基于J2项摄动的MMS任务编队优化设计

Magnetospheric MultiScale（MMS）任务利用椭圆轨道远地点附近的正四面体航天器编队，协同完成对地球磁层结构和动力学特性的测量和分析。采用基于轨道根数的相对运动模型，分析了主航天器轨道根数对J2项影响下四面体平均性能指标——质量因子均值和平均边长均值的影响规律，并由此提出一种编队轨道优化设计方案，将其应用于第1阶段MMS任务的四面体构形设计中。该方案的设计变量包括主航天器的6个轨道根数和3个从航天器的15个相对轨道根数（除相对半长轴外），目标函数既考虑到四面体编队的平均性能，又兼顾了3个从航天器相对运动的受摄影响。仿真算例显示，在不施加主动控制的条件下，利用该方案设计远地点附近平均性能保持最优的四面体编队是可行的。     

GPS-based relative navigation for the Proba-3 formation flying mission

The primary objective of the Proba-3 mission is to build a solar coronagraph composed of two satellites flying in close formation on a high elliptical orbit and tightly controlled at apogee. Both spacecraft will embark a low-cost GPS receiver, originally designed for low-Earth orbits, to support the mission operations and planning during the perigee passage, when the GPS constellation is visible. The paper demonstrates the possibility of extending the utilization range of the GPS-based navigation system to serve as sensor for formation acquisition and coarse formation keeping. The results presented in the paper aim at achieving an unprecedented degree of realism using a high-fidelity simulation environment with hardware-in-the-loop capabilities. A modified version of the flight-proven PRISMA navigation system, composed of two single-frequency Phoenix GPS receivers and an advanced real-time onboard navigation filter, has been retained for this analysis. For several-day long simulations, the GPS receivers are replaced by software emulation to accelerate the simulation process. Special attention has been paid to the receiver link budget and to the selection of a proper attitude profile. Overall the paper demonstrates that, despite a limited GPS tracking time, the onboard navigation filter gets enough measurements to perform a relative orbit determination accurate at the centimeter level at perigee. Afterwards, the orbit prediction performance depends mainly on the quality of the onboard modeling of the differential solar radiation pressure acting on the satellites. When not taken into account, this perturbation is responsible for relative navigation errors at apogee up to 50 m. The errors can be reduced to only 10 m if the navigation filter is able to model this disturbance with 70% fidelity.     

Design of satellite constellations with continuous coverage on elliptic orbits of <Emphasis Type="Italic">Molniya</Emphasis> type

New methods of choosing the structures of satellite constellations (SC) on elliptical orbits of the Molniya type are presented. The methods, using critical inclination and putting the orbit apogee in the Earth’s hemisphere with an area of continuous coverage, are based on geometrical analysis of two-dimensional representation of the coverage conditions and SC motion in the space of inertial longitude of the orbit ascending node and time. The coverage conditions are represented in the form of a certain region. Dynamics of all satellites in this space is represented by uniform motion along a straight line approximately parallel to the ordinate axis, while the satellite system forms a grid. The problem of choosing a minimal (as far as the number of satellites is concerned) SC configuration can be formulated as a search for the most sparse grid. The contemporary advanced methods of computational geometry serve as an algorithmic basis for the problem solution. Design of SC for continuous coverage of latitude belts with the use of kinematically regular systems is considered. A method of analyzing single-track systems for continuous coverage of arbitrary geographic regions is described, which makes a region at any time instant observable by at least one satellite of the system. As an example, SC on elliptical orbits are considered with periods of ～4, 12, and 24 hours.     

Estimation of the current density and analysis of the geometry of the current system surrounding the Earth

The results of an investigation of the distribution of plasma pressure, pressure gradients, and magnetic field near the equatorial plane in the plasma ring surrounding the Earth under magneto-quiet conditions are presented. Observational data obtained during the international THEMIS mission are used. The picture of the distribution of transverse-current density near the equatorial plane was obtained under assumption of observing the magnetostatic balance condition at geocentric distances from 6 to 12R _E. In estimating the integral transverse current it was accepted that in daytime sector the magnetic-field minima on magnetic field lines are not localized in the equatorial plane. Estimates of the integral transverse current were obtained, which demonstrate the possibility of closing nighttime transverse currents at geocentric distances of up to ～12R _E inside the magnetosphere, which form a high-latitudinal continuation of the ring current.     

