Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

Motion of deformable planets and stability of their stationary rotations

A mechanical system consisting from N deformable spheres interacting according to the law of gravity is considered as a model of planetary system. Deformations of the viscoelastic spheres are described according to the model of the theory of elasticity of small deformations, the Kelvin-Voigt model of viscous forces, and occur under the action of gravitational fields and fields of centrifugal forces. Approximate equations describing motions of the centers of mass of the spheres and their rotations relative to the centers of mass are constructed by the method of separation of motions on the basis of solving quasistatic problems of the theory of viscoelasticity with allowance made for smallness of sphere deformations. Using the first integral of conservation of the angular momentum of the system relative to its center of mass, the expression for the changed potential energy is obtained with the use of the Routh method. An investigation of stationary rotations is carried out, and it is shown that all of them are unstable, if the number of planets is more than two.     

Analysis of evolution of multi-orbit perturbed trajectories of a spacecraft in a central field of attraction

Properties of differential equations of multi-orbit trajectory motion of a spacecraft are investigated analytically. The spacecraft moves under the action of small perturbations (in particular, low thrust) in the plane of a central Newtonian field of attraction. The conditions are specified for existence of a partial singular aperiodic solution, in the neighborhood of which the behavior of osculating elements changes sharply. In this case, phase variables (the angular position of the pericenter and the true anomaly) are found to undergo the sharpest changes. The exact superposition of solutions is suggested for the equations of motion transformed to the form of a quasi-linear, weakly non-stationary system: a partial singular aperiodic solution and fast solutions oscillating around it. Asymptotic representations are obtained for both components of the superposition. They are fairly exact in the region of smallness of perturbing terms at a long variation of the argument.     

Planar oscillations of a vibrating dumbbell-like body in a central field of forces

The problem of planar motions of a dumbbell-like body of variable length in a central field of Newtonian attraction is considered both in the exact formulation and in satellite approximation. In the satellite approximation the true anomaly of the center of mass is used as an independent variable, which has allowed us to represent the equation of planar oscillations of the dumbbell in the form similar to the Beletskii equation. Some exact solutions to the inverse problem are given both in the complete formulation and in satellite approximation. Under an assumption of small orbit eccentricity and amplitude of the dumbbell vibrations the conditions of existence are found for families of almost periodic motions and splitting separatrices. The phenomena of alternation of regular and chaotic motions are established numerically, as well as chaos suppression with increasing frequency of vibrations. Using the method of averaging the stabilization of tangent equilibria is proved to be impossible.     

Role of the ionosphere for the atmospheric evolution of planets

We have synthesized current understanding, mainly observations, with regard to ion escape mechanisms to space from the ionosphere and exosphere of Titan and Earth-type planets, with the intent to provide an improved input for models of atmospheric evolution on early Earth and Earth-type planets and exoplanets. We focus on the role of the ionosphere and its non-linear response to solar parameters, all of which have been underestimated in current models of ancient atmospheric escape (4 billion years ago). Factors that have been overlooked include the following: (1) Much larger variation of O(+) outflow than H(+) outflow from the terrestrial ionosphere, depending on solar and geomagnetic activities (an important consideration when attempting to determine the oxidized state of the atmosphere of early Earth); (2) magnetization of the ionopause, which keeps ionospheric ions from escaping and controls many other escape processes; (3) extra ionization by, for example, the critical ionization velocity mechanism, which expands the ionosphere to greater altitudes than current models predict; and (4) the large escape of cold ions from the dense, expanded ionosphere of Titan. Here we offer, as a guideline for quantitative simulations, a qualitative diagnosis of increases or decreases of non-thermal escape related to the ionosphere for magnetized and unmagnetized planets in response to changes in solar parameters (i.e., solar EUV/FUV flux, solar wind dynamic pressure, and interplanetary magnetic field).     

Possibilities for the detection of microbial life on extrasolar planets

We consider possibilities for the remote detection of microbial life on extrasolar planets. The Darwin/Terrestrial Planet Finder (TPF) telescope concepts for observations of terrestrial planets focus on indirect searches for life through the detection of atmospheric gases related to life processes. Direct detection of extraterrestrial life may also be possible through well-designed searches for microbial life forms. Satellites in Earth orbit routinely monitor colonies of terrestrial algae in oceans and lakes by analysis of reflected ocean light in the visible region of the spectrum. These remote sensing techniques suggest strategies for extrasolar searches for signatures of chlorophylls and related photosynthetic compounds associated with life. However, identification of such life-related compounds on extrasolar planets would require observations through strong, interfering absorptions and scattering radiances from the remote atmospheres and landmasses. Techniques for removal of interfering radiances have been extensively developed for remote sensing from Earth orbit. Comparable techniques would have to be developed for extrasolar planet observations also, but doing so would be challenging for a remote planet. Darwin/TPF coronagraph concepts operating in the visible seem to be best suited for searches for extrasolar microbial life forms with instruments that can be projected for the 2010-2020 decades, although resolution and signal-to-noise ratio constraints severely limit detection possibilities on terrestrial-type planets. The generation of telescopes with large apertures and extremely high spatial resolutions that will follow Darwin/TPF could offer striking possibilities for the direct detection of extrasolar microbial life.     

