以木星的卫星运动演示开普勒第三定律

介绍用普通设备观测木星的伽利略卫星来演示开普勒第三定律，并计算出中心天体——木星的质量，这一方法可以用作中学物理实验和中学生社团活动的内容．     

巧用开普勒第三定律解决天体运动问题

在天体运行中,会有绕同一个中心天体运动的行星或卫星问题;卫星与它所绕行的天体的同步问题;卫星在轨期间的变轨问题;卫星之间的追及和相遇问题。应用开普勒第三定律是解决这些问题的重要途径。     

开普勒三定律和万有引力定律的几何证明

在高中教材中“由开普勒定律推导出万有引力定律”“由万有引力定律推导开普勒定律”,采用的是近似方法求解,结果不能令人信服。在大学教材或者相关文献中都是通过微积分知识求解,学生不易理解。本文采用哈密顿速度矢量图,结合简单的几何知识,巧妙地解决了上述问题。     

开普勒第二定律的建立

 约翰·开普勒(ＪｏｈａｎｎｅｓＫｅｐｌｅｒ,1571-1630)是德国著名的天文学家和物理学家,一生在多方面对科学的发展做出了贡献,尤其在天文学领域,他经过多年的努力探索,建立了开普勒三定律,从而使人们对行星的运动有了更加明确清晰的认识,也为牛顿发现万有引力定律奠定了基础。正是由于这一卓越的科学成就,开普勒被后人称为“天空的立法者”。本文就他建立开普勒第二定律的过程做一探讨。1.第谷与开普勒的合作科学的发展不仅需要理论,而且不能离开观察实验。在科学向前发展的过程中,有时理论这只脚向前先迈一步,有时观察实验这只脚向前先迈一步。     

文艺复兴时期的开普勒

 数学家、天文学家、物理学家约翰尼斯·开普勒(JohannesKepler)(1571～1630)根据第谷·布拉赫的丰富而精确的天文观测资料,建立行星运动三定律,使其成为指导天体力学的基本定律,被人们称为“天空的立法者”。他继承和发展了哥白尼的日心学说,为人类认识宇宙的奥秘贡献了自己的智慧和心血。目前有关开普勒研究的文章大多集中于他对行星运动三定律的证明和论述,但是“历史的价值在于恢复其过去丰富多彩的活生生的生命。”如果我们公正地回复到历史的来龙去脉中,而不是用现代的观点编织历史,新科学的产生、新世界观的形成要比传统诠释所描述的复杂得多。     

对物理师范生“学生的知识”掌握情况的调查研究

“关于学生的知识”是教师把握学生某知识点的掌握情况和学习困难点的知识,是学科教学知识 (PCK)的核心要素.本研究在了解初中生(N =80)和高中生(N =73)关于牛顿第三定律的掌握情况及困难点的基 础上,让153名大三、大四的物理师范生对学生的作答情况进行预测,并将此结果与学生的真实作答情况进行对比, 从而了解师范生“关于学生的知识”.结果发现物理师范生普遍高估初中生而低估高中生,并且难以从概念内涵上出 发准确把握学生的学习困难点.而后,进一步访谈10名师范生,分析师范生预测不准确的原因并提出相应的教学建 议.     

牛顿第一定律教学的四点突破

对牛顿第一定律教学的研究一直是教师的关注点.从最近的课堂观察发现许多年轻教师,对学生前概念的顽固程度重视不够,缺乏对定律本身内容的深刻理解,对科学史的事实缺乏全面了解.牛顿第一定律是动力学的基础,没有牛顿第一定律就没有第二、第三定律.不管从知识本身的理解、科学研究方法的创新还是科学精神的熏陶,都应该非常重视牛顿第一定律的教学.基于以上的思考,笔者认为牛顿第一定律的教学至少要突破以下四点.     

