Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

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.     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

一种基于图像的星体表面撞击坑自动提取方法

以星体表面的图像数据为基础,根据撞击坑的向阳面呈亮色调而背阳面呈暗色调的原理,提出了一种基于图像的星体表面撞击坑自动提取方法。该方法先用自适应双阈值分割法对星体表面的光学图像进行分割处理,获取图像中明暗区域的形状和位置信息;再用统计学原理分析明暗区域组成结构、像平面上光照方向,结合相关的约束条件来匹配同一撞击坑的明暗区域,同时拟合出撞击坑的外边缘并确定其半径、位置等信息。实验结果表明,该方法能够从常见的星体表面光学图像中快速、可靠地提取出撞击坑的中心位置和半径大小,具有较宽的普适应性和一定的应用价值。     

Parametric study of the diversion of a near Earth object on an Earth intersecting trajectory

To date, NASA's “Near Earth Object Program” has discovered over 5500 comets and asteroids on trajectories that bring them within “the neighborhood” of Earth's orbit. Nearly 1000 of these objects are classified as “potentially hazardous,” passing within 0.05 astronomical units of Earth's orbit. Discovery rates of such threatening bodies increase each year. Given this multitude of threats, in addition to evidence that the planet has absorbed many impacts over its history, it is reasonable to assume that another object will strike the Earth at some point in the future. Consequently, researchers have studied and proposed several mitigation techniques for such an occurrence. This study seeks to determine how effectively the attachment of a tether and ballast mass would divert the trajectory of such threatening objects. Specifically, the study analyzes the effects over time of such a system on objects of varying orbital semimajor axis and eccentricity, using various tether lengths and ballast masses. It was determined that the technique is most effective for NEOs with high eccentricity and small semimajor axis, and that system performance increases as tether length and ballast mass increase.     

Taxonomy of the extrasolar planet

When a star is described as a spectral class G2V, we know that the star is similar to our Sun. We know its approximate mass, temperature, age, and size. When working with an extrasolar planet database, it is very useful to have a taxonomy scale (classification) such as, for example, the Harvard classification for stars. The taxonomy has to be easily interpreted and present the most relevant information about extrasolar planets. I propose an extrasolar planet taxonomy scale with four parameters. The first parameter concerns the mass of an extrasolar planet in the form of units of the mass of other known planets, where M represents the mass of Mercury, E that of Earth, N Neptune, and J Jupiter. The second parameter is the planet's distance from its parent star (semimajor axis) described in a logarithm with base 10. The third parameter is the mean Dyson temperature of the extrasolar planet, for which I established four main temperature classes: F represents the Freezing class, W the Water class, G the Gaseous class, and R the Roasters class. I devised one additional class, however: P, the Pulsar class, which concerns extrasolar planets orbiting pulsar stars. The fourth parameter is eccentricity. If the attributes of the surface of the extrasolar planet are known, we are able to establish this additional parameter where t represents a terrestrial planet, g a gaseous planet, and i an ice planet. According to this taxonomy scale, for example, Earth is 1E0W0t, Neptune is 1N1.5F0i, and extrasolar planet 55 Cnc e is 9E-1.8R1.     

Optimal interplanetary rendezvous combining electric sail and high thrust propulsion system

The aim of this paper is to study, from a mission analysis point of view, the performance of a hybrid propulsion concept for a two-dimensional transfer towards a planet of the Solar System. The propulsion system is obtained by combining a chemical thruster, used for the phases of Earth escape and/or target planet capture, with an electric sail, which provides a continuous thrust during the heliocentric transfer. Two possible mission scenarios are investigated: in the first case the sailcraft reaches the target planet with zero hyperbolic excess velocity, thus performing a classical rendezvous mission in a heliocentric framework. In the second mission scenario, a given final hyperbolic excess velocity relative to the planet is tolerated in order to decrease the mission flight time. The amount of final hyperbolic excess velocity is used as a simulation parameter for a tradeoff study in which the minimum flight time is related to the total velocity variation required by the chemical thruster to accomplish the mission, that is, for Earth escape and planetary capture.     

Modal control of the planar motion of a long flexible beam in orbit

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems are investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit is analyzed. In this study, first order effects of gravity-gradient are included, whereas external perturbations and related orbital station keeping maneuvers are neglected. A mathematical model which describes the system deflections within the orbital plane has been developed by treating the beam as having a maximum of three discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of this system are simulated and, in addition, the effects of the control devices are considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, is examined. The effect of varying the number of modes in the model as well as the number and location of the control devices are also considered.     

Optimal impulse point-to-elliptical orbit transfers of a spacecraft

The paper deals with energetically optimal multi-impulse transfer of a spacecraft in the central Newtonian gravity field near a planet. At the initial state of the transfer the distance from the spacecraft to the center of attraction, its radial and transversal velocity projections are known. At the end of the transfer the spacecraft must be located in the elliptical orbit with the given area and energy constants. The distance from the spacecraft to the center of attraction is bounded above and below, the transfer time being unspecified. The initial orbit intersects the inner boundary of the given ring.All the optimal solutions have been obtained by analytical way. A number of new solutions has been found for the given problem in comparison with the case of the transfer from the orbit at the free initial point.Up to five impulses can be applied on the optimal trajectories. The numerical simulation of the problem is carried out. It shows that all obtained solutions give not only local but global optimal energetic input on the corresponding conditions.     