An estimate of the prevalence of biocompatible and habitable planets

A Monte Carlo computer model of extra-solar planetary formation and evolution, which includes the planetary geochemical carbon cycle, is presented. The results of a run of one million galactic disc stars are shown where the aim was to assess the possible abundance of both biocompatible and habitable planets. (Biocompatible planets are defined as worlds where the long-term presence of surface liquid water provides environmental conditions suitable for the origin and evolution of life. Habitable planets are those worlds with more specifically Earthlike conditions). The model gives an estimate of 1 biocompatible planet per 39 stars, with the subset of habitable planets being much rarer at 1 such planet per 413 stars. The nearest biocompatible planet may thus lie approximately 14 LY distant and the nearest habitable planet approximately 31 LY away. If planets form in multiple star systems then the above planet/star ratios may be more than doubled. By applying the results to stars in the solar neighbourhood, it is possible to identify 28 stars at distances of < 22 LY with a non-zero probability of possessing a biocompatible planet.     

A reappraisal of the habitability of planets around M dwarf stars

Stable, hydrogen-burning, M dwarf stars make up about 75% of all stars in the Galaxy. They are extremely long-lived, and because they are much smaller in mass than the Sun (between 0.5 and 0.08 M(Sun)), their temperature and stellar luminosity are low and peaked in the red. We have re-examined what is known at present about the potential for a terrestrial planet forming within, or migrating into, the classic liquid-surface-water habitable zone close to an M dwarf star. Observations of protoplanetary disks suggest that planet-building materials are common around M dwarfs, but N-body simulations differ in their estimations of the likelihood of potentially habitable, wet planets that reside within their habitable zones, which are only about one-fifth to 1/50th of the width of that for a G star. Particularly in light of the claimed detection of the planets with masses as small as 5.5 and 7.5 M(Earth) orbiting M stars, there seems no reason to exclude the possibility of terrestrial planets. Tidally locked synchronous rotation within the narrow habitable zone does not necessarily lead to atmospheric collapse, and active stellar flaring may not be as much of an evolutionarily disadvantageous factor as has previously been supposed. We conclude that M dwarf stars may indeed be viable hosts for planets on which the origin and evolution of life can occur. A number of planetary processes such as cessation of geothermal activity or thermal and nonthermal atmospheric loss processes may limit the duration of planetary habitability to periods far shorter than the extreme lifetime of the M dwarf star. Nevertheless, it makes sense to include M dwarf stars in programs that seek to find habitable worlds and evidence of life. This paper presents the summary conclusions of an interdisciplinary workshop (http://mstars.seti.org) sponsored by the NASA Astrobiology Institute and convened at the SETI Institute.     

From Earth's orbit to the outer planets and beyond: Psychological issues in space

Current planning for the first interplanetary expedition to Mars envisions a crew of 6 or 7 people and a mission duration of around 2.5 years. However, this time frame is much less than that expected on expeditions to the outer solar system, where total mission durations of 10 years or more are likely. Although future technological breakthroughs in propulsion systems and space vehicle construction may speed up transit times, for now we must realistically consider the psychological impact of missions lasting for one or more decades.Available information largely deals with on-orbit missions. In research that involved Mir and ISS missions lasting up to 7 months, our group and others have studied the effects of psychological and interpersonal issues on crewmembers and on the crew-ground relationship. We also studied the positive effects of being in space. However, human expeditions to the outer planets and beyond will introduce a number of new psychological and interpersonal stressors that have not been experienced before. There will be unprecedented levels of isolation and monotony, real-time communication with the Earth will not be possible, the crew will have to work autonomously, there will be great dependence on computers and other technical resources located on board, and the Earth will become an insignificant dot in space or will even disappear from view entirely.Strategies for dealing with psychological issues involving missions to the outer solar system and beyond will be considered and discussed, including those related to new technologies being considered for interstellar missions, such as traveling at a significant fraction of the speed of light, putting crewmembers in suspended animation, or creating giant self-contained generation ships of colonists who will not return to Earth.     

