李都,刘颖,姜付锦

• 1:黄陂区第一中学

摘要(Abstract)：

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。

关键词(KeyWords)： 开普勒定律;万有引力定律;哈密顿定理;矢量图;几何方法

Abstract:

Keywords:

基金项目(Foundation): 湖北省教育学会教师教育专业委员会2020年课题(HBJSJY2020-027)资助

作者(Author): 李都,刘颖,姜付锦

参考文献(References)：

• [1] 何尧荣.万有引力距离平方反比关系的三种不同思维层次的推导[J].物理教学探讨，2016,34(5):36-37+39.HE Y R.Thederivation of three different thinking levels of the inverse squared relation of gravitational distance[J].Discussion on Physics Teaching,2016,34(5):36-37+39.(in Chinese)
• [2] 甘志国.圆锥曲线光学性质的证明及其应用[J].数学教学，2017(9):16-18+37.GAN Z G.Proof of the optical properties of conic section and its application[J].Mathematics Teaching,2017(9):16-18+37.(in Chinese)
• [3] 林棉璇.用高中知识正确理解开普勒第二定律[J].物理教师，2019,40(12):57-58+61.LIN M X.Correctly understanding Kepler's second law with high school knowledge[J].Physics Teacher,2019,40 (12):57-58+61.(in Chinese)
• [4] 赵曰峰.椭圆运动中万有引力定律表达式的推导兼谈卫星椭圆运动的运行参量及应用[J].物理教师，2019,40(12):54-57.ZHAO Y F.Derivation of the expression of the law of universal gravitation in elliptical motion and on the operating parameters and application of satellite elliptical motion[J].Physics Teacher,2019,40(12):54-57.(in Chinese)
• [5] 聂剑军，徐顺海.椭圆轨道下引力与距离的平方成反比的证明[J].宜春学院学报，2010,32(8):8-9.NIE J J,Xu S H.Proof that gravity is inversely proportional to the square of distance under elliptical orbit[J].Journal of Yichun University,2010,32(8):8-9.(in Chinese)
• [6] 孔庆国，郑红伟.利用椭圆知识和物理规律解析天体运动问题[J].物理教师，2013,34(9):63-64.KONG Q G,ZHENG H W.Using ellipse knowledge and physical laws to analyze celestial motion[J].Physics Teacher,2013,34(9):63-64.(in Chinese)
• [7] DERBES D.Reinventing the wheel:How do graphic solutions to the Kepler problems[J].American Journal of Physics,2001,69(4):481-489.
• [8] DOUGLAS W.Tiberiis.Comment on “Reinventing the wheel:Hodographic solutions to the Kepler problems,” by David Derbes[J].American Journal of Physics,2002,70(1):79-79.
• [9] CHAKERIAN D.Central Force Laws,Hodographs,and PolarReciprocals[J].Mathematics Magazine,2001,74(1):3-18.
• [10] 李开玮.利用几何知识求解天体运动轨道[J].物理与工程，2021,31(3):36-38.LI K W.Solving the orbit of celestial bodies by using geometric knowledge[J].Physics and Engineering,2021,31(3):36-38.(in Chinese)