中心力场质点机械能及机械能与离心率之间关系的简洁推导

A Concise Derivation of the Particle's Mechanical Energy and the Relation between Eccentricity and Mechanical Energy in the Central Force Field

文章基于比耐(Binet)公式和近日点的机械能导出轨道离心率e和机械能E之间的关系式,同时还推导了不同轨道上质点机械能E的表达式.该方法通俗易懂,避免了复杂的积分运算,便于学生更好地理解中心力场质点轨道运动的问题.

The article derives the relation between the eccentricity e and mechanical E on the Binet formula and the mechanical energy of the perihelion, and also derives the formula of the particle＇ s mechanical energy E in different orbit. This method is easy to understand, avoiding the complex integral operation, and enhance students＇ understanding of the problem.