The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.

TOPOLOGY OF CONFIGURATION SPACE FOR A THREE-BODY PROBLEM

A mechanics system consisting of three mass points on sphere S 2 is considered. The configuration space of the system is a fibre bundle over S 2 . It is proved that first Chern class of the bundle is -2 c 1(γ) where γ is the canonical line bundle over the complex projective space CP 1=S 2 , which shows the bundle is non trivial. The information about the first Chern class makes the cohomology groups and homotopy groups of the configuration space worked out. In addition the effects of these topolo gical properties of the configuration space on the behavior in large scale of the system, as the number of equilibrium positions, periodic orbits and reduced phase space, are discussed.

Formulation of the Post-Newtonian Equations of Motion of the Restricted Three Body Problem

In the present work the geodesic equation represents the equations of motion of the particles along the geodesics is derived. The deviation of the curved space-time metric tensor from that of the Minkowski tensor is considered as a perturbation. The quantities is expanded in powers of c-2. The equations of motion of the relativistic three body problem in the PN formalism are obtained.

Existence and uniqueness of a class of double pyramidal central configurations in six-body problems

Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combinedly the algebraic method and numerical calculation. It is found that there exists a planar curl triangle region G in a square Q such that any point in G and given by the ratio of the two diagonal lengths of the diamond base and the ratio of one diagonal length of the base to the height of the double pyramid configuration determines a unique double pyramid central configuration, while all points in Q-G have no referance to any central configuration.

The L_(p) Shephard problem on entropy of log-concave functions

this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.

The Shephard Type Problems for General L_p-Centroid Bodies

In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.

Restricted Three-Body Problem in Cylindrical Coordinates System

In this paper, the equations of motion for spatial restricted circular three body problem will be established using the cylindrical coordinates. Initial value procedure that can be used to compute both the cylindrical and Cartesian coordinates and velocities is also developed.

On the Analog of Shephard Problem for L_p-polar Projection Bodies

For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)^(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.

Restricted Three-Body Problem in Different Coordinate Systems

In this paper of the series, the equations of motion for the spatial circular restricted three-body problem in sidereal spherical coordinates system were established. Initial value procedure that can be used to compute both the spherical and Cartesian sidereal coordinates and velocities was also developed. The application of the procedure was illustrated by numerical example and graphical representations of the variations of the two sidereal coordinate systems.

A Series Solution Approach to the Circular Restricted Gravitational Three-Body Dynamical Problem

The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.

Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of <i>L</i>₄in the Photogravitational Restricted Three Body Problem

Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.

The Overseas Reception of Chinese Science Fiction Works from a Perspective of Western Interpretation Preference——A Case Study of Reader's Reception of Liu Cixin's The Three-Body Problem in the USA

The Three-Body Problem, written by Liu Cixin, won the 2015 Hugo Award for Best Novel, with over 200,000 copies in English already sold. This gure is hundreds of times the average sales volume of Chinese novels in the USA. Through qualitative and quantitative analyses of overseas readers' comments on The Three-Body Problem posted on the online platforms of Goodreads and Amazon, this paper concludes that the novel's success overseas lies in its catering to the concerns of overseas readers. The ThreeBody Problem is popular among overseas readership thanks to its re ection on the ultimate existence of mankind, science ction vision & imagination, literary familiarity & identi cation, ideological di erence-triggered cultural curiosity, and a good translation. This paper attempts to interpret Liu Cixin's work on the map of world literature from the perspective of overseas readers' preferences to provide references for contemporary Chinese science ction creation and overseas reception.

Chaos in Planar, Circular, Restricted Three-Body Problem

In this article we analyze the motion of a test particle of a planar, circular, restricted three-body problem in resonance, using the Kustaanheimo-Stiefel formalism. We show that a good qualitative description of the motion can be reduced to three simple equations for semi-major axis, eccentricity and resonance angle. Studying these equations reveals the onset of chaos, and sheds a new light on its weak nature. The 7:4 resonance is used as an example.

翻译修辞学视角下科幻作品“走出去”英译策略探析——以《三体》及The Three Body Problem为例

翻译与修辞是两个相互独立的语言研究领域,却在理论与实践运行上存在理念和方法的重叠,翻译修辞学随之诞生。该学科作为翻译研究的分支学科,是一门新生学科,其研究仍处于初步摸索阶段。运用翻译修辞学指导具体实践不仅能够改善译文水平,还能反哺理论的发展。该文运用修辞学家哈里克提出的4种象征资源,探究中国科幻巨作《三体》系列第一部及其英译本The Three Body Problem中所运用的英译策略及其效果。研究发现,《三体》英译本积极运用了4种修辞策略,建立起译本认同,促进了作品的海外传播。可见,科幻作品英译过程中,合理运用修辞策略指导翻译能加强译本目标语群体的认同构建,有利于中国科幻作品“走出去”,传播中国文化。

GENERALIZED HOMOGENEOUS FUNCTIONS AND THE TWO-BODY PROBLEM

A generalization of the homogeneous function concept is studied.An application is done with a solution of the two-body problem.

Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary

This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.

Numerical Computation of Figure-eight Solution for 3-body Problems

The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.

Solar Radiation Pressure Effects on Stability of Periodic Orbits in Restricted Four-Body Problem

In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).

A Final Solution to the Mind-Body Problem by Quantum Language

Recently we proposed “quantum language”, which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes = Kant epistemology. And further we believe that quantum language is the only scientifically successful theory in dualistic idealism. If this turn is regarded as progress in the history of western philosophy (i.e., if “philosophical progress” is defined by “approaching to quantum language”), we should study the linguistic mind-body problem more than the epistemological mind-body problem. In this paper, we show that to solve the mind-body problem and to propose “measurement axiom” in quantum language are equivalent. Since our approach is always within dualistic idealism, we believe that our linguistic answer is the only true solution to the mind-body problem.

Dynamics of Satellite Formation Utilizing the Perturbed Restricted Three-Body Problem

The dynamics of satellites formation is of great interest for the space mission. This work discusses a more efficient model of the relative motion dynamics of satellites formation. The model is based on employing the concepts restricted three-body problem (R3BP) and for more accuracy, it considers the effects of both oblateness and radiation pressure on deputy relative motion w.r.t the chief satellite. A model of deputy relative motion w.r.t the chief satellite is derived in the local-vertical local-horizontal system and simplified assuming the concept of the circular restricted three-body problem (CR3BP). The deputy equations of motion were rewritten in the form of recurrence relations and solved numerically using the Lie series approach. Assuming that the formation is revolving around the Moon in the Earth-Moon system, the effects of both oblateness and radiation pressure on the deputy satellite orbit were assessed through a particular example of satellites formation. A comparison between the perturbed and unperturbed R3BP shows a significant difference in the deputy relative position that has to be considered for the formation dynamics.