Hydrodynamic Analogy for the Solution to the Doubly Averaged Hill Problem Disturbed by Precession of the Orbit Plane of a Disturbing Body

A hydrodynamic analogy for the solution to a satellite version of the restricted three-body problem is considered with allowance made for precession of the disturbing body orbit. Applying, in the first approximation, the analytical solution to a doubly averaged equation system obtained in 1961 by M.L. Lidov, we consider the precession of the disturbing body orbit as some disturbing factor. The appropriate model enables us to describe the general pattern of integral curves in the entire area of their existence as a picture of flow lines of the potential motion of some fictitious homogeneous incompressible fluid. For the synthesis of an adequate mathematical model, a method similar to the Pade approximation is used. The obtained model and its discrete continual analog allow us to present, in a pictorial form, the disturbance of orbits under the effect of precession of the disturbing body orbit.     

改进的次时间最优控制

本文在[1][2]基础上进一步探讨了次时间最优控制的改进问题,深入地阐明了次时间最优控制的某些特性后,提出了一个新的改进的设计方法。按照这种方法设计控制系统,不但实用而且可以大幅度提高次时间最优控制的最优性。并用实例比较了各种方法,证明了本文提出的方法的优越性。本文提出的方法应用于工程设计,对于提高系统的最优性是非常有效的。     

Stability of triangle libration points in generalized restricted circular three-body problem

Equilibrium positions of a small-mass body are considered with respect to a precessing dumbbell. The dumbbell represents two rigidly fixed spherical gravitating bodies. Such a system can be considered as a model of a binary asteroid. Stability of relative equilibrium positions with equal distances from the small mass to the attracting centers is studied. By analogy with the classical restricted three-body problem, these positions are referred to as triangle libration points. It is shown that the character of stability of these libration points is determined by three constant parameters: nutation angle and angular velocity of precession, as well as the ratio of masses at the ends of the dumbbell. Stability conditions are derived in the linear approximation, and the regions of stability and instability in the space of problem parameters are constructed. The paper is a continuation of [1].     

Estimation of an Admissible Domain of Uncontrolled Disturbances during Reorientation of an Asymmetric Rigid Body

A nonlinear game problem of the reorientation of an asymmetric rigid body is considered for the case of uncontrolled disturbances, only their estimates being known. The domain of admissible controls is limited by an ellipsoid or a sphere. In the case of a sphere, the limitation corresponds to a pair of swiveling (vernier) engines. A method [1–4] of solving this problem is developed based on equivalent linearization of nonlinear conflict-controlled systems. Direct estimates are found of the admissible (with respect to executing a reorientation) domain of uncontrolled disturbances, as a function of both the given constraints on the controls and the initial location of the body. These estimates are convenient at the first stage of a solution process, when the possibility is determined of using the controls proposed in [1–4] in order to support the necessary reorientation. If the aforementioned estimates are satisfied with a safety margin, then (at the second stage of the solution) a particular value of the guaranteed time of reorientation can be found by iteration algorithms [1–4]. The results of calculations are presented.     

Stationary Motions of a Homogeneous Meteor Ring in the Gravitational Field of a Center

The problem of studying a ring in the gravitational field of a center arose after the discovery of Saturn's rings by Galileo and subsequent discovery of the rings of other planets of the Solar System. Modern theoretical investigations of the existence and stability of planetary rings are mostly related to studies of plane differentially rotating discs [1]. As opposed to this line of research, this paper follows the approach established in classical works [2–4].     

The Tanaka-Enome criterion and solar activity in October–November 2003 as observed by the Large Pulkovo Radio Telescope

We present the results of spectral and polarization observations of two large sunspot groups, NOAA 0484 and NOAA 0486 + 0488, which determine high solar activity in October–November 2003. The observations are made with the Large Pulkovo Radio Telescope (LPRT) in the range 2.7–20 cm, the one-dimensional (E-W) resolution of observations being 1–6 arc min, respectively. The main characteristics of the corona radio emission above these active regions are measured, allowing us to follow their dynamics during the entire period of their existence on the solar disk with a period of one day. The analysis of the obtained results is presented from the point of view of the well-known Tanaka-Enome criterion [1–2] (on the basis of this criterion one can predict strong flares from characteristics of radio emission of an active region in quasi-quiet state). Using the activity in October–November 2003 as an example, we demonstrate the capabilities of a new method for estimating the level of solar activity. It was developed on the basis of long-term observations of the Sun by LPRT [3].Translated from Kosmicheskie Issledovaniya, Vol. 42, No. 6, 2004, pp. 585–594.Original Russian Text Copyright © 2004 by Borisevich, Ilin, Korzhavin, Peterova, Topchilo, Shpitalnaya.     

