Kuiper带天体的原始分布模拟

用包括太阳、8颗大行星、冥王星和UB313以及无质量实验粒子在内的N体问题的天体动力学模型,取当前观测的天体轨道根数为初始条件,对具有确定轨道根数的551个Kuiper主带内的小天体进行了10亿年的轨道反演数值模拟.结果显示:当前观测的这些Kuiper 天体中的1/3以上在10亿年前就位于该区域,少部分位于海王星轨道之内,其他在5OAU之外;在4.5亿年前,整个Kuiper主带内的天体呈较好的正态分布,海王星3:2共振带内没有像今天这样的天体聚集现象.     

基于脉冲星计时的航天器自主定位误差估计方法

目前很多学者希望从"X射线脉冲星自主导航"的导航算法研究入手,利用数据分析或仿真进行验证.其中关于航天器自主定位的误差估计方法、误差量级和各种影响因素的讨论,并没有在给定详细初始条件的基础上系统性地说明问题.为了分析上述问题,需从天体测量学的角度出发,对自主定位的各种误差源及其影响因素进行探讨和误差量级的估计.首先,由...     

科德韦尔天体目视观测指南(一)

什么是科德韦尔天体?玩目视观测的天文爱好者们,大多数都喜欢观测深空天体。深空天体里,比较容易观测的,就是著名的梅西叶天体了。不过,如果你把梅西叶天体基本都看遍了,甚至梅西叶天体马拉松都成功地跑过了,那么还有哪些深空天体值得一看呢?     

第三体摄动分析解的一种表达式

在太阳系中,大行星、小行星和卫星（包括自然卫星和人造卫星）等对应的运动问题,都可以处理成受摄二体问题,而摄动源又多为第三体,作为第三体的摄动天体,有的比运动天体离中心天体近,有的则相反,前者称为内摄内体,全者则称为外摄天体,对一个具体的运动天体,可以同时出现这两个摄动天体,但是,只要运动天体与摄动天体的轨道都建立在以中心天体（质心）为坐标原点的同一坐标系内,那么在一定条件下（即除运动天体与摄动天体     

梅西叶天体和梅西叶天体马拉松

梅西叶天体 梅西叶天体,简称M天体,是梅西叶星表中所包含的全部110个天体的总称。M是梅西叶的字头,星表中每个天体都用自己的编号来表示,例如M1是金牛座的蟹状星云,M31是仙女座大星云等等。     

如何选择照相机进行天体摄影

如何选择照相机进行天体摄影河南读者蔡明来信问：在拍摄天体照片时，使用什么样的照相机？回答这个问题首先要搞清楚什么叫天体摄影。天体摄影主要是指拍摄太阳、月亮、行星，及星团星云等天体照片，清楚地记录下来它们的表面特征和物理现象。天体在底片上的成像大小可以...     

追寻科德韦尔天体（1）

往前一个系列中向大家介绍了梅西叶天体星表,对于星表中深空天体的观测价值相信大家都有目共睹了。但是,我们可以注意到,这份星表依然存在一些缺陷。我们之前介绍过,梅西叶编纂星表的目的是为了避兔这些云雾状的天体千扰他的寻彗工作,并不是因为对深空天体怀有兴趣。这就导致不少明亮的深空天体没有被编入梅西叶星表,比如著名的毕星团和英仙座双星团。此外,梅西叶在北半球观测,因此星表中的天体主委集中在北天,南天的天体非常少,这对南半球乃至北半球低纬度的天文爱好者来说是非常不利的。而有一份深空天体墨表就是为了弥补梅西叶星表这两个缺陷而编纂的,这就是我们接下来要介绍的科德韦尔深空天体墨表。     

