Internal Gravitational Field of a Thin Homogeneous Ring

The potential of gravity forces is found inside a thin homogeneous ring when the ring’s mean radius is much larger than the diameter of its cross section. Rings with elliptic and almost circular cross sections are considered.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 260–268.Original Russian Text Copyright © 2005 by Kasatkin.     

Translational–Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: II

The problem of a rendezvous in the central Newtonian gravitational field is considered for a controlled spacecraft and an uncontrollable spacecraft moving along an elliptic Keplerian orbit. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. In the first variant of the equations of motion a quaternion variable characterizes the orientation of an instantaneous orbit of the spacecraft and the spacecraft location in the orbit, while in the second variant it characterizes the orientation of the plane of the spacecraft instantaneous orbit and the location of a generalized pericenter in the orbit. The quaternion variable used in the second variant of the equations of motion is a quaternion osculating element of the spacecraft orbit. The problem of a rendezvous of two spacecraft is formulated as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle.     

弱引力下小行星动量驱动机器人的可控跳跃行为

以小行星表面着陆探测为背景,提出一种动量驱动机器人(MoRo)以满足弱引力复杂环境下的探测需求。该机器人利用弱引力环境下的摩擦和碰撞特性,通过主动辨识环境参数,规划和控制动量轮以产生期望的驱动力矩,完成可控性跳跃及腾空后的稳定拍照等任务。首先,基于MoRo的动量轮刹车机构特性,分析了MoRo在弱引力环境下的跳跃机理并对其跳跃方式进行了规划;接着考虑动量轮驱动机构三闭环伺服系统的非线性特性,基于Herze碰撞模型和Karnopp摩擦模型建立了MoRo在小行星表面的跳跃行为动力学模型;其次,使用机器学习算法建立环境参数和MoRo运动的函数关系,并基于环境参数规划动量轮转速实现跳跃距离和腾空高度的可控。最后,通过数值仿真校验了MoRo跳跃规划方法和控制方法的可行性。     

Solving Optimization Problems for the Flight Trajectories of a Spacecraft with a High-Thrust Jet Engine in Pulse Formulation for an Arbitrary Gravitational Field in a Vacuum

A mathematically well-posed technique is suggested to obtain first-order necessary conditions of local optimality for the problems of optimization to be solved in a pulse formulation for flight trajectories of a spacecraft with a high-thrust jet engine (HTJE) in an arbitrary gravitational field in vacuum. The technique is based on the Lagrange principle of derestriction for conditional extremum problems in a function space. It allows one to formalize an algorithm of change from the problems of optimization to a boundary-value problem for a system of ordinary differential equations in the case of any optimization problem for which the pulse formulation makes sense. In this work, such a change is made for the case of optimizing the flight trajectories of a spacecraft with a HTJE when terminal and intermediate conditions (like equalities, inequalities, and the terminal functional of minimization) are taken in a general form. As an example of the application of the suggested technique, we consider in this work, within the framework of a bounded circular three-point problem in pulse formulation, the problem of constructing the flight trajectories of a spacecraft with a HTJE through one or several libration points (including the case of going through all libration points) of the Earth–Moon system. The spacecraft is launched from a circular orbit of an Earth's artificial satellite and, upon passing through a point (or points) of libration, returns to the initial orbit. The expenditure of mass (characteristic velocity) is minimized at a restricted time of transfer.     

Test-Particle Trajectories in a “Sheared” Stationary Field: Newton–Lorentz and First Order Drift Numerical Simulations1

We study a magnetic field distribution that is nonuniform and sheared like in tangential discontinuities. This distribution is an input parameter for the numerical integration of the equations of motion of the test-particle and of its guiding center. Two different electric field distributions are alternatively tested. In the first case, the electric field is uniform and constant like the electric field prescribed in the large-scale, steady-state reconnection models. The numerical solution shows that in this case the test-particle is trapped within the discontinuity into a region where (i) B goes to zero or (ii) the magnetic vector becomes exactly parallel to the electric field. In the second case, we consider an electric field, which is nonuniform. Its components are computed such that the zero order (or electric) drift is everywhere perpendicular to the discontinuity surface and its value is conserved throughout the simulation. In this case the numerically integrated trajectory of the test-particle penetrates the discontinuity for any angle of shear of B. Direct comparison between exact (Newton–Lorentz) and approximated (first order drift) numerical solutions shows that the mathematical singularities of the latter do not correspond to any physical singularity of the exact equation of motion of the particle.     

One Class of Motions for a Satellite Carrying a Strong Magnet

The attitude motion of an artificial satellite carrying a strong magnet is studied. The approximate first integrals of the problem, i.e., adiabatic invariants, are indicated. The basic properties of the satellite motions close to the regular precessions with slowly varying parameters are established via the analysis of the adiabatic invariants.     

