平方反比有心力作用下质点椭圆轨道运动的若干均值关系  

Several mean-value relations of a moving mass point on elliptic trajectory under inverse squared centric force

作　　者：周国全[1] 唐宇轩 祁宁[1] ZHOU Guo-quan;TANG Yu-xuan;QI Ning(School of Physics and Technology,Wuhan University,Wuhan,Hubei 430072,China)

机构地区：[1]武汉大学物理科学与技术学院,湖北武汉430072

出　　处：《大学物理》2023年第8期6-10,共5页College Physics

基　　金：武汉大学本科教育质量建设综合改革项目(2022ZG235)资助。

摘　　要：基于平方反比有心力作用下的质点的束缚态椭圆轨道运动的开普勒运动规律,以及机械能守恒律与角动量守恒定律,计算了质点的椭圆轨道运动的一些特征参量(速率、极半径、转动惯量、角速度、动能、势能等)的周期平均值,并证明了若干均值关系,讨论了2个典型的均值特征点.根据计算所得的椭圆轨道的动能、势能等特征量的周期平均值,直接证实了位力定理,最后讨论和强调了这些均值关系之于物理教学的参考意义.Based on Kepler's three laws,and the conservation laws of mechanic energy and angular moment about a mass point moving on an elliptic trajectory under an inverse-squared centric force,the mean values within a period of some typical physical quantity(polar radiurs,speed,angular speed,angular momentum,rotation inertia,kinetical energy,potential energy,and so on),are calculated and several interesting and useful mean-value relations are found and proved.A unique mean-value point on the path of the mass point is emphasized.The Virial theorem is direct proved by means of these calculated mean values.The physical meanings,and teaching reference significance of these findings are also emphasized.

关 键 词：万有引力 椭圆轨道 均值点 均值关系 位力定理 平方反比有心力 

分 类 号：O4-1[理学—物理]