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万有引力普遍存在,但万有引力定律公式只适用于质点或均质球之间万有引力大小的计算.牛顿从物理学的角度证明了质量均匀的球体和球外一质点间的万有引力,可等效成球的质量集中在球心,从而转化为两质点之间的万有引力的计算.这一结论为人们所熟悉并应用,但不知道如何证明,通常物理学书籍也没有证明过程.本文试从数学的角度利用微积分证明这一结论,以便让更多的人接受、理解和运用.
Universal gravitation is ubiquitous, but the law of universal gravitation is only applicable to the calculation of the gravitational gravitation between particle or homogenized sphere.Newton proves, from a physical point of view, that the gravitational force between a sphere of uniform mass and a particle outside the sphere can be equivalent to a sphere The mass is concentrated at the center of the sphere, which translates into the calculation of the gravitation between the two points.This conclusion is familiar and applied, but we do not know how to prove it, nor do the physics books usually prove the process.This paper tries to make use of mathematics Calculus proves this conclusion so that more people can accept, understand and apply it.