On the asteroid hazard

The concept of “space patrol” is considered, aimed at discovering and cataloging the majority of celestial bodies that constitute a menace for the Earth [1, 2]. The scheme of “optical barrier” formed by telescopes of the space patrol is analyzed, requirements to the observation system are formulated, and some schemes of sighting the optical barrier region are suggested (for reliable detection of the celestial bodies approaching the Earth and for determination of their orbits). A comparison is made of capabilities of electro-jet engines and traditional chemical engines for arrangement of patrol spacecraft constellation in the Earth’s orbit.     

A minicomputer finite elements program for microgravity hydroelastic analysis

A general hydroelastic analysis formulation is presented by using Green's function. Emphasis is placed on the case of an incompressible fluid model which is applicable to flexible tank hydroelastic analysis. Variational formulation of the sloshing problem is established in order to obtain a numerical treatment by a mixed finite element method. A minicomputer program is illustrated and the hydroelastic analysis technique is checked as an efficient and accurate approach with some numerical solutions.     

Time and energy characteristics of UV flashes in the atmosphere: Data of the <Emphasis Type="Italic">Universitetsky-Tatiana</Emphasis> satellite

Using a detector of near ultra-violet (UV) emission (wavelength range 300–400 nm) [1] onboard the Universitetsky-Tatiana satellite with an orbit height of 950 km and inclination of 81° we have detected and studied short UV flashes [2–5]. In this paper the observed UV flashes are classified according to the type of their time profiles, and the times of emission intensity rise and decay are investigated in every flash. Using the data on time profiles it turned out to be possible to estimate the flash energy in the atmosphere even in case of saturation of a signal measuring channel at the maximum of emission. The energy spectrum of observed flashes is estimated. Time and energy characteristics of the flashes are important for choosing a model of development of electric discharges in the upper atmosphere that are responsible for observed emission.     

Determination of the inertia tensor of the <Emphasis Type="Italic">International Space Station</Emphasis> on the basis of telemetry data

We describe the method and results of determination of the inertia tensor of the International Space Station using telemetry data related to its attitude motion and the total angular momentum of gyrodines. A linear system of differential equations describing the variation of the total angular momentum of gyrodines on some time interval is derived on the basis of the data related to the station orientation in the same time interval. This linear system represents the theorem related to the variation of the total angular momentum of the station and gyrodines and takes into account the action of gravitational and aerodynamic moments upon the station. The solution to the system depends linearly on the components of the inertia tensor of the station and on the parameters specifying the aerodynamic moment. The estimates of these quantities are carried out by the least squares method on the condition of the best approximation by the solutions to the considered linear system of the telemetry values of the total angular momentum of the gyrodines.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 135–146.Original Russian Text Copyright © 2005 by Banit, Belyaev, Dobrinskaya, Efimov, Sazonov, Stazhkov.     

Families of periodic solutions to Hamiltonian systems: Nonsymmetrical periodic solutions for a planar restricted three-body problem

A monodromy matrix calculated at a single arbitrary point of the periodic solution to a Hamiltonian system allows one to obtain both the direction of continuation for the family of solutions of the first (in Poincarés sense) kind and the multiplicity and direction of branching for periodic solutions of the second kind. In case of resonances 1 : 1 and 1 : 2 one needs to take into account the structure of elementary divisors of the monodromy matrix. Using the planar circular restricted three-body problem as an example, the infiniteness of the process of branching for a nonintegrable system and its finiteness for an integrable system are demonstrated. It is proved that periodic solutions of both first and second kinds which are obtained by continuation of symmetric periodic solutions of a restricted problem are also symmetric. The only exception is the case of resonance 1 : 1 and two second-order cells of the monodromy matrix in the Jordanian form. In this case, all periodic solutions of the second kind turned out to be nonsymmetrical. Examples of the families of nonsymmetrical periodic solutions are given.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 88–110.Original Russian Text Copyright © 2005 by Kreisman.     

