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.     

Families of periodic solutions in three-dimensional restricted three-body problem

Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v _z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If |s| ≤ 1, then transformation of the subspace (z, v _z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ? can be rationally expressed through 2π,φ = 2π·p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace (z, v _z ) are determined by matrix M. If |s| < 1, we have two new families, while only one exists at resonances 1: 1 (s = 1) and 2: 1 (s = ?1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.     

A Concept of Guidance for an Air-Launch Vehicle with Compensation of Initial Downrange and Launch Time Errors at Direct Insertion into a Rendezvous Point in the Orbit

A flying launcher (airplane carrier) can generate initial errors in position and time of launch. In order to compensate for these errors, one should have two control parameters in addition to those that provide for a spacecraft's injection into a preset orbit. We suggest the concept of controlling the trajectory of injection by choosing thrust values (within allowable regions of control) of second-stage engines or/and of a space booster of the Polyot carrier launcher. As an example, a rendezvous of the spacecraft at the end of its boost phase with the International Space Station (ISS) is considered. The methodology of the suggested approach can be extended to other mobile systems of launch to rendezvous orbits.     

Electron flux variations at altitudes of 600–800 km in the second half of 2014. preliminary results of an experiment using RELEC equipment onboard the satellite <Emphasis Type="Italic">VERNOV</Emphasis>

The results of measurements of fluxes and spectra carried out using the RELEC (relativistic electrons) equipment onboard the VERNOV satellite in the second half of 2014 are presented. The VERNOV satellite was launched on July 8, 2014 in a sun-synchronous orbit with an altitude from 640 to 830 km and an inclination of 98.4°. Scientific information from the satellite was first received on July 20, 2014. The comparative analysis of electron fluxes using data from RELEC and using experimental data on the electron detection by satellites Elektro-L (positioned at a geostationary orbit) and Meteor-M no. 2 (positioned at a circular polar orbit at an altitude of about 800 km as the VERNOV satellite) will make it possible to study the spatial distribution pattern of energetic electrons in near-Earth space in more detail.     

太阳同步卫星的轨道设计

在轨道六要素的基础上，分析了卫星太阳同步轨道设计时降(升)交点地方时、升交点赤经，以及冻结轨道参数等的确定方法。并给出了在轨道交点周期、回归圈数、回归周期、重复周期和其他因素等约束条件下的轨道设计要点。最后给出了一个轨道高度750～800km，卫星太阳同步轨道、冻结轨道和回归轨道的算例。     

利用升交点经度进行轨道设计的方法

以升交点经度的范围来描述所有能覆盖到目标的轨道。利用球面三角方法详细讨论了在考虑地球形状Ｊ２项的摄动影响时，各种情况下能覆盖目标点的轨道的升交点经度范围，并将其推广到对区域目标的覆盖，给出了完整的解析表达式。结合实例给出了利用该表达式进行有连续覆盖、覆盖次数及过顶时间要求时的轨道设计方法。该方法的优点是无需进行轨道读物计算，仅用解析表达式即可快速地设计出满足覆盖要求的轨道。     

On Saturn’s rotation relative to a center of mass under the action of the gravitational moments of the Sun and Jupiter

Saturn’s rotation relative to a center of mass is considered within an elliptic restricted three-body problem. It is assumed that Saturn is a solid under the action of gravity of the Sun and Jupiter. The motions of Saturn and Jupiter are considered elliptic with small eccentricities e_S and e_J, respectively; the mean motion of Jupiter n_J is also small. We obtain the averaged Hamiltonian function for a small parameter of ε = n_J and integrals of evolution equations. The main effects of the influence of Jupiter on Saturn’s rotation are described: (α) the evolution of the constant parameters of regular precession for the angular momentum vector I₂; (β) the occurrence of new libration zones of oscillations I₂ near the plane of the celestial equator parallel to the plane of the Jupiter’s orbit; (γ) the occurrence of additional unstable equilibria of vector I₂ at the points of the north and south poles of the celestial sphere and, as a result, the existence of homoclinic trajectories; and (δ) the existence of periodic trajectories with arbitrarily large periods near the homoclinic trajectory. It is shown that the effects of (β), (γ), and (δ) are caused by the eccentricity e of the Jupiter’s orbit and are practically independent of Jupiter’s mass (within satellite approximation).     

