The Investigation of the Dynamical Evolution of Extrasolar Three-planetary System GJ 3138

This article is devoted to studying the dynamical evolution and orbital stability of compact extrasolar threeplanetary system GJ 3138. In this system, all semimajor axes are less than 0.7 au. The modeling of planetary motion is performed using the averaged semi-analytical motion theory of the second order in planetary masses,which the authors construct. Unknown and known with errors orbital elements vary in allowable limits to obtain a set of initial conditions. Each of these initial conditions is applied for the modeling of planetary motion. The assumption about the stability of observed planetary systems allows to eliminate the initial conditions leading to excessive growth of the orbital eccentricities and inclinations and to identify those under which these orbital elements conserve moderate values over the whole modeling interval. Thus, it becomes possible to limit the range of possible values of unknown orbital elements and determine their most probable values in terms of stability.

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

Orbital evolution of a planet with tidal dissipation in a restricted three-body system

The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit’s eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution;when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.

Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem

The restricted three-body problem(RTBP) is a fundamental model in celestial mechanics.Periodic orbits in the synodic frame play a very important role in understanding the dynamics of the RTBP model.Most of these periodic orbits,when interpreted in the sidereal frame,are actually resonant periodic orbits.As a result,numerical computation of the periodic orbits is also one approach for researchers to understand the orbital resonances of the three-body problem.Extensive studies have been carried out on this topic,concerning either the circular case or the elliptic case of this model.In this paper,we make a brief review of the history and current status of the studies on resonant periodic orbits in the RTBP model.Starting from the unperturbed two-body problem,we organize the review paper by the two cases of this model—the circular restricted three-body problem and the elliptic restricted three-body problem.

大城市工业用地布局演变中的城市问题研究——以西安市为例

改革开放以来在我国经济转型过程中大城市工业用地的规模和布局发生了巨大变化,并影响城市的空间形态。以西安市为例,基于多源数据,采用定量与定性相结合方法,研究发现1974—2019年西安市工业用地面积呈先持续增长后快速减少变化趋势,空间布局在园区化集聚的过程中具有显著的工业用地郊区化与城市中心用地去工业化特征,布局模式则经历了由改革开放初期“组团布局+扇形扩展”向增量规划时期“圈层扩展+跳跃扩张+轴向集聚”至存量规划时期“外围园区化集聚”转变。帮助企业纾困、城市增长、生活居住条件改善与土地经济价值是推动工业用地布局演变的主要驱动力。工业用地郊区化与城市中心去工业化加剧了职住分离、交通拥堵等城市问题,不利于城市健康可持续发展。

Time Dilation Cosmology 2

This paper is a further elaboration of the author’s Time Dilation Cosmology (TDC) holographic model that ties gravitation and celestial mechanics and kinematics directly to time dilation, resolving all the major conundrums in astrophysics, and ties astrophysics directly to quantum physics. It begins with a brief summary of the TDC model and contains the new derivation for the time dilation version of the formula for summing relativistic velocities, Einstein’s gravitational constant and the time dilation versions for the Lorentz factor and the Euclidean norm of the 3d velocity vector, the two of which can then be used in the Four-velocity formula. It is demonstrated how orbital curvature is manifested as the resultant of two time dilation-manifested velocities. It also explains why an interferometer cannot distinguish free fall from zero gravity and further elaborates on the author’s previous explanations of how spiral galaxies are formed, and contains mathematical proof that Black Holes are actually Magnetospheric Eternally Collapsing Objects (MECOs) that are massless spacetime vortices.

Effect of Orbital Characteristic of Inclined Third-body on Motion of Secondary-body for a Hierarchical Triple Systems

The influence of a third-body's orbital elements on the second-body's motion in a hierarchical triple system is a crucial problem in astrophysics.Most prolonged evaluation studies have focused on a distant zero-inclined thirdbody.This study presents a new perspective on second-body motion equations that addresses a perturbing-body in an elliptic orbit derived with consideration of the axial-tilt(obliquity)of the primary.The proposed model is compared by the dual-averaged method and the N-body problem algorithm.After validation,a generalized threebody model is derived to investigate the effects of the third-body's orbital elements on secondary-body motion behavior.The proposed model considers short-time oscillations that affect secular evaluation and applies to exoplanets with all the primary and third body eccentricities,inclinations,and mass ratios.It is shown that the obliquity of the primary(or third-body's inclination)must be considered for precise long-term assessment,even in highly-hierarchical systems.

Time Dilation Cosmology

This model ties gravitation and celestial mechanics and kinematics directly to time dilation. It is a new theory of cosmology and the evolution of galaxies. Space and time are not two separate things, but two aspects of a single thing, “spacetime”. Whatever affects space, affects time, and vice-versa. If time speeds up, space must contract to maintain the speed of light, c, and when space thickens into a mass, it is harder to evolve forward, and time appears to slow. If spatial events are spinning as time passes, then the forward direction of time is spinning. This is Einstein’s curvature in the forward direction of time. Herein, the basis is outlined for time dilation cosmology in a spacetime/quantum continuum, including the time dilation-based derivation of the mass of the Cosmic Microwave Background Radiation (CMBR), and time dilation formulas are derived for stellar system orbital, and galactic rotation, velocities, the force in time in Newtons, the Hamiltonian, the Hubble shift, the empirical gravitational constant, G, and other formulas, showing their direct relationship to the difference in the rate of time between the far distant observer’s invariant 1 s/s rate of time and the slower rate of time at the coordinate point, proving the universe is not composed of separate bodies moving through space, but is an evolving 3-dimensional holographic continuum containing varying densities evolving forward in the forward direction of time, the 4th dimension, at apparently different rates of time, the velocities merely being compensation for those slower rates of time in a continuum evolving forward overall at c, which is why light propagates at c, even from a moving source. As per General Relativity, if there is no rate of time difference between coordinate points, there is no gravitational attraction between those points, and no gravitationally induced velocity. This model resolves all the major conundrums in astrophysics, eliminating Dark Energy and Dark Matter, and ties astrophysics directly to quantum physics.