A Modification of the Method of Transporting Trajectory

Further development of an approximate method for optimizing a flight with an ideally controlled small thrust is proposed. The method is based on the employment of the transporting trajectory and considered in [1–3]. A detailed analysis of the means of improving the accuracy of this method suggested in [2, 3] is carried out, and the solution is presented in finite form. The proposed approach is applied to the flights making flybys of many celestial bodies. In the case of small bodies the solution is also obtained in finite form. A numerical example is considered confirming the high efficiency of this method.     

Planetary rings as relics of plasma pre-rings

A possibility is discussed that the rings of large planets observed in the modern epoch are relics of some pre-rings consisting of magnetized plasma (according to a hypothesis by H. Alfven). The solution to a model problem published in [36, 37] is used. Its main result is a mechanism of stratification of an evolutionally mature plasma pre-ring into a large number of narrow elite rings separated by anti-rings (gaps). Another result is the theoretical substantiation of the presence in the near-planetary space of a region of existence and stability (in what follows it is referred to as ES-region) of plasma rings. The data obtained in the course of the Voyager, Galileo, and Cassini missions are used below for verification of the model on which the solutions presented in [36, 37] are based.     

The Initial Stage of “Space Debris” Cloud Formation during Planetary Satellite Breakdown

The process of formation of a particles cloud (space debris) during breakdown of the Earth’s Artificial Satellite (EAS) is considered. A system of equations of motion is derived, and its analytical solution in the linear approximation for circular orbits is presented. The distinction between this solution and an exact numerical solution is indicated. The cases of satellite breakdown at the apogee and perigee on an elliptic orbit are also considered, and some characteristics of these processes are compared.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 269–273.Original Russian Text Copyright © 2005 by Gorelov, Zarubkin.     

Design and development of correlation techniques to maintain a space surveillance system catalogue

A growing interest exists in a future, autonomous European Space Surveillance System (ESSS). Currently, most of the knowledge about Earth-orbiting space objects is based on information provided by the USASPACECOM. This paper presents the required initial orbit determination (IOD) and correlation techniques to process optical measurements. Former studies were focused on the handling of radar measurements, which are summarised with the aim of describing a global procedure for processing hybrid measurement types (combination of radar and optic data for catalogue maintenance). The introduction of manoeuvres are presented due to their importance in the space object catalogue maintenance.The detection of uncatalogued objects and the successful correlation of already catalogued objects involve two different tasks for telescopes: survey and tasking. Assumptions for both strategies are developed on the basis of the previous work developed at the University of Berne (see [T. Flohrer, T. Schildknecht, R. Musci, E. Stöveken, Performance estimation for GEO space surveillance, Advances in Space Research 35 (2005). [1]; T. Flohrer, T. Schildknecht, R. Musci, Proposed strategies for optical observations in a future European Space Surveillance Network, presented in the 36th COSPAR Scientific Assembly (2006). [2]; R. Musci, T. Schildknecht, M. Ploner, Orbit improvement for GEO objects using follow-up observations, Advances in Space Research 34 (2004). [3]; R. Musci, T. Schildknecht, M. Ploner, G. Beutler, Orbit improvement for GTO objects using follow-up observations, Advances in Space Research 35 (2005). [4]; R. Musci, T. Schildknecht, T. Flohrer, G. Beutler, Concept for a catalogue of space debris in GEO, Proceedings of the Fourth European Conference on Space Debris, (ESA SP-587, 2005). [5]]). When a new object appears in the field of view, initial orbit determination must be performed. When only one telescope per site is available, the initial measurements are separated by only a few seconds. Therefore, the initial orbit determination is quite inaccurate due to bad mathematical conditioning of the problem. In order to improve the accuracy of the initial orbit determination, several follow-up observations of the object are required. This implies that the telescope needs to track the detected objects over a long period, and therefore the time available for surveying is reduced. By processing the additional follow-up measurements, separated now by a few hours, the initial orbit determination gives more accurate results and the object can be recovered after an orbital revolution. When several telescopes per site are available, the optical strategies may be modified. The survey tasks can be distributed between the available telescopes. In this way the number of images corresponding to each object increases and to track the detected object over long periods is not always needed. Numerical results will be shown in order to evaluate the accuracy and features of the different telescope strategies. A key point for performing efficiently the cataloguing process is the calculation of the estimated state vector covariance matrix. The covariance matrix analysis allows an adaptive tasking-survey telescope scheduling. Moreover, the implementation of a proper batch orbit determination process by means of a square root information filter (SRIF) requires a realistic initial covariance matrix.Hybrid measurements are available from objects that can be observed through both radar and optical sensors (e.g. GTO objects). The batch orbit determination and correlation process of hybrid measurements is also based on SRIF using an extended measurement model. Both the initial orbit determination methods using radar and optical measurements have to be sufficiently accurate to initialise SRIF correctly. In order to avoid filter divergence, the estimated covariance must be correctly updated after processing both kinds of measurements. The implemented algorithms are explained and their performance is shown through realistic simulations.Techniques to detect and characterise object manoeuvres during the cataloguing process have been developed and implemented. Four main groups of manoeuvre objects have been established by means of their observed permitted orbital ranges (GEO, LEO, MEO–GPS, Molniya). The study is based on the historical TLEs files. When an object with an uncatalogued orbit appears, a comparison between the new orbit and the orbits contained in the permitted ranges of one of the manoeuvre groups is performed. If the required Δa and/or Δi to convert the lost orbit into the detected orbit seems to be feasible, a manoeuvre will be identified and the orbit will be updated in the catalogue. Otherwise, it will be decided that a new object was found. For this purpose, a procedure to estimate the manoeuvres and reset orbits have been developed.     

