Kepler方程的Noether-Lie对称性与守恒量

研究Kepler方程的对称性与守恒量。给出Kepler方程的Noether-Lie对称性的定义和判据,以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量。     

From centripetal forces to conic orbits: a path through the early sections of Newton’s Principia

In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687.     

Kepler’s theory of the soul: a study on epistemology

Kepler is mainly known among historians of science for his astronomical theories and his approaches to problems having to do with philosophy of science and ontology. This paper attempts to contribute to Kepler studies by providing a discussion of a topic not frequently considered, namely Kepler’s theory of the soul, a general theory of knowledge whose central problem is what makes knowledge possible, rather than what makes knowledge true, as happens in the case of Descartes’s and Bacon’s epistemologies. Kepler’s theory consists of four issues: the theory of the different sorts of soul—that is, the human soul, the animal soul, the vegetable soul, and the Earth soul—concerning their faculties, the differences and the resemblances emerging among them, the relation they maintain with their own bodies and the world, and the distinction soul–world. The paper discusses these issues from a historical perspective, that is, it reconstructs the way they appear in three periods of Kepler’s career: the period prior to the publication of the Mysterium cosmographicum, the period from 1596 to 1611, and the period of the Harmonices mundi libri V. Finally, Kepler’s epistemology is briefly contrasted with Descartes’s and Bacon’s in order to suggest that Kepler’s could be seen as a third way to understand the philosophical origins of Modernity.     

开普勒第三定律与谐和思想

本文介绍了开普勒的宇宙模型的几何学描述,并通过几何学和音乐理论的结合,把每个行星的律音频率与它的运动角速度相类比,得到了用数学定量描述的开普勒第三定律,揭示了开普勒的谐和思想的内涵。     

Harmony and simplicity: aesthetic virtues and the rise of testability

Copernicus claimed that his system was preferable in part on the grounds of its superior harmony and simplicity, but left very few hints as to what was meant by these terms. Copernicus’s pupil, Rheticus, was more forthcoming. Kepler, influenced by Rheticus, articulated further the nature of the virtues of harmony and simplicity. I argue that these terms are metaphors for the structural features of the Copernican system that make it more able to effectively exploit the available data. So it is a mistake to conclude that early Copernicans could only offer aesthetic or pragmatic arguments; they could and did offer evidential ones as well. Moreover, the evidential arguments they offered parallel current arguments in the philosophical literature.     

Underdetermination and decomposition in Kepler's Astronomia Nova

This paper examines the underdetermination between the Ptolemaic, Copernican, and the Tychonic theories of planetary motions and its attempted resolution by Kepler. I argue that past philosophical analyses of the problem of the planetary motions have not adequately grasped a method through which the underdetermination might have been resolved. This method involves a procedure of what I characterize as decomposition and identification. I show that this procedure is used by Kepler in the first half of the Astronomia Nova, where he ultimately claims to have refuted the Ptolemaic theory, thus partially overcoming the underdetermination. Finally, I compare this method with other views of scientific inference such as bootstrapping.     

用矢量法证明开普勒三定律

给出一种运用矢量的特点和性质构造矢量函数 ,来证明开普勒三定律的方法     

Rationality in the Discovery of Empirical Laws

In this paper I argue against the traditional viewthat in discovery processes there is no place forrational decisions. First I argue that some historicalprocesses in which an empirical law was developed,were rational. Second, I identify some of themethodological rules that we can follow in order to berational when constructing an empirical law. Finally,I argue that people who deny that scientific discoverycan be rational do not understand the nature ofmethodological rules.     

点燃科学圣火的人们

本文摘自作者所著的《物理学与人类文明十六讲》一书,该书由高等教育出版社出版。作者介绍了提出“日心说”的曲折经历,哥白尼、布鲁诺、伽利略等人遭受的迫害,开普勒的不幸人生遭遇,以及他们为真理而献身的精神。