Large and sharp changes of solar wind dynamic pressure and disturbances of the magnetospheric magnetic field at geosynchronous orbit caused by these variations

The large and sharp changes of solar wind dynamic pressure, found from the INTERBALL-1 satellite and WIND spacecraft data, are compared with simultaneous magnetic field disturbances in the magnetosphere measured by geosynchronous GOES-8, GOES-9, and GOES-10 satellites. For this purpose, about 200 events in the solar wind, associated with sharp changes of the dynamic pressure, were selected from the INTERBALL-1 satellite data obtained during 1996–1999. The large and sharp changes of the solar wind dynamic pressure were shown to result in rapid variations of the magnetic field strength in the outer magnetosphere, the increase (drop) of the solar wind dynamic pressure always lead to an increase (drop) of the geosynchronous magnetic field magnitude. The value of the geomagnetic field variation strongly depends on the local time of the observation point, reaching a maximum value near the noon meridian. It is shown that the direction of the B _z component of the interplanetary magnetic field has virtually no effect on the geomagnetic field variation because of a sharp jump of pressure. The time shift between an event in the solar wind and its response in the magnetosphere at a geosynchronous orbit essentially depends on the inclination of the front of a solar wind disturbance to the Sun-Earth line.     

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.     

椭圆轨道卫星对地全球覆盖电推进控制

针对椭圆轨道卫星近/远地点的星下点对全球或特定纬度区域的访问问题，提出一种连续小推力下的对地覆盖控制策略。首先，推导了自然摄动对卫星拱线变化的影响，并探讨了进行小推力覆盖控制的必要性。然后，针对燃料消耗的优化问题，将控制方程展开成含傅里叶级数的形式，用以获得便于星上计算的解析形式的次优解，同时探讨了截取阶数与优化程度的关系。在进行拱线控制的同时，通过合理设置约束，对椭圆轨道的近地点高度进行保护，确保卫星安全运行。仿真结果表明，提出的方法能够以适当的燃料消耗代价实现椭圆轨道的近/远地点的全球覆盖控制或特定纬度区域的反复推扫，且控制力在可接受的范围内。     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

Numerical simulation of effects of the August 11, 1999 solar eclipse in the outer ionosphere

The results of a numerical simulation of such parameters of the topside ionosphere as concentration N _e and temperature T _e of electrons, and concentration n(H⁺) and fluxes along the magnetic field lines Φ(H⁺) of H⁺ ions at an altitude of ～2000 km for the conditions of the August 11, 1999 solar eclipse are presented. The calculations were performed using the Global Self-consistent Model of the Thermosphere, Ionosphere, and Protonosphere of the Earth (GSM TIP). It is shown that during the eclipse, in addition to a region of decreased values of T _e in the Northern Hemisphere and in the magnetically conjugate region in the Southern Hemisphere, regions of electron heating emerge in both hemispheres. Simultaneously, an extended region of decreased values of N _e comes into existence and moves behind the Moon’s shadow. Regions with decreased (down to ～30%) and enhanced (up to ～50%) concentrations of H⁺ ions are detected in the global distribution of these ions.     

Heating and acceleration of charged particles during magnetic dipolarizations

In this paper, we analyzed the thermal and energy characteristics of the plasma components observed during the magnetic dipolarizations in the near tail by the Cluster satellites. It was previously found that the first dipolarization the ratio of proton and electron temperatures (T _p/T _e) was ~6–7. At the time of the observation of the first dipolarization front T _p/T _e decreases by up to ~3–4. The minimum value T _p/T _e (~2.0) is observed behind the front during the turbulent dipolarization phase. Decreases in T _p/T _e observed at this time are associated with an increase in T _e, whereas the proton temperature either decreases or remains unchanged. Decreases of the value T _p/T _e during the magnetic dipolarizations coincide with increase in wave activity in the wide frequency band up to electron gyrofrequency f _ce. High-frequency modes can resonantly interact with electrons causing their heating. The acceleration of ions with different masses up to energies of several hundred kiloelectron-volts is also observed during dipolarizations. In this case, the index of the energy spectrum decreases (a fraction of energetic ions increases) during the enhancement of low-frequency electromagnetic fluctuations at frequencies that correspond to the gyrofrequency of this ion component. Thus, we can conclude that the processes of the interaction between waves and particles play an important role in increasing the energy of plasma particles during magnetic dipolarizations.     