Oscillatory Thermocapillary Flows in Simulated Floating-zones with Time-dependent Temperature Boundary Conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier–Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L=20 [mm] and a diameter D=20 (mm) is considered. A temperature difference ΔT=30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave', but after a transient time the instability is described by the dynamic model of a ‘standing wave', with an azimuthal spatial distribution corresponding to m=1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

Oscillatory thermocapillary flows in simulated floating-zones with time-dependent temperature boundary conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier-Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L = 20 [mm] and a diameter D = 20 (mm) is considered. A temperature difference ΔT = 30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave’, but after a transient time the instability is described by the dynamic model of a ‘standing wave’, with an azimuthal spatial distribution corresponding to m = 1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

Generalized Problem of Two Fixed Centers or the Darboux-Gredeaks Problem

A brief review of publications on the problem of two fixed centers is given, including its generalizations and astronomical applications. A comparison of the Darboux potential with that of Eve Gredeaks is made. An account of the basic points of development of modern high-precision theories of the motion of planetary satellites, based on the Gredeaks’ intermediate orbit, is given.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 194–200.Original Russian Text Copyright © 2005 by Lukyanov, Emeljanov, Shirmin.Dedicated to the memory of Professor Evgenii Petrovich Aksenov     

Planar inertial motion of an elastic cluster of three bodies

A problem of planar inertial motion of three bodies connected in the form of a triangle by an elastic imponderable filament is considered, as well as a particular case of the problem of motion of a closed chain of n bodies. This configuration can be a basis for extended planar constructions in deep space.The bodies are considered as material points. The paper elaborates a subject of [1]     

Thermocapillary simulation of single bubble dynamics in zero gravity

The lack of significant buoyancy effects in zero gravity conditions poses an issue with fluid transfer in a stagnant liquid. In this paper bubble movement in a stagnant liquid is analysed and presented numerically using a computational fluid dynamics (CFD) approach. The governing continuum conservation equations for two phase flow are solved using the commercial software package Ansys-Fluent v.13 and the Volume of Fluid (VOF) method is used to track the liquid/gas interface in 2D and 3D domains. The simulation results are in reasonable agreement with the earlier experimental observations, the VOF algorithm is found to be a valuable tool for studying the phenomena of gas–liquid interaction. The flow is driven via Marangoni influence induced by the temperature difference which in turn drives the bubble from the cold to the hot region. A range of thermal Reynolds (Re_T) and Marangoni numbers (Ma_T) are selected for the numerical simulations, specifically Re_T=13–658 and Ma_T=214–10,721 respectively. The results indicate that the inherent velocity of bubbles decreases with an increase of the Marangoni number, a result that is line with the results of previous space experiments (Kang et al., 2008) [1]. An expression for predicting the scaled velocity of bubble has been derived based on the data obtained in the present numerical study. Some three-dimensional simulations are also performed to compare and examine the results with two-dimensional simulations.