Earth orbits (IGSO) based on IGS MGEX data from 2014 and 2015. The resulting orbits have been validated with SLR, long-arc orbit fits, orbit misclosures, and by the satellite clock corrections based on the orbits. The validation results confirm that—compared to ECOM2—ECOM-TB significantly (factor 3–4) improves the POD of QZS-1 in ON-mode for orbits with different arc lengths (one, three, and five days). Moderate orbit improvements are achieved for BDS2 MEO satellites—especially if ECOM-TB is supported by pseudo-stochastic pulses (the model is then called ECOM-TBP). For BDS2 IGSOs, ECOM-TB with its 9 SRP parameters appears to be over-parameterized. For use with BDS2 IGSO spacecraft we therefore developed a minimized model version called ECOM-TBMP, which is based on the same axis decomposition as ECOM-TB, but has only 2 SRP parameters and is supported by pseudo-stochastic parameters, as well. This model shows a similar performance as ECOM-TB with short arcs, but an improved performance with (3-day) long-arcs. The new SRP models have been activated in CODE’s IGS MGEX solution in Summer 2018. Like the other ECOM models the ECOM-TB derivatives might be used together with an a priori model.     

太阳帆飞行器轨道动力学分析

通过分析对轨道要素影响最大的加速度分量,使太阳帆总是位于光压力沿这个加速度方向的分量最大的方位。通过分析轨道要素调整时的相互影响关系,提出了同时修正多种轨道偏差的控制方案。对处于地球静止轨道上太阳帆飞行器的轨道调整进行了数值仿真。结果证明利用太阳光压力进行轨道调整是可行的,而且有利的太阳方位是进行快速有效的轨道调整的必要条件。     

Heliotropic dust rings for Earth climate engineering

This paper examines the concept of a Sun-pointing elliptical Earth ring comprised of dust grains to offset global warming. A new family of non-Keplerian periodic orbits, under the effects of solar radiation pressure and the Earth’s J₂ oblateness perturbation, is used to increase the lifetime of the passive cloud of particles and, thus, increase the efficiency of this geoengineering strategy. An analytical model is used to predict the orbit evolution of the dust ring due to solar-radiation pressure and the J₂ effect. The attenuation of the solar radiation can then be calculated from the ring model. In comparison to circular orbits, eccentric orbits yield a more stable environment for small grain sizes and therefore achieve higher efficiencies when the orbit decay of the material is considered. Moreover, the novel orbital dynamics experienced by high area-to-mass ratio objects, influenced by solar radiation pressure and the J₂ effect, ensure the ring will maintain a permanent heliotropic shape, with dust spending the largest portion of time on the Sun facing side of the orbit. It is envisaged that small dust grains can be released from a circular generator orbit with an initial impulse to enter an eccentric orbit with Sun-facing apogee. Finally, a lowest estimate of 1 × 10¹² kg of material is computed as the total mass required to offset the effects of global warming.     

基于非开普勒轨道的高超声速临近空间飞行器自主天文导航研究

针对航天器自主导航方法不适合高超声速临近空间飞行器的问题, 研究了基于非开普勒轨道的高超声速临近空间飞行器自主天文导航方案. 论述了基于非开普勒轨道的自主天文导航机理, 通过对高超声速临近空间飞行器受力分析, 建立了动力学方程; 利用矢量倒数法则推导出空间运动方程; 设计了基于非开普勒轨道的状态模型和基于星光折射间接敏感地平的观测模型, 采用卡尔曼滤波进行了仿真验证. 仿真结果表明, 基于非开普勒轨道的高超声速临近空间飞行器自主天文导航可达到较高的位置和速度精度.      

航天器在轨道运行中太阳帆板的温度问题

本文应用能量平衡的基本原理, 获得了航天器在几种典型热工况中太阳帆板的能量平衡的基本方程以及宇宙空间的热辐射角系数基本方程.利用数值积分法, 得到了角系数的数值以及太阳帆板在不同的轨道所承受的最大温度波动, 在考虑这一温度效应后, 用有限元法分析计算了太阳能电池帆板的固有频率特性.计算结果表明, 航天器在空间轨道运行时, 通过阴区和阳区所产生的温度变化对太阳帆板的动力学特性影响是不容忽略的问题.      