Study of notches in the Earth’s plasmasphere based on data of the <Emphasis Type="Italic">MAGION-5</Emphasis> satellite

Depleted narrow (localized in longitude) regions (field tubes) in the plasmasphere, recently discovered in He⁺ radiation measurements on the IMAGE spacecraft, were first directly observed by the Magion-5 satellite. The low-density regions (notches) occupy <～ 10–30° in longitude and extend from L ～ 2–3 to the plasmasphere boundary in neighboring plasmasphere regions with larger densities. The Magion-5 data give evidence that in the low-density regions temperature is enhanced as compared to the neighboring denser plasmasphere regions. Formation of notches in the plasmasphere is, apparently, associated with AE intensification during weak magnetic storms, while strong magnetic storms usually result in the overall reduction of plasmasphere dimensions. However, even a strong magnetic storm on April 6–7, 2000 (max K _p = 9-and min D _st ～ ?290 nT), but accompanied by an isolated AE impulse, resulted in a density decrease only in the longitudinally limited post-midnight sector of the plasmasphere.     

On the possibility of long-term maintenance of geostationary satellite attitude without using the external information sensors and inertial sensors

The problem of maintaining spacecraft attitude during the loss of information from attitude sensors and inertial sensors is considered. The problem is solved on the basis of the force gyro stabilization principle with producing an angular momentum in the plane of orbit. The redundant mode of attitude maintenance is developed for spacecraft of the Yamal series. The results of testing the mode during the in-flight tests of the Yamal-200 spacecraft are presented.     

Turbulent fluctuations of plasma and magnetic field parameters in the magnetosheath and the low-latitude boundary layer formation: Multisatellite observations on March 2, 1996

The results of simultaneous analysis of plasma and magnetic field characteristics measured on the INTERBALL/Tail Probe, WIND and Geotail satellites on March 2, 1996, are presented. During these observations the INTERBALL/Tail Probe crossed the low-latitude boundary layer, and the WIND and Geotail satellites measured the solar wind’s and magnetosheath’s parameters, respectively. The plasma and magnetic field characteristics in these regions have been compared. The data of the Corall, Electron, and MIF instruments on the INTERBALL/Tail Probe satellite are analyzed. Fluctuations of the magnetic field components and plasma velocity in the solar wind and magnetosheath, measured onboard the WIND and Geotail satellites, are compared. The causes resulting in appearance of plasma jet flows in the low-latitude boundary layer are analyzed. The amplitude of magnetic field fluctuations in the magnetosheath for a studied magnetosphere boundary crossing is shown to exceed the magnetic field value below the magnetopause near the cusp. The possibility of local violation of pressure balance on the magnetopause is discussed, as well as penetration of magnetosheath plasma into the magnetosphere, as a result of magnetic field and plasma flux fluctuations in the magnetosheath.     

Forecasting the velocity of quasi-stationary solar wind and the intensity of geomagnetic disturbances produced by it

A brief review is given of contemporary approaches to solving the problem of medium-term forecast of the velocity of quasi-stationary solar wind (SW) and of the intensity of geomagnetic disturbances caused by it. At the present time, two promising models of calculating the velocity of quasi-stationary SW at the Earth’s orbit are realized. One model is the semi-empirical model of Wang-Sheeley-Arge (WSA) which allows one to calculate the dependence V(t) of SW velocity at the Earth’s orbit using measured values of the photospheric magnetic field. This model is based on calculation of the local divergence f _S of magnetic field lines. The second model is semi-empirical model by Eselevich-Fainshtein-Rudenko (EFR). It is based on calculation in a potential approximation of the area of foot points on the solar surface of open magnetic tubes (sources of fast quasistationary SW). The new Bd-technology is used in these calculations, allowing one to calculate instantaneous distributions of the magnetic field above the entire visible surface of the Sun. Using predicted V(t) profiles, one can in EFR model calculate also the intensity of geomagnetic disturbances caused by quasi-stationary SW. This intensity is expressed through the K _p index. In this paper the EFR model is discussed in detail. Some examples of epignosis and real forecast of V(t) and K _p (t) are discussed. A comparison of the results of applying these two models for the SW velocity forecasting is presented.     

