Gravitational Potential | 引力势

📚 Gravitational Potential | 引力势

Gravitational potential is one of the most important field concepts in CIE A-Level Physics. It leads directly to gravitational potential energy, escape velocity, satellite total energy and the shape of gravitational fields. This article explains the definition, equations, graphs and common exam applications.

引力势是 CIE A-level 物理中最重要的场概念之一。它直接联系引力势能、逃逸速度、卫星总能量和引力场的图像。本文讲解定义、公式、图线以及常见考试应用。

1. Definition of Gravitational Potential | 引力势的定义

In CIE A-Level Physics, gravitational potential φ at a point is defined as the work done per unit mass in bringing a small test mass from infinity to that point. It is a scalar quantity, and its SI unit is J kg⁻¹. The definition uses a small test mass so that the source field is not disturbed.

在 CIE A-level 物理中，某点的引力势 φ 定义为把一个小试验质量从无穷远移到该点过程中每单位质量所做的功。它是标量，SI 单位是 J kg⁻¹。定义中使用小试验质量是为了不扰动源场。

At infinity the potential is chosen to be zero. Because gravity is attractive, a mass moving from infinity towards a planet has work done on it by the field. This makes gravitational potential at all finite distances negative for a point mass.

无穷远处的势被规定为零。因为万有引力是吸引力，质量从无穷远靠近行星时引力场对它做正功。因此对于点质量，所有有限距离处的引力势都是负值。

φ = W / m

2. Why Infinity is the Zero Reference | 为什么选择无穷远为零势点

Zero potential at infinity is a natural convention for inverse-square laws. It means a body at infinity has zero gravitational potential energy relative to the source. As the body moves closer, the field does positive work, so the potential energy must decrease below zero.

对于平方反比定律，无穷远为零势点是一个自然的约定。它意味着无穷远的物体相对源质量具有零引力势能。随着物体靠近，引力场做正功，因此势能必须降到零以下。

This choice also makes the expression for potential mathematically simple: φ = −GM/r. If another zero point were chosen, the formula would require an added constant.

这个选择还使势的表达式数学上很简单：φ = −GM/r。如果选择别的零点，公式就需要额外加一个常数。

3. Formula for a Point Mass | 点质量的引力势公式

For a point mass M, or a uniform spherical mass outside its surface, the gravitational potential at a distance r from the centre is:

对于点质量 M，或均匀球体外部的点，距离球心 r 处的引力势为：

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