连续小推力非开普勒悬浮轨道研究综述

连续小推力非开普勒悬浮轨道在深空探测与地球极地观测任务中有着重要的应用前景。归纳了电推进、太阳帆推进等连续小推力技术的发展历程与现状;阐述了日心、行星悬浮轨道的动力学特性、稳定性、轨道保持策略;分析了三体问题下人工拉格朗日点的优势及其在深空探测方面的应用;讨论了悬浮轨道编队飞行的研究方法与控制策略。最后针对小推力悬浮轨道研究发展面临的难题,提出了研究新思路和应用新方向。     

Spacecraft formation and orbit control using differential attitude-dependent solar radiation pressure

This paper introduces a linear model for spacecraft formation dynamics subject to attitude-dependent solar radiation pressure (SRP) disturbance, with the SRP model accounting for both absorption and specular/diffuse reflection. Spacecraft attitude is represented in modified Rodriguez parameters (MRPs), which also parameterize the orientation of individual facets for a spacecraft with fixed geometry. Compared to earlier work, this model incorporates analytic approximation of the SRP-perturbed chief orbit behavior in a manner enabling its use in applications with infrequent guidance updates. Control examples are shown for single-plate representations of hypothetical spacecraft with generally realistic optical parameters. The results demonstrate the validity of the model and the feasibility of SRP-based formation and rendezvous control in orbits around small bodies and in high orbits around the Earth such as the GEO belt.     

Possible influence of cosmic rays on climate through thunderstorm clouds

With decreasing of cosmic ray (CR) intensity caused by increasing of solar activity (SA) or in some short periods of Forbush-decreases, the intensity of secondary CR relativistic electrons decreases and the probability of formation of thunderstorm clouds and discharges between clouds or between clouds and ground is also expected to decrease. This will influence on weather and climate. In this case is very important to have more detail information on the atmospheric electric field distribution in the atmosphere, additional to information what gave now electric field sensors (EFS) only in about one point near the ground. We show that CR not only influenced on atmospheric electric field phenomenon, but can give practically continuous information on the atmospheric electric field distribution in the atmosphere. We extend our theory of CR atmospheric electric field effect on electron–photon, muon and neutron component including different multiplicities. We take into account that about 0.07 of neutron monitor counting rate caused by negative soft muons captured by lead nucleons and formed mesoatoms with generation of several MeV energy neutrons from lead. In this case the neutron monitor or neutron super-monitor works as analyzer that detects muons of only one, negative sign. It is very important because the atmospheric electric field effect have opposite signs for positive and negative muons that main part of this effect in the muon telescope or in ionization chamber is compensated and we can observe only small part of total effect of one sign muons. On the basis of our general theory of CR atmospheric electric field effects with taking into account of negative soft muon acceleration and deceleration in the Earth atmosphere (in dependence of direction and intensity of electric field) we discuss the possibility of existing this effect in CR neutron monitor counting rate and in different multiplicities and calculate the expected effects in dependence of atmospheric electric field distribution in the atmosphere. We show that the comparison of observed effects with theoretically expected will give important information on the value of atmospheric electric field and its distribution in the atmosphere. We consider also the possible influence of secondary relativistic electrons of CR and relativistic electrons precipitated from the Earth’s radiation belts on thunderstorms and lightnings, and through this – on climate change.     