Peculiarities of long-wave radio bursts from solar flares preceding strong geomagnetic storms

Radio bursts in the frequency range of 100–1500 kHz, recorded in 1997–2000 on the INTERBALL-1 satellite during the solar flares preceding the strong geomagnetic storms with D _st < ?100 nT, are analyzed in this paper. The observed long-wave III-type radio bursts of solar origin at frequencies of 1460 and 780 kHz were characterized by large values of the flux S _f = 10^?15 ?10^?17 W/m² Hz and duration longer than 10 min. The rapid frequency drift of a modulated radio burst continued up to a frequency of 250 kHz, which testified that the exciting agent (a beam of energetic electrons) propagated from the Sun to the Earth. All such flares were characterized by the appearance of halo coronal mass ejections, observed by the LASCO/SOHO, and by the presence of a southward B_z-component of the IMF, measured on the ACE and WIND spacecraft. In addition, shortly after radio bursts, the INTERBALL-1 satellite has recorded the fluxes of energetic electrons with E > 40 keV.     

Pressing Issues of the Day in Studying Deep Space

Two problems in studying deep space are discussed that are, in the author's opinion, the most important. The first is soil sampling from the smaller bodies of the Solar System, such as the Martian satellite Phobos and asteroids of groups C and S of the Main Asteroid Belt. This soil (so-called primordial substance) can help to elucidate some problems of the Solar System's formation; in particular, to construct a reliable model of the internal structure of the Earth. The second problem is to reveal all sufficiently large asteroids penetrating inside the Earth's orbit and to catalog those asteroids that are hazardous from the viewpoint of collision with the Earth. To this end, it is suggested to launch five or six Earth-orbiting spacecraft with telescopes capable of recording objects down to a brightness of 22– 25 ^m . It is pointed out that both problems can be solved in the near future using comparatively cheap standardized space vehicles launched into near-Earth orbits by the Soyuz carrier rocket and boosted further by electro-jet engines of small thrust.     

Ionization losses of the Earth’s radiation belt protons according to the radial diffusion theory

Using modern models of the plasmasphere and exosphere, radial profiles of the rates of ionization losses of protons with μ = 0.3–10 keV/nT (μ is the first adiabatic invariant) of the Earth’s radiation belts (ERBs) have been constructed. To calculate Coulomb losses of protons, we used the ISEE-1 satellite data at L = 3–9 and CRRES satellite data at L ≤ 3 (L is the McIlwain parameter). The relation of contributions of Coulomb losses and charge exchange in the rate of ionization losses of protons has been considered. We have discovered the effect of subtracting Coulomb losses from charge exchange of ERB protons for small μ and L, which can imitate a local particle source. It has been demonstrated that, with decreasing L, the rate of ionization losses of ERB protons decreases as a whole. The radial dependence of this rate only has a negative gradient in the narrow range (ΔL ~ 0.5) in the region of the plasmapause and only for protons with μ > 1.2 keV/nT.     

Experiment on the <Emphasis Type="Italic">Vernov</Emphasis> satellite: Transient energetic processes in the Earth’s atmosphere and magnetosphere. Part I: Description of the experiment

The program of physical studies on the Vernov satellite launched on July 8, 2014 into a polar (640 × 830 km) solar-synchronous orbit with an inclination of 98.4° is presented. We described the complex of scientific equipment on this satellite in detail, including multidirectional gamma-ray detectors, electron spectrometers, red and ultra-violet detectors, and wave probes. The experiment on the Vernov satellite is mainly aimed at a comprehensive study of the processes of generation of transient phenomena in the optical and gamma-ray ranges in the Earth’s atmosphere (such as high-altitude breakdown on runaway relativistic electrons), the study of the action on the atmosphere of electrons precipitated from the radiation belts, and low- and high-frequency electromagnetic waves of both space and atmospheric origin.     

