IB Physics: Gravitational Field Laws and Field Strength Calculations | IB物理：引力场定律与场强计算

📚 IB Physics: Gravitational Field Laws and Field Strength Calculations | IB物理：引力场定律与场强计算

Gravitational fields are one of the most intuitive yet mathematically rich topics in IB Physics. Every object with mass generates a gravitational field, and understanding how to calculate field strength is essential for tackling both Paper 1 and Paper 2 questions. This guide breaks down the core laws and walks you through every type of field-strength calculation you will encounter in the IB syllabus.

引力场是IB物理中既直观又充满数学内涵的专题之一。任何具有质量的物体都会产生引力场，掌握场强的计算方法是应对Paper 1和Paper 2试题的关键。本指南将拆解核心定律，并带你逐步掌握IB课程大纲中出现的每一类场强计算问题。

1. What Is a Gravitational Field? | 什么是引力场？

A gravitational field is a region of space in which a mass experiences a gravitational force. The field is generated by any object that has mass. It is a vector field, meaning every point in the field has both a magnitude and a direction.

引力场是空间中质量会感受到引力的区域。任何具有质量的物体都会产生引力场。引力场是矢量场，即场中每一点都具有大小和方向。

By convention, gravitational field lines point towards the mass that creates the field, indicating that gravitational forces are always attractive. For a spherical mass such as a planet, the field lines radiate inward and the field is radial, not uniform. The closer you are to the mass, the denser the field lines and the stronger the field.

按惯例，引力场线指向产生场的质量，表明引力总是吸引力。对于球形质量（如行星），场线向内辐射，场呈径向分布而非均匀分布。越靠近质量，场线越密集，场越强。

There are two ways to describe a gravitational field in IB Physics: field strength g, which we focus on here, and gravitational potential V, which we cover in a separate revision guide.

在IB物理中，描述引力场有两种方式：场强 g（本文重点）和引力势 V（在另一篇复习指南中介绍）。

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

Newton’s law of universal gravitation states that any two point masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

牛顿万有引力定律指出，任意两个质点之间相互吸引，引力大小与两质量之积成正比，与它们之间距离的平方成反比。

F = G m₁m₂ / r²

Here, F is the magnitude of the gravitational force in newtons, G is the universal gravitational constant, m₁ and m₂ are the two masses in kilograms, and r is the distance between their centres in metres.

其中，F 为引力大小（单位 N），G 为万有引力常量，m₁ 和 m₂ 为两个质量（单位 kg），r 为两者质心之间的距离（单位 m）。

The value of G is 6.67 × 10⁻¹¹ N m² kg⁻². This value is provided in the IB Physics data booklet, but you should know how to use it in calculations and understand that it is extremely small, which explains why gravitational forces are only noticeable for very large masses.

G 的值为 6.67 × 10⁻¹¹ N m² kg⁻²。该值在IB物理数据手册中会给出，但你应知道如何在计算中运用它，并理解它极其微小，这解释了为什么引力只有在质量极大时才显著。

The r in the equation is always measured from the centre of one mass to the centre of the other. For objects at or near the surface of a planet, r is measured from the planet’s centre, not from its surface.

方程中的 r 始终从第一个质量的质心量到第二个质量的质心。对于行星表面附近的物体，r 从行星中心量起，而不是从表面量起。

3. Defining Gravitational Field Strength | 引力场强的定义

Gravitational field strength g 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 g 定义为：放在某点的微小测试质量所受的引力大小与测试质量之比。

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