Stability of resonance rotation of a satellite with respect to its center of mass in the orbit plane

The stability of resonance oscillations and rotations of a satellite in the plane of its orbit in the case when the difference of the moments of inertia with respect to the principal axes lying in the orbit plane is small is determined at a given rotation number m by the sign of function Φ_m(e), introduced by F.L. Chernous’ko in 1963. In this paper, convenient analytical representations of functions Φ_m(e) are described in the form of integrals and series of Bessel functions regular at e → 1^?. Values of Φ_m(1) are calculated in explicit form. A theorem about the double asymptotic form of functions Φ_m(e) at m → ∞ and e → 1^? is proved by the saddlepoint method.     

On the belt of energetic electrons at <Emphasis Type="Italic">L</Emphasis> = 2.75 in the Earth’s magnetosphere

In 1964, during flights of the ELECTRON satellites the narrow belts of energetic electrons (E _e ≈ 6MeV) have been discovered in the Earth’s magnetosphere at L ≈ 2.75. The same structures approximately at the same magnetic shells were found in 2004 by the CORONAS-F and SERVIS-1 satellites. A comparison of the results of these experiments is presented. It is shown that the additional narrow belts of energetic electrons occur after intense magnetic storms (D _st > 100 nT), in our cases, having a double-triple structure. The lifetime of these belts is a few months and their disappearance had a gradual character. The obtained results separated in time by 40 years suggest the constancy of the sources of particles of the Earth’s radiation belts and processes occurring in the magnetosphere, which ensures not only existence of the radiation belts, but also the recurrence of various exotic phenomena in the belts similar to the belt of energetic electrons at the inner magnetic shells.     

Radial propagation velocity of energetic particle injections according to measurements onboard the <Emphasis Type="Italic">Cluster</Emphasis> satellites

Injections of energetic electrons with a dispersion over energies were observed during the February 23, 2004 (at about 03:20 UT) substorm onboard the Cluster satellites in the vicinity of perigee near the midnight meridian. The delays in the particle observation caused by the energy dependence of the magnetic drift velocities made it possible to determine the position and time of the beginning of the drift, tracing the trajectories of the leading center of particles back in time in the magnetospheric model. The comparisons of the measurements of four satellites allowed us to determine the radial propagation of the injection front with a velocity of 100–150 km/s at a distance of 7–9 R _E. The comparison with a few previous measurements shows a substantial slowing down of injections as they approached the Earth, and this confirms the prospects of this method for more detailed study of propagation of plasma injection into the inner magnetosphere.     

Spatial structure of Pc5 waves in the outer magnetosphere according to observations onboard the THEMIS satellites

We have analyzed oscillations in the Pc5 range recorded in the outer region of the evening magnetosphere onboard 5 THEMIS satellites when all vehicles were moving with a small distance along one and the same orbit. Gradients of the spatial structure of oscillations and fluxes of energetic protons are determined. The observed phase shifts of the oscillation field between the satellites are presumably caused by their sunward (westward) propagation with azimuthal wave numbers m ～ 30–60. According the data of particle detectors, non-equilibrium character of the distribution of protons is found: their non-monotonous distribution in energy and sharp spatial heterogeneity. The calculated parameters of plasma and oscillations are not consistent with the assumption on drift-mirror instability as a source of the oscillations. A complete theory of these waves should include effects of the finite Larmor radius and simultaneous existence of two types of nonequilibrium plasma.     

Deployment history and design considerations for space reactor power systems

The history of the deployment of nuclear reactors in Earth orbits is reviewed with emphases on lessons learned and the operation and safety experiences. The former Soviet Union's “BUK” power systems, with SiGe thermoelectric conversion and fast neutron energy spectrum reactors, powered a total of 31 Radar Ocean Reconnaissance Satellites (RORSATs) from 1970 to 1988 in 260 km orbit. Two of the former Soviet Union's TOPAZ reactors, with in-core thermionic conversion and epithermal neutron energy spectrum, powered two Cosmos missions launched in 1987 in ～800 km orbit. The US’ SNAP-10A system, with SiGe energy conversion and a thermal neutron energy spectrum reactor, was launched in 1965 in 1300 km orbit. The three reactor systems used liquid NaK-78 coolant, stainless steel structure and highly enriched uranium fuel (90–96 wt%) and operated at a reactor exit temperature of 833–973 K. The BUK reactors used U-Mo fuel rods, TOPAZ used UO₂ fuel rods and four ZrH moderator disks, and the SNAP-10A used moderated U-ZrH fuel rods. These low power space reactor systems were designed for short missions (～0.5 kW_e and ～1 year for SNAP-10A, <3.0 kW_e and <6 months for BUK, and ～5.5 kW_e and up to 1 year for TOPAZ). The deactivated BUK reactors at the end of mission, which varied in duration from a few hours to ～4.5 months, were boosted into ～800 km storage orbit with a decay life of more than 600 year. The ejection of the last 16 BUK reactor fuel cores caused significant contamination of Earth orbits with NaK droplets that varied in sizes from a few microns to 5 cm. Power systems to enhance or enable future interplanetary exploration, in-situ resources utilization on Mars and the Moon, and civilian missions in 1000–3000 km orbits would generate significantly more power of 10's to 100's kW_e for 5–10 years, or even longer. A number of design options to enhance the operation reliability and safety of these high power space reactor power systems are presented and discussed.     