What makes a planet habitable, and how to search for habitable planets in other solar systems

The availability of liquid water is the most important factor that makes a planet habitable, because water is a very effective polar molecule and hence an excellent solvent and facilitator for the complex chemistry of life. Its presence presupposes a planet with a significant mass that guarantees the presence of a substantial atmosphere, and a reasonable spinning rate to avoid overheating. It also implies that the planet is at moderate distances from its central star, a range that is called the Ecosphere or the Habitable Zone. Since the evolution of life to high intelligence seems to take billions of years, it requires also that the central star must be neither too massive, that will produce a lot of lethal UV radiation and will have too short a life-span to allow life to evolve, nor of very small mass which will be producing too feeble a radiation to sustain life. The detection of free Oxygen in the atmosphere of a planet is a very strong evidence for the presence of life, because Oxygen is highly reactive and would rapidly disappear by combining with other elements, unless it is continuously replenished by life as the by-product of the process of photosynthesis that builds food for life (sugars) from CO2 and H2O.     

非质心特征点相对位置和姿态估计方法研究

卫星编队飞行中,从星星体上偏离质心的任意特征点,其相对位置和相对姿态运动耦合。本文针对任意点的相对状态估计问题,推导了耦合相对轨道动力学方程和无陀螺相对姿态动力学方程,并且基于PSD敏感器对主星上点光源的视线测量值,提出了基于特征点耦合动力学和质心传统动力学的两种相对状态估计策略。针对每种策略分别设计了EKF和UKF两种滤波算法对相对状态进行估计。最后通过数学仿真对算法的有效性进行了验证,并对其计算量进行了分析。结果表明,四种算法均能对特征点的相对状态进行较高精度的估计。     

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).     

超前偏置比例导引律及其实现方法

红外寻制导的导弹只能探测跟踪目标(飞机)的热辐射中心,即发动机尾喷流中心。它离飞机质心有一段距离h,为了有效地杀伤目标,提高杀伤概率,必须使命中点前移一段距离h,为此我们对此进行了研究。本文导出了空间飞行时实现超前偏置的相对运动方程和导引律,并提出简化导引律方案,探讨了控制系统实现的方法。     

Tides and the evolution of planetary habitability

Tides raised on a planet by the gravity of its host star can reduce the planet's orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars ( less or similar to 0.35 M(circle)). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, approximately 5 M(circle) planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.     

Conditions of the Maximum Principle in the Problem of Optimal Control over an Aggregate of Dynamic Systems and Their Application to Solution of the Problems of Optimal Control of Spacecraft Motion

The necessary first-order conditions of strong local optimality (conditions of maximum principle) are considered for the problems of optimal control over a set of dynamic systems. To derive them a method is suggested based on the Lagrange principle of removing constraints in the problems on a conditional extremum in a functional space. An algorithm of conversion from the problem of optimal control of an aggregate of dynamic systems to a multipoint boundary value problem is suggested for a set of systems of ordinary differential equations with the complete set of conditions necessary for its solution. An example of application of the methods and algorithm proposed is considered: the solution of the problem of constructing the trajectories of a spacecraft flight at a constant altitude above a preset area (or above a preset point) of a planet's surface in a vacuum (for a planet with atmosphere beyond the atmosphere). The spacecraft is launched from a certain circular orbit of a planet's satellite. This orbit is to be determined (optimized). Then the satellite is injected to the desired trajectory segment (or desired point) of a flyby above the planet's surface at a specified altitude. After the flyby the satellite is returned to the initial circular orbit. A method is proposed of correct accounting for constraints imposed on overload (mixed restrictions of inequality type) and on the distance from the planet center: extended (nonpointlike) intermediate (phase) restrictions of the equality type.     

Why space exploration should be a global project

Apollo should not serve as a model for the many programs for lunar and planetary exploration currently making headway: it was a unilateral effort whose generous budget would be inconceivable today. Yet President Kennedy was an advocate of cooperation in major space missions, an attitude that makes perfect sense today, when so many agencies have ambitious exploration plans. The importance of President G.W. Bush's ‘Vision for Space Exploration’, by providing a focus for NASA and others, has been underestimated. It should give us a chance to find out whether a long-term objective of moving humans off the home planet is really feasible—surely the point of exploration.     

Mechanics of very long tethered systems

A space elevator has been proposed as an alternate method for launching satellites; however, the materials available now are not strong enough to support the stress generated in the structure. On the other hand, with the existing technology, a partial elevator is feasible. In this paper, the mechanics of a very long tethered system that functions as a partial elevator is studied. For such a system, the center of mass, center of gravity, and center of orbit are not coincident; disregarding this distinction can lead to erroneous results. A relation between these three points is presented in this paper. A consistent stress distribution along the tether is obtained by taking into account the distinction between these points. Dynamics of the system consisting of two end bodies, the tether (with mass), and a climber is examined. The equations of motion are derived using the Lagrangian formulation and analyzed numerically.     

Ballistics of a nonfragmenting meteor body with allowance made for mass outflow in the non-isothermal atmosphere. I

The paper is devoted to studying the motion of meteor bodies with mass outflow in a planet’s atmosphere, taking into account the non-isothermal character of the latter. Analytical solutions are obtained at the constant parameter of mass outflow in the model of a nonfragmenting meteoroid. A theoretical analysis of the derived regularities of the ballistics of such bodies is presented.     

Resonance Effects when Moving a Small Spacecraft around the Center of Mass in a Deployable Tether System

Cosmic Research - The resonance motions of a small spacecraft relative to the center of mass when deploying a tether system are analyzed. The tether system is deployed from a base spacecraft moving...