特殊BL Lac型天体的VLBI观测研究

BL Lac型天体是一类特殊的活动星系核,根据辐射能谱的不同可以分为低峰值频率BL Lac型天体(LBLs),中间峰值频率BL Lac型天体(IBLs),高峰值频率BL Lac型天体(HBLs),以及极高峰值频率BL Lac型天体(UHBLs)。不同类型BL Lac型天体具有不同的辐射特性,通过射电、光学、X射线、伽玛射线等多波段的观测可以发现很多特殊类型及辐射特性的BL Lac型天体,而甚长干涉测量技术(Very Long Baseline Interferometry,VLBI)是目前分辨率最高的观测技术,也是探测致密核区结构的唯一手段。主要介绍目前对BL Lac型天体的VLBI观测研究概况,以及对其中一些特殊BL Lac型天体VLBI研究的进展及初步结果。     

梅西叶天体马拉松观测攻略

110个梅西叶天体,是天文爱好者最乐于观测的深空天体目标。你可能观测过其中的一部分天体,但你有没有想过进行这样一个挑战：在一晚上的时闻里,观测尽量多的、甚至全部的梅西叶天体？这项观测运动,称之为梅西叶天体马拉松（下文简称“梅马”）。     

梅西耶天体观测马拉松

梅西耶天体观测马拉松朱晔华编译在一个夜晚观测１００个以上的Ｍ天体的活动，叫作“梅西耶天体马拉松”。１７８１年，法国天文学家查理斯·梅西耶（Ｃｈ·Ｍｅｓｓｉｅｒ）将他所观测到的星云状天体汇编成梅酉耶星表，表中包含１０３个星云、星团和星系类天体，后人又增...     

Investigation of periodic orbits in elliptical galaxies using the method of implicit functions

Existence of periodic orbits inside elliptical galaxies has been investigated. Necessary conditions for regular, small amplitude periodic motion around the center of galaxy have been derived using implicit functions and solved by approximating through Taylor's series. The solution procedure requires to obtain functions of partial derivatives of dependent variables with respect to initial conditions. Derivation of these functions can be accomplished through solving a set of ordinary differential equations by proper choices of associated initial conditions. The results obtained show complete agreement with those obtained through the application of Poincaré-Lindstedt's method.     

An approximate integral and solution for eccentric planetary type orbits in the restricted problem of three bodies

The circular restricted problem of three bodies is investigated analytically with respect to the problem of deriving a second integral of motion besides the well known Jacobian Integral. The second integral is searched for as a correction the angular momentum integral valid in the two body case. A partial differential equation equivalent to the problem is derived and solved approximately by an asymptotic Fourier method assuming either sufficiently small values for the dimensionless mass parameter or sufficiently large distances from the barycentre. The solution of the partial equation then leads to a function of the coordinates, velocities and time being nearly constant, which means that its variation with time is about 40–300 times less than that of the pure angular momentum. By averaging over the remaining fluctuating part of the quasi-integral we are able to integrate the first order equations using a renormalization transformation. This leads to an explicit expression for the approximate solution of the circular problem which describes the motion of the third body orbiting both primaries with nonvanishing initial eccentricity (eccentric planetary type orbits). One of the main results is an explicit formula for the frequency of the perihelion motion of the third body which depends on the mass parameter, the initial distance of the third body from the barycentre and the initial eccentricity. Finally we study orbits of the P-Type, being defined as solutions of the restricted problem with circular initial conditions (vanishing initial eccentricity).     

A Simplified Kinetic Element Formulation for the Rotation of a Perturbed Mass-Asymmetric Rigid Body

Euler's equations, describing the rotation of an arbitrarily torqued mass asymmetric rigid body, are scaled using linear transformations that lead to a simplified set of first order ordinary differential equations without the explicit appearance of the principal moments of inertia. These scaled differential equations provide trivial access to an analytical solution and two constants of integration for the case of torque-free motion. Two additional representations for the third constant of integration are chosen to complete two new kinetic element sets that describe an osculating solution using the variation of parameters. The elements' physical representations are amplitudes and either angular displacement or initial time constant in the torque-free solution. These new kinetic elements lead to a considerably simplified variation of parameters solution to Euler's equations. The resulting variational equations are quite compact. To investigate error propagation behaviour of these new variational formulations in computer simulations, they are compared to the unmodified equations without kinematic coupling but under the influence of simulated gravity-gradient torques.     