H-reversal trajectory: A new mission application for high-performance solar sails

The aim of this paper is to quantify the performance of a flat solar sail to perform a double angular momentum reversal maneuver and produce a new class of two-dimensional, non-Keplerian orbits in the ecliptic plane. For a given pair of orbital parameters, the orbital period and the perihelion distance, it is possible to find the minimum solar sail characteristic acceleration required to fulfil a double angular momentum reversal trajectory. This problem is addressed using an optimal formulation and is solved through an indirect approach. The new trajectories are symmetrical with respect to the sun-perihelion line and exhibit a bean-like shape. Two main difficulties must be properly taken into account. On one side the sail is required to perform a rapid reorientation maneuver when it approaches the perihelion. Suitable simulations have shown that such a maneuver is feasible. In the second place the new trajectories require the use of high performance solar sails. For example, assuming an orbital period equal to 5 years, the required solar sail characteristic acceleration is greater than 3.4 mm/s². Such a value, although beyond the currently available sail performance, is comparable to what is required by the original concept of H-reversal maneuvers introduced by Vulpetti in 1996.     

Surface shape control of integrated paraboloid space reflector consisting of sub-reflectors exploiting modulated solar pressure

Reflectors are very critical space elements and can be used not only as solar collectors/reflectors, telecommunication radio antennas and telescopes but also for dual-usage such as solar sails and solar concentrators to probe and sublimate materials from asteroids when actively controlling the surface shape. In this paper, the surface shape of a slack reflector with negligible elastic deformations will be controlled to be a paraboloid by actively modulating the solar radiation pressure (SRP) force using reflectivity control devices (RCDs) across the reflector. Nonlinear static equilibrium equations for an arbitrary infinitesimal within the reflector along the radial, circumferential and transverse directions are established considering the external modulated SRP force and internal tensions respectively. The coupled radial stress differential governing equation and reflectivity algebraic equation are obtained for the paraboloid reflector by the help of the formulation of an inverse problem based on equilibrium equations previously established. Some analytical and numerical analysis for reflectors with ideal and non-perfect SRP force models are performed respectively. The conclusions concerning about how to control the reflector’s surface shape successfully using allowed reflectivity, resulting in reasonable stress range, moreover, how to get the feasible solutions influenced by the reflector’s size parameters, are all based on the presented analytical and numerical analysis.     

X-ray, γ-emission and energetic particles in near-Earth space as measured by CORONAS-F satellite: From maximum to minimum of the last solar cycle

The Russian solar observatory CORONAS-F was launched into a circular orbit on July 31, 2001 and operated until December 12, 2005. Two main aims of this experiment were: (1) simultaneous study of solar hard X-ray and γ-ray emission and charged solar energetic particles, (2) detailed investigation of how solar energetic particles influence the near-Earth space environment. The CORONAS-F satellite orbit allows one to measure both solar energetic particle dynamics and variations of the solar particle boundary penetration as well as relativistic electrons of the Earth’s outer radiation belt during and after magnetic storms. We have found that significant enhancements of relativistic electron flux in the outer radiation belt were observed not only during strong magnetic storms near solar maximum but also after weak storms caused by high speed solar wind streams. Relativistic electrons of the Earth’s outer radiation belt cause volumetric ionization in the microcircuits of spacecraft causing them to malfunction, and solar energetic particles form an important source of radiation damage in near-Earth space. Therefore, the present results and future research in relativistic electron flux dynamics are very important.     

The cosmic ray ground level enhancement of 6 November 1997.

The relativistic solar proton event of 6 November 1997 resulted in the first ground-level enhancement (GLE) of solar cycle 23. The earliest onset was around 1215 UT but was up to 15 minutes later at some neutron monitor locations. The time of maximum intensity also varied significantly over the world-wide neutron monitor network. The modeled particle distributions and spectra are presented. The apparent particle arrival direction is found to be largely consistent with propagation outward from the sun along interplanetary magnetic field lines.     