一种火箭发射场坪流场的环形线汇描述方法

针对火箭发射场坪流场分布规律,基于势流法提出环形线汇描述方法,推导了环形线汇流场的速度势和速度的计算公式,建立了流场的FLUENT仿真模型并进行计算,将环形线汇理论计算结果与仿真结果进行对比。结果表明,不同火箭半径和入口流速对环形线汇和FLUENT仿真两种方法计算结果的相关性没有影响,随着箭井间隙增大,两种方法计算结果的相关度减小;环形线汇方法能够描述发射场坪流场变化趋势,在箭井间隙较小且误差允许时可以作为发射场坪流场的简化描述方法。     

Meteor wake in high frame-rate images--implications for the chemistry of ablated organic compounds

Extraterrestrial organic matter may have been chemically altered into forms more ameanable for prebiotic chemistry in the wake of a meteor after ablation. We measured the rate of cooling of the plasma in the meteor wake from the intensity decay just behind a meteoroid by freezing its motion in high frame-rate 1000 frames/s video images, with an intensified camera that has a short phosphor decay time. Though the resulting cooling rate was found to be lower than theoretically predicted, our calculations indicated that there would have been insufficient collisions to break apart large organic compounds before most reactive radicals and electrons were lost from the air plasma. Organic molecules delivered from space to the early Earth via meteors might therefore have survived in a chemically altered form. In addition, we discovered that relatively small meteoroids generated far-ultraviolet emission that is absorbed in the immediate environment of the meteoroid, which may chemically alter the atmosphere over a much larger region than previously recognized.     

Structure of the Large-Scale Vortex Motions in the Ionosphere E Region

It is shown that the dissipative-centrifugal instability (DCI) revealed earlier for large-scale two-dimension vortex motions of the neutral gas in a fast-rotating atmosphere is also possible for similar motions of a weakly ionized gas in the magnetic field when one takes into account electrodynamics forces (the induction deceleration and gyroscopic force caused by the Hall current) in the absence of dissipation. In the case of a conductive atmosphere, strictly anticyclone motion at a DCI of the neutral atmosphere could be impossible or (depending on the Hall conductivity value) it could even change to a cyclone motion. Experimental results that can be considered as a confirmation of the theoretical conclusions are presented.     

Absolute IR-spectra from the measurement of Fourier-spectrometers aboard Meteor 25 and 28

It is well known that temperature- and watervapour-profiles, ozone concentration, other atmospheric constituents and the surface-radiation of the Earth can be determined by remote sensing in the IR radiation range with the aid of a satellite.

The narrow-band radiation measurements for remote sensing of the atmosphere and the Earth-surface can be realized either by various radiometers working in selected frequency channels or, continuously in a given frequency range, by spectrometers with fixed spectral resolution.

Fourier-spectrometers (FS) have been used in Earth-orbit only four times up to now: Nimbus 3, Nimbus 4, Meteor 25 and Meteor 28.

The most important technical parameters, the working regime and some aspects of date processing of the FSs working aboard of Meteor 25 and Meteor 28 are given. For the determination of calibrated absolute spectra a method is used that is based on the experience of the first experiment and on the long time stability of the spectrometers. The results obtained in laboratory calibration tests and in the orbit are described.     

Gravitational Convection of a Liquid Mixture in a Horizontal Cylindrical Gap at Moderate Grashof Numbers

Weak concentration convection which arises in the process of diffusion of impurities into the solvent filling a gap between two coaxial cylinders is studied experimentally. It is found that convective motion in the range of Grashof numbers 10³–5 × 10⁴ has a clear boundary-layer character. Near the inner porous cylinder, which is a source of impurity, a diffusion boundary layer passing into a two-dimensional convective plume is formed. The data on the structure and thickness of this layer are presented depending on the integral flux of impurity. The prospects of making an experiment in order to discover concentration convection onboard an orbital station are discussed.     

Optimization of Flight Trajectories of a Spacecraft with Electric Propulsion Using the Gravitational Maneuver

Necessary conditions of optimality of the use of a gravitational maneuver during a flight are obtained, and a mathematical model for its study is proposed. With the help of the developed method of optimization of a trajectory of an interplanetary flight using a favorable gravitational maneuver, estimations of a spacecraft's transport capabilities are made for flights to Mercury and for the delivery of a solar probe into the near vicinity of the Sun.     

Doppler Detection of Gravitational Bursts Using the Earth's Satellites

We discuss the possibility of detection of low-frequency gravitational waves by means of Doppler tracking of a relatively close satellite of the Earth. A detailed analysis is performed of electromagnetic fluctuations in the space communication channel and of the instrumental noise of receiving–transmitting systems. It is shown that when certain compensating procedures are used, one can detect gravitational radiation generated in star collapses and coalescences of binaries in our Galaxy in the frequency range from 2 × 10^–3 to 5 × 10^–1 Hz and with a metric variation amplitude of 10^–15 and higher.     

Gravitational settling time of solid grains in gaseous protoplanets

Gravitational settling time of solid grains in a gaseous protoplanet has been calculated for three different initial grain sizes using the distribution of the physical variables inside the protoplanet, values of the physical variables at different depths being obtained by solving the structure equations. In all cases the sedimentation time is found to be short, in agreement with that obtained by others with different approach.