Computation of Partial Derivatives of Perturbed Motion Using the Arcs of Osculating and Superosculating Orbits

The methods for analytical determination of partial derivatives of the current parameters of motion with respect to their initial values are described. The methods take into account principal perturbations and are based on the use of the osculating and superosculating intermediate orbits constructed earlier by the author. These orbits ensure the first-, second-, and third-order contact to the real trajectory at the initial time. The solution for parameters of the intermediate motion and partial derivatives of these parameters is given in a universal closed form. The partial derivatives on long time intervals are computed using a step-by-step procedure combined with the Encke method of special perturbations, in which the intermediate orbits are used as the reference. The numerical results show that the new approach can be efficiently used for solving the problem of differential correction of orbits of asteroids and comets on the basis of observational data.     

Dynamic Elastic Tides

This is an exploration of dynamic tides on elastic bodies. The body is thought of as a dynamical system described by its modes of oscillation. The dynamics of these modes are governed by differential equations that depend on the rheology. The modes are damped by dissipation. Tidal friction occurs as exterior bodies excite the modes and the modes act back on the tide raising body. The whole process is governed by a closed set of differential equations. Standard results from tidal theory are recovered in a two-timescale approximation to the solution of these differential equations.     

Numerical integration of the variational equations of satellite orbits

A recurrent power series (RPS) method is constructed for the numerical integration of the equations of motion together with the variational equations of N point masses orbiting around an oblate spheroid. By the term “variational equations” we mean the equations of the partial derivatives of the bodies’ position and velocity components with respect to the initial conditions, the relative masses and the spheroid's oblateness coefficients J₂ and J₄. The construction of recursive relations for the partial derivatives involved in the variational equations is based on partial differentiation of the corresponding recursive relations for the integration of the equations of motion. Since the number of the auxiliary variables needed for this complex system becomes tremendously large when N>1, special care must be taken during computer implementation, so as to minimize the amount of computer memory needed as well as the cost in CPU time. The RPS method constructed in this way is tested for N=1,…,4 using real initial conditions of the Saturnian satellite system. For various sets of satellites, we monitor the behaviour of all the corresponding partial derivatives. The results show a prominent difference in the behaviour of the partial derivatives between resonant and non-resonant orbital systems.     

Existence of the solution of Szebehely's equation in three dimensions using a two-parametric family of orbits

The three-dimensional inverse problem is investigated. A quasi-linear system of partial differential equations is derived for the determination of the potential. The solution of this system is studied by a method of differential geometry. A necessary condition for the solution is derived and the determination of the potential is reduced to algebraic equations written in vectorial form. A few examples are also given.     

Application of KS-transformation in the problem of investigation of the motion of unusual minor planets and comets

A review is presented of the author's results on application of regularizing and stabilizing KS- transformation in the problem of investigation of the motion of unusual minor planets and comets. Two models of the motion of a minor body are considered, viz. the perturbed two body problem and the perturbed restricted three body problem. The variational equations in KS-variables and transformations for obtaining the matrix of partial derivatives of the instantaneous physical parameters of motion with respect to their initial values are presented. The peculiarities of the implementation of the algorithms developed as programs on a computer are described. The original results of the investigation of the efficiency of the developed algorithms and programs are discussed using as an example the motion of unusual minor planets Icarus and Geographos as well as comets Halley, Honda-Mrkos-Pajdusakova and Gehrels 3.     

An Encke-type special perturbation method

In this paper, a combination analytical-numerical integration method for solving the differential equations of a modified set of Lagrange's planetary equations is described. The integration method is an Encke-type method because it involves integrating the deviations between the actual trajectory and a reference trajectory. The reference trajectory is obtained from an analytical solution containing the dominant secular and periodic effects of the gravitational field of the primary body. A set of nonsingular elements is used so that the method will be valid for all circular and elliptical motions. It is shown that the method is an accurate and efficient means of satellite ephemeris generation.This paper was presented at the AIAA/AAS Meeting, Princeton University, August 1969.