考虑太阳摄动的小行星附近轨道动力学

本文研究了艳后星(216 Kleopatra)和爱神星(433 Eros)附近的周期轨道,在考虑太阳引力摄动的情况下,发现了以往所遗漏的216 Kleopatra轨道族和环绕433 Eros的12族周期轨道,并且给出了它们的特性。研究结果表明,太阳引力对小行星平衡点位置的影响很小,但是对平衡点上航天器运动的影响较大。同族不稳定轨道中,大Jacobi常数轨道更容易在摄动后保持轨道原来特性,这很好地解释了小行星卫星在较远轨道上长期存在的可能性。     

Dynamics of solar cosmic ray events: Processes at large heliocentric distances (⪢1 AU)

Observations of solar cosmic ray events far from the sun (?1 AU) became possible after the launch of Pioneer 10 in 1972. Four spacecraft have now travelled beyond the orbit of Jupiter - Pioneer 10/11 and Voyager 1/2 — and are producing a growing body of distant observations of solar cosmic ray events. Initial studies using Pioneer 10/11 data out to ～6 AU interpreted flare particle observations in terms of a diffusion model, including the effects of convection and adiabatic energy loss. This model enjoyed general success in explaining the time-intensity profiles in cases where the spacecraft connection longitude at the sun did not change significantly with time. The results implied that the radial diffusion coefficient (K_r) increased slowly with distance over that radial range. More recent results at larger distances imply that K_r may begin to decrease beyond ～5 AU. It is not yet clear whether the standard diffusion model will be adequate to explain solar events well beyond 5 AU. The fact that large events at very large distances can last up to two solar rotations implies that solar wind stream structure will also play a role in the event dynamics. In general, however, observations at large distances offer perhaps the best hope of separating interplanetary propagation effects from coronal storage and propagation effects which frequently dominate observed event profiles at 1 AU.     

基于目标特性的航天器太阳光压面积计算方法

太阳光压是影响深空探测航天器轨道确定与预报精度最主要的摄动力.针对实际任务需求,采用了一种基于目标特性的光压面积建模与计算方法,根据航天器形状、尺寸、表面材料以及材料光学特性等信息,实现了分析型光压模型的建立与求解,提高了计算效率和精度,可快速计算目标在光照方向上的光压面积、投影面积以及光压比例因子等参数.通过长方体光压面积理论值与仿真值的对比,验证了该方法的准确性和有效性.针对复杂结构探测器开展了光压面积计算,可为深空探测航天器精密定轨中的光压模型解算、定轨及预报提供参考.      

A torus-shaped solar sail accelerated via thermal desorption of coating

A torus-shaped sail consists of a reflective membrane attached to an inflatable torus-shaped rim. The sail’s deployment from its stowed configuration is initiated by introducing inflation pressure into the toroidal rim with an attached circular flat membrane coated by heat-sensitive materials that undergo thermal desorption (TD) from a solid to a gas phase. Our study of the deployment and acceleration of the sail is split into three steps: at a particular heliocentric distance a torus-shaped sail is deployed by a gas inflated into the toroidal rim and the membrane is kept flat by the pressure of the gas; under heating by solar radiation, the membrane coat undergoes TD and the sail is accelerated via TD of coating and solar radiation pressure (SRP); when TD ends, the sail utilizes thrust only from SRP. We study the stability of the torus-shaped sail and deflection and vibration of the flat membrane due to the acceleration by TD and SRP.     

ULF wave index as magnetospheric and space-weather parameters

Waves in the Ultra Low Frequency (ULF) band owe their existence to solar wind turbulence and transport momentum and energy from the solar wind to the magnetosphere and farther down. Therefore an index based on ULF wave power could better characterize solar wind–magnetosphere interaction than K_P, Dst, AE, etc. indices which described mainly quasi-study state condition of the system. We have shown that the ULF wave index accurately characterize relativistic electron dynamics in the magnetosphere as these waves are closely associated with circulation, diffusion and energization of relativistic electrons in the magnetosphere. High speed solar wind streams also act as a significant driver of activity in the Earth’s magnetosphere co-rotating interaction region and are responsible for geomagnetic activities. In the present paper, we have analyzed various cases related with very weak (quiet) days, weak days, storm days and eclipse events and discussed the utility of the ULF wave index to explain the magnetospheric dynamics and associated properties. We have tried to explain that the ULF wave index can equally be useful as a space weather parameter like the other indices.     

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with $i\approx$?20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200?y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.