The Pull of Gravity | 引力的吸引

📚 The Pull of Gravity | 引力的吸引

This CIE A-Level Physics revision guide explains the gravitational field model, Newton’s law of gravitation, gravitational potential, circular orbits, geostationary satellites and escape velocity.

本 CIE A-Level 物理复习指南讲解引力场模型、牛顿万有引力定律、引力势、圆周轨道、地球同步卫星和逃逸速度。

1. Newton’s Law of Universal Gravitation | 牛顿万有引力定律

Newton’s law of universal gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation.

牛顿万有引力定律指出，每个质点都会吸引另一个质点，引力大小与两质点的质量乘积成正比，与它们之间距离的平方成反比。

F = Gm₁m₂ / r²

Here, G = 6.67 × 10⁻¹¹ N m² kg⁻² is the universal gravitational constant. The formula gives only the magnitude of the force; the force is always attractive and acts along the line joining the centres of mass.

式中 G = 6.67 × 10⁻¹¹ N m² kg⁻² 为万有引力常量。该公式只表示力的大小；引力总是相互吸引，并且沿着两物体质心的连线作用。

For extended bodies such as planets, the law applies if their masses are spherically symmetric or if the distance is measured between their centres of mass. CIE problems usually treat objects as point masses or uniform spheres.

对于行星等有体积的物体，若质量球对称分布，或距离按质心间距计算，该定律仍然适用。CIE 题目通常把物体视为质点或均匀球体。

• Gravitational force is always attractive, never repulsive.
• 引力总是吸引，从不排斥。
• The law is an inverse-square law: doubling the separation reduces the force to one quarter.
• 这是一个平方反比定律：距离加倍，力变为原来的四分之一。

2. Gravitational Field Strength | 引力场强度

The gravitational field strength at a point is defined as the gravitational force per unit mass acting on a small test mass placed at that point.

引力场强度定义为作用在位于该点的小检验质量上的引力每单位质量。

g = F / m

Its SI unit is N kg⁻¹, which is equivalent to m s⁻². This is why gravitational field strength at Earth’s surface is often quoted as 9.81 N kg⁻¹ or 9.81 m s⁻².

其国际单位是 N kg⁻¹，等价于 m s⁻²。因此地球表面的引力场强度常写作 9.81 N kg⁻¹ 或 9.81 m s⁻²。

Because the gravitational force on a mass m is F = mg, the acceleration produced is a = F/m = g. Hence gravitational field strength has the same numerical value as free-fall acceleration due to gravity.

由于质量 m 所受引力为 F = mg，产生的加速度为 a = F/m = g。因此引力场强度的数值与自由落体加速度相同。

Field strength is a vector quantity: its direction is the direction of the gravitational force on a small test mass. Near a point

Published by TutorHao | A-Level Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）