Apogee manoeuvre with a restartable liquid bipropellant motor

Unified Propulsion Systems present perceptible advantages for geostationary spacecrafts design: mass savings, as the ergols tanks are the same for the apogee motor and for the Attitude and Orbit Control System, higher performance, as specific impulse of bi-ergols motors is higher than the one of solid propellant motors and higher operational flexibility as the fuel amount can be adapted to the real flight conditions and as biliquid motors are restartable. On the other hand, the use of these propulsion systems for geostationary spacecrafts sets quite new mission analysis problems: the “predictability” of each delivered Delta-V is rather coarse (the corresponding uncertainty is about 4% for the existing motors). Also, only midlevel thrusters (about 400N) are available and so the finite burn losses associated with long burns arcs have to be minimized. This paper surveys the problems resulting from these new operational constraints and deals successively with the following items: optimal splitting up of the apogee manoeuvre, taking into account the possible dispersions on each Delta-V and the on-station longitude acquisition; minimization of the finite burn losses; adaptation of the apogee manoeuvre to the initial orbit parameters corresponding to the first North-South station-keeping cycle. The operation procedures derived from this survey will be used for the future launch of the ARABSAT spacecraft and for the following spacecrafts of the SPACEBUS family.     

On the features of long-term evolution of a high-apogee orbit of the SPECTR-R spacecraft

The practical tasks related to qualitative investigation of long-term evolution of high-apogee orbits of artificial Earth satellites (AES), for which the main perturbing factors are gravitational perturbations from the Moon and the Sun, are considered. Attention is given to the problem of the ballistic lifetime of similar orbits, and the issues associated with possibilities of the correction of orbits for ensuring the required duration of their ballistic lifetime are considered. The orbit of the SPECTR-R spacecraft launched in July of 2011 is considered as an example.     

A small parameter method in problems of maneuvering space vehicles with aerodynamic efficiency

The motion of a satellite with aerodynamic efficiency along a low near-circular orbit is considered in the paper. The controls of bank angle γ and lift coefficient C_y are used as control functions. The introduction of a small parameter ($\text{? = (}\text{?}{}_0\text{· S · g}{}_0\text{2G}\text{)}$) makes it possible to integrate an adjoint system of equations and to obtain an approximate solution to the complete problem in the class of piecewise-constant control functions. Maximum values for the coordinates of heading angle η and lateral derivation from the plane of a reference orbit ?, which are connected with orbit plane angle by the relation cos i = cos ? · cos h, are used as criteria of maneuvering capability for a satellite with aerodynamic efficiency. Optimal programs for bank angle and incidence variation are derived and the influence of lift-to-drag ratio on the vehicle maneuvering capabilities has been estimated.It is shown that the process of the optimal motion is a special kind of gravitational skipping similar to the Keplerian motion but with continuous descent.     

美国AEHF军事通信卫星推进系统及其在首发星上的应用

美国先进极高频（AEHF）项目将采用4颗运行于地球同步轨道（GEO）的AE—HF军事通信卫星。AEHF卫星的推进系统由远地点发动机、姿态控制发动机组和双模式霍尔电推进子系统组成。首发星AEHF-1是世界上首个采用霍尔电推进系统执行发射后轨道提升任夯的GEO卫星。AEHF-1卫星星箭分离后,远地点发动机未能正常工作,因此...     

考虑地球扁率效应的两圆轨道之间的双共切最优转移

两圆轨道之间的双共切转移轨道是其近地点和远地点分别在这两个圆轨道上的椭圆轨道。本文用两次冲量法给出了沿双共切椭圆轨道实现从一圆轨道向另一圆轨道转移的最优方案，并考虑到地球扁率造成的轨道摄动。文中的所谓圆轨道指的是变轨时刻的密切轨道为圆形的轨道，是对近圆轨道的近似替找。