Time,gravity and the exterior angle of parallelism

Applying calculus to the horizontal and vertical unit hyperbolas we derive the obtuse exterior and the acute angle of parallelism formulas for the arc length of a unit circle. When the analogous arc length of a hyperbola is figured, we further define metric distance with radian measure. Employing a non-conventional velocity of light formula, we explain several aspects of physics with a logical geometry. The hyperbolic geometry Lobacevskii angle of parallelism is mathematically measured to agree with the physical measure, without using the gravitational constant, but rather the electromagnetic spectrum and geodesics. Space is hereby measured with units of radians and time. Half-angle formulas for slopes and boosts pertain to spinor algebra. The new light velocity is justified when its derivative results in Einstein's mass–energy formula. Relativity is reformulated with these half-angle formulas.     

比萨斜塔实验趣谈

从理论上分析了比萨斜塔实验.     

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students’ development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.     

伽利略卫星导航系统的初步性能评估

伽利略卫星导航系统是由欧盟和欧洲航天局联合打造的全球卫星导航系统。基于MGEX全球数据监测网的实测数据,对伽利略卫星导航系统的观测数据质量、单点定位和精密单点定位性能展开了评估。评估结果显示:目前伽利略系统导航卫星数较少,尚不具备全天时导航定位能力;伽利略系统多路径误差大小量级为分米级,E5频段信号的多路径效应最小,而E5b频段信号的多路径效应最为严重;一般情况下伪距单点定位平面精度可达5 m以内,高程精度可达10 m以内;动态精密单点定位平面精度可达5 dm以内,高程精度可达5 dm以内。     

But Still, It Moves: Tides, Stellar Parallax, and Galileo’s Commitment to the Copernican Theory

Galileo found the Copernican heliocentric theory of the universe so persuasive owing to its mathematical elegance that he embraced it even when his theory of the tides stood in opposition to it. Further support for Galileo’s deep commitment to the Copernican heliocentric theory is found in his recently discovered unpublished observations of the double star Mizar in 1617, which exhibited no annual stellar parallax and hence indicated that the Earth does not move, in contradiction to the Copernican heliocentric theory. Further, Galileo did not mention this contradiction in his Dialogue Concerning the Two Chief World Systems of 1632. I conclude that he was so deeply committed to the Copernican heliocentric theory that he was unswayed even when observations undermined it, and I suggest that if he had published his observations on the double star Mizar, general acceptance of the Copernican heliocentric theory by astronomers would have been delayed even more than it was. Christopher M. Graney teaches physics and astronomy at Jefferson Community College in Louisville, Kentucky, and runs the college’s observatory at Otter Creek Park in Louisville.     

倾角和摩擦系数的不均匀性对伽利略斜面实验核心结果的影响

伽利略斜面实验的核心结果是小球走过的路程正比于时间的平方,但倾角和摩擦系数的局部不均匀性会导致局部加速度的不均匀性.本文用一个简化模型计入倾角和摩擦系数的不均匀性,数值计算发现这些不均匀性不仅引入随机误差,而且导致路程与时间偏离平方关系.如果保持倾角情况不变,减小摩擦系数使球从无滑滚动变为有滑滚动,路程与时间对于平方关系的偏离程度会增大而不是减小.这个结论虽然与直觉相反,但却与物理学史的相关研究得到的结论相符.为了排除小球被释放时的随机因素的影响,本文在实验中设计了零初速度释放小球的装置,还设计了一个更方便的测量摩擦系数的方法.     

国际天文年：同一个地球，同一片星空——2009国际天文年清华大学活动纪实

天文学是历史最悠久的学科之一,一直以来对人类的文化、生活有着深远的影响．400年前,伽利略首次将望远镜指向天空,开启了人类天文学发展史新的篇章．为纪念这一事件,国际天文学联合会和联合国教科文组织将2009年定为国际天文年．本文主要介绍2009国际天文年的文化背景以及这一全球盛典的主要活动．     

GPS 和 Galileo 空间信号仿真及分析

介绍和详细分析了GPS和Galileo的空间信号。将Galileo空间信号结构及特性与GPS进行了比较,对接收机接收天线接收的射频信号进行下变频并予以分析。为避免信号混叠,仿真中先采用带通滤波器对射频信号进行滤波,然后采用过采样(过采样因子等于8)进行下变频处理。GPS和Galileo信号通过功率归一化加上高斯白噪声产生。对GPS采用的C/A码和Galileo采用的BOC(1,1)码进行比较,发现后者的中心波峰较窄,尽管这一特点使接收机的跟踪处理更为复杂,但提供了较好的接收性能,尤其在多路效应情况下也更为有效。仿真结果为GPS/Galileo双频软件接收机捕获和跟踪算法设计提供了很好的理论基础。     

机械能守恒定律和相对性原理

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