解决动态多中心问题的自学习差异进化算法

为解决动态环境下的多中心优化问题,提出自学习差异进化算法。通过评估特定个体检测到环境变化,自学习算子将群体引至新的环境,并保持群体的拓扑结构不变,以继续当前的进化趋势。采用邻域搜索机制加快算法的收敛速度,引入随机个体迁入机制增加群体多样性。实验以周期动态函数为测试对象,比较自学习差异进化算法与部分智能优化算法的性能,结果表明,新算法有更快的收敛速度和更好的环境适应能力。

半分析方法在地球卫星100yr尺度长期预报中的性能评估

为了能够充分掌握空间目标的长期演化规律和分布情况,对它们的轨道进行长期预报是一种常用的方法.相比于几天的短期预报,长期预报更加关心计算速度以及几个主要轨道根数的精度.这里的主要根数指的是决定轨道形状的半长径a和偏心率e以及决定轨道空间指向的轨道倾角i和升交点经度?.考虑到以上这些需求,半分析方法是一种十分合适的预报手段.它首先在一个轨道周期内消除短周期项,而后用数值方法计算剩下的平均系统.虽然半分析法不是一种新方法,但几乎找不到定量评估其性能的文献.定量给出了半分析法在常用地球卫星轨道中的精度和速度,通过这些结果可以帮助了解半分析法在长期预报中的适用性.对于半分析法在一些特殊算例中的异常表现,也讨论了原因和可能的解决方法.在半分析的实现方法和精度选择上,均采用了比较通用的方法,希望结果可以为相关半分析工作提供有价值的参考.

一类具非零角动量的平面三体系统的数值分析

对一类具非零角动量的平面三体系统研究其三体构形对系统演化的影响。根据Agekian和Anosova提出的构形图(homology map),三体系统按其构形特点分属于4个不同的区域。通过数值计算,考察了初始位置位于不同区域中的构形颗粒(homologydrop)的演化,并就有关性质与Heinamaki等人研究的角动量为零的三体系统作了比较指出,构形颗粒的组成系统全部发生解体的时间在L区域最早,H区域最晚,这与零角动量系统不同。还对4个区域的三体系统的寿命进行了统计分析,得到了各区域中未解体的系统数随时间指数衰减的函数关系。

两个可能具有2:1平运动共振结构系统的稳定性研究

通过分析现有视向速度资料提供的轨道拟合解,发现HD 155358和24 Sextanis两系统都有可能处于2:1平运动共振状态.主要讨论了两系统共振结构的动力学稳定性问题,计算了两系统最优拟合值1σ置信区间内大量样本的混沌指标?emax.结果表明:HD155358系统长期稳定,不依赖于平运动共振的保护.但是,24 Sextanis系统如果要维持长期稳定,2:1平运动共振保护是必要条件.

Improved semi-analytical computation of center manifolds near collinear libration points

In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semianalytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.

Stability of the coplanar planetary four-body system

We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their orbits.The system is stable if there is no exchange or cross of orbits.Starting from the Sundman inequality,the equation of the kinematical boundaries is derived.We discuss a reasonable situation,where two planets with known orbits are more massive than the third one.The boundaries of possible motions are controlled by the parameter c^2E.If the actual value of c^2E is less than or equal to a critical value(c^2 E)cr,then the regions of possible motions are bounded and therefore the system is stable.The criteria obtained in special cases are applied to the Solar System and the currently known extrasolar planetary systems.Our results are checked using N-body integrator.

A simple existence proof of Schubart periodic orbit with arbitrary masses

This paper gives an analytic existence proof of the Schubart periodic orbit with arbitrary masses, a periodic orbit with singularities in the collinear three-body problem. A ＂turning point＂ technique is introduced to exclude the possibility of extra collisions and the existence of this orbit follows by a continuity argument on differential equations generated by the regularized Hamiltonian.

Influence of non-equilibrium reactions on the optimization of aerothrust aeroassisted maneuver with orbital change

The spaceplane is perspective vehicle due to wide maneuverability in comparison with a space capsule. Its maneuverability is expressed by the larger flight range and also by a possibility to rotate orbital inclination in the atmosphere by the aerodynamic and thrust forces. Orbital plane atmospheric rotation maneuvers can significantly reduce fuel costs compared to rocket-dynamic non-coplanar maneuver. However, this maneuver occurs at Mach numbers about 25, and such velocities lead to non-equilibrium chemical reactions in the shock wave. Such reactions change a physicochemical air property, and it affects aerodynamic coefficients. This paper investigates the influence of non-equilibrium reactions on the aerothrust aeroassisted maneuver with orbital change.The approach is to solve an optimization problem using the differential evolution algorithm with a temperature limitation. The spaceplane aerodynamic coefficients are determined by the numerical solution of the Reynolds-averaged Navier-Stokes equations. The aerodynamic calculations are conducted for the cases of perfect and non-equilibrium gases. A comparison of optimal trajectories,control laws, and fuel costs is made between models of perfect and non-equilibrium gases. The effect of a chemically reacting gas on the finite parameters is also evaluated using control laws obtained for a perfect gas.