Large-size space debris flyby in low earth orbits

the analysis of NORAD catalogue of space objects executed with respect to the overall sizes of upper-stages and last stages of carrier rockets allows the classification of 5 groups of large-size space debris (LSSD). These groups are defined according to the proximity of orbital inclinations of the involved objects. The orbits within a group have various values of deviations in the Right Ascension of the Ascending Node (RAAN). It is proposed to use the RAANs deviations' evolution portrait to clarify the orbital planes’ relative spatial distribution in a group so that the RAAN deviations should be calculated with respect to the concrete precessing orbital plane of the concrete object. In case of the first three groups (inclinations i = 71°, i = 74°, i = 81°) the straight lines of the RAAN relative deviations almost do not intersect each other. So the simple, successive flyby of group’s elements is effective, but the significant value of total ΔV is required to form drift orbits. In case of the fifth group (Sun-synchronous orbits) these straight lines chaotically intersect each other for many times due to the noticeable differences in values of semi-major axes and orbital inclinations. The intersections’ existence makes it possible to create such a flyby sequence for LSSD group when the orbit of one LSSD object simultaneously serves as the drift orbit to attain another LSSD object. This flyby scheme requiring less ΔV was called “diagonal.” The RAANs deviations’ evolution portrait built for the fourth group (to be studied in the paper) contains both types of lines, so the simultaneous combination of diagonal and successive flyby schemes is possible. The value of total ΔV and temporal costs were calculated to cover all the elements of the 4th group. The article is also enriched by the results obtained for the flyby problem solution in case of all the five mentioned LSSD groups. The general recommendations are given concerned with the required reserve of total ΔV and with amount of detachable de-orbiting units onboard the maneuvering platform and onboard the refueling vehicle.     

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earths oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellites rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 111–125.Original Russian Text Copyright © 2005 by Tikhonov.     

组合体与飞船联合轨道维持

通过组合体与飞船联合轨道维持解决了组合体和飞船轨道多特征参数的控制问题。建立了升交点经度、轨道高度和偏心率的控制方程以及基于时间关联特性的升交点赤经和制动点高度耦合控制方程和偏心率保持的双冲量耦合控制方程。结合组合体与飞船的飞行特点,制定了组合体轨道维持实现升交点赤经和轨道偏心率以及飞船轨道维持实现制动点高度的联合控制策略。耦合控制方程使得组合体和飞船轨道维持的控制量分配合理,融合了各次控制之间存在的耦合影响,设计了联合轨道维持策略迭代计算流程。基于神舟九号交会对接飞行过程,通过多组仿真算例校验了组合体与飞船轨道多特征参数的联合优化控制,具有较好的工程应用价值。     

Sporadic structures and small-scale irregularity in the nighttime polar ionosphere in the period of high solar activity according to the data of radio occultation measurements on satellite-to-satellite paths

Results of the analysis of 327 sessions of radio occultation on satellite-to-satellite paths are presented. The data are taken in the nighttime polar ionosphere in the regions with latitudes of 67°–88°, and in the period of high solar activity from October 26, 2003 to November 9, 2003. Typical ionospheric changes in the amplitude and phase of decimeter radio waves on paths GPS satellites-CHAMP satellite are presented. It is demonstrated that these data make it possible to determine characteristics of the sporadic E _s structures in the lower ionosphere at heights of 75–120 km. Histograms of distribution of the lower and upper boundaries, thickness, and intensity of the E _s structures are presented. Dispersion and spectra of amplitude fluctuations of decimeter radio waves caused by small-scale irregularity of the ionospheric plasma are analyzed. The relation of the polar E _s structures and intensity of small-scale plasma irregularity to various manifestations of solar activity is discussed. The efficiency of monitoring the ionospheric disturbances caused by shock waves of the solar wind by the radio occultation method on satellite-to-satellite paths is demonstrated.