物伞系统空间运动模式分析

以物伞回收系统为背景,通过理论建模和数值仿真的方法,得出物伞回收系统两种基本空间运动模式（平面摆动和圆锥运动）,分析了其产生原因。利用空投录像验证了文章分析结果,其结论可为工程设计部门提供重要理论参考。     

自适应天线互耦影响研究

用等效网络法推导了考虑互耦影响时阵列的输出信号解析式和信噪比,仿真了不同阵元间距时,自适应直线阵的方向图和输出信噪比,得到了一些有用的结论。     

Peristaltic transport of a viscoelastic fluid in a channel

This paper is devoted to the study of the peristaltic transport of viscoelastic non-Newtonian fluids with fractional Maxwell model in a channel. Approximate analytical solutions have been constructed using Adomian decomposition method under the assumption of long wave boundary layer type approximation and low Reynolds number. The effects of relaxation time, fractional parameters and amplitude on the pressure difference and friction force along one wavelength are received and analyzed. The study is limited to one way coupling model with forward effect of the fluid on the peristaltic wall. It is evident from the result that pressure diminishes with increase in relaxation time and the effects of both fractional parameters on pressure are opposite to each other. The influences of these parameters on friction force are opposite to that of pressure.     

High-resolution simulations of the final assembly of Earth-like planets. 2. Water delivery and planetary habitability

The water content and habitability of terrestrial planets are determined during their final assembly, from perhaps 100 1,000-km "planetary embryos " and a swarm of billions of 1-10-km "planetesimals. " During this process, we assume that water-rich material is accreted by terrestrial planets via impacts of water-rich bodies that originate in the outer asteroid region. We present analysis of water delivery and planetary habitability in five high-resolution simulations containing about 10 times more particles than in previous simulations. These simulations formed 15 terrestrial planets from 0.4 to 2.6 Earth masses, including five planets in the habitable zone. Every planet from each simulation accreted at least the Earth's current water budget; most accreted several times that amount (assuming no impact depletion). Each planet accreted at least five water-rich embryos and planetesimals from the past 2.5 astronomical units; most accreted 10-20 water-rich bodies. We present a new model for water delivery to terrestrial planets in dynamically calm systems, with low-eccentricity or low-mass giant planets-such systems may be very common in the Galaxy. We suggest that water is accreted in comparable amounts from a few planetary embryos in a " hit or miss " way and from millions of planetesimals in a statistically robust process. Variations in water content are likely to be caused by fluctuations in the number of water-rich embryos accreted, as well as from systematic effects, such as planetary mass and location, and giant planet properties.     

Transition of Planar Rotational Motion of an Asymmetric Spacecraft into Oscillatory Motion at Its Reentry into the Atmosphere

The motion of a spacecraft with small asymmetry relative to its center of mass is considered. The restoring aerodynamic moment of the spacecraft is described by the Fourier series in terms of the angle of attack with the two first sinusoidal and the first cosinusoidal terms. A solution for the angle of attack in the undisturbed rotational motion is found. The analytical expression is obtained for the integral of action taken along the separatrices that separate the rotational and oscillatory regions of the phase portrait of a system. The transition of the spacecraft's motion from planar rotational to oscillatory is investigated. This transition is caused by a slow variation of moment characteristic coefficients, as well as by the presence of small asymmetry and damping and slow variation of their coefficients. Analytical formulas are obtained for determining the times of transition from rotational to oscillatory motion, as well as for the critical angular velocity of beyond-the-atmosphere rotation. When this critical velocity is exceeded, body rotation proceeds for a long time interval (planar autorotation arises).     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

三维喷流流场中固体颗粒效应的粒子仿真方法研究

采用粒子仿真跟踪颗粒相运动轨迹，采用高效ENO格式求解NS方程，数值模拟了有攻角条件下含颗粒相的横向喷流与超音速物体绕流形成的干扰流场。结果表明上述方法是研究气－相两相流动的有效途径，颗粒相存在对喷流流场结构及物体所受的气动力和气动热具有一定影响。     

月面巡视探测器运动控制方法研究

基于动力学的运动控制是星球探测车研制中的关键技术之一。本文以某多轮驱动、多轮转向的月面巡视探测器运动控制为背景,在建立其三自由度动力学模型的基础上,研究了常规增量式PID和模糊自适应PID控制算法,并进行了仿真比较。典型车轮失效情况下的仿真表明,模糊自适应PID方法能够有效控制月面巡视探测器四轮失效的情况,而常规PID方法能够有效控制探测器三轮失效的情况。模糊自适应PID方法对参数扰动敏感性低,鲁棒性更强,较好地处理了常规控制方法可能产生的小超调与快速性的矛盾。