浅析法拉第电磁感应定律的理解和应用

电磁感应是中职物理教学中的重点内容,这部分学习的好坏直接关系到《电工基础》等专业课程的学习.基于中职学生现状,本着“去繁从简,保留本质”的原则,本文在阐述电磁感应定律的基础上,对解题过程中涉及到电路问题、力学问题和能量问题进行了分析,并对解决方法和途径进行了探索.     

开普勒问题的矢量解法

直接利用矢量解法求解开普勒问题,不必借助于比奈方程．该方法简明扼要,物理图像清晰．     

The Kepler problem in the Snyder space

In this paper the Kepler problem in the non-commutative Snyder scenario was studied. The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the non-commutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and then the consequences in the precession of the orbit of Mercury were calculated. The result could be used for finding an estimated value for the non-commutative deformation parameter.     

Quantization of the Kepler manifold

A representation ofSO(2,n+1), the maximal finite dimensional dynamical group of then-dimensional Kepler problem, is obtained by means of (pseudo) differential operators acting onL ₂(S ⁿ ). This representation is unitary when restricted toSO(2) SO (n+1), i.e. to the physically relevant subgroup.     

Conformal regularization of the Kepler Problem

The manifoldM of null rays through the origin of ^2,n+1 is diffeomorphic toS ¹×S ⁿ , and it is a homogeneous space of SO(2,n+1). This group therefore acts onT*M, which we show to be the generating manifold of the extended phase space of the regularized Kepler Problem. A local canonical chart inT*M is found such that the restriction to the subbundle of the null nonvanishing covectors is given byp ₀+H(q,p)=0, whereH(q,p) is the Hamiltonian of the Kepler Problem. By means of this construction, we get some results that clarify and complete the previous approaches to the problem.     

Spinor regularization of then-dimensional Kepler problem

A Clifford algebraic construction is shown to yield a simple generalization to any dimension of the Kustaanheimo-Stiefel regularization for the Kepler problem.     

Explicit solution of the Kepler equation

An explicit solution of the Kepler equation is expressed in terms of the Lambert hyperfunction. Calculation of this function, for example, by making use of the Maple software package, enables one to efficiently obtain the numerical solution of the Kepler equation.     

Kepler motion on single-sheet hyperboloid

The classical Kepler–Coulomb problem on the single-sheeted hyperboloid H ³ ₁ is solved in the framework of the Hamilton–Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.     

Variations on the Kepler problem

The elliptical orbits resulting from Newtonian gravitation are generated with a multifaceted symmetry, mainly resulting from their conservation of both angular momentum and a vector fixing their orientation in space—the Laplace or Runge-Lenz vector. From the ancient formalisms of celestial mechanics, I show a rather counterintuitive behavior of the classical hydrogen atom, whose orbits respond in a direction perpendicular to a weak externally-applied electric field. I then show how the same results can be obtained more easily and directly from the intrinsic symmetry of the Kepler problem. If the atom is subjected to an oscillating electric field, it enjoys symmetry in the time domain as well, which is manifest by quasi-energy states defined only modulo ħω. Using the Runge-Lenz vector in place of the radius vector leads to an exactly-solvable model Hamiltonian for an atom in an oscillating electric field—embodying one of the few meaningful exact solutions in quantum mechanics, and a member of an even more exclusive set of exact solutions having a time-dependent Hamiltonian. I further show that, as long as the atom suffers no change in principal quantum number, incident radiation will produce harmonic radiation with polarization perpendicular to the incident radiation. This unusual polarization results from the perpendicular response of the wavefunction, and is distinguished from most usual harmonic radiation resulting from a scalar nonlinear susceptibility. Finally, I speculate on how this radiation might be observed.     

A generalization of the Kepler problem

A generalization of the Kepler problem is constructed and analyzed. These generalized Kepler problems are parametrized by a triple (D, κ, μ), where the dimension D is an integer ≥3, the curvature κ is a real number, and the magnetic charge μ is a half-integer if D is odd and zero or half if D is even. The key to constructing these generalized Kepler problems is the observation that the Young powers of the fundamental spinors on a punctured space with cylindrical metric are the right analogs of the Dirac monopoles. The text was submitted by the authors in English.