Gravitation: IB & OCR Physics Essentials | 万有引力考点精讲 (IB OCR 物理)

📚 Gravitation: IB & OCR Physics Essentials | 万有引力考点精讲 (IB OCR 物理)

Gravitation is the universal force of attraction acting between all matter. From Newton’s law to satellite orbits, mastering gravitational concepts is essential for IB and OCR A-level Physics. In this revision guide, we break down every key point, formula and exam tip to help you excel.

万有引力是作用于所有物质之间的基本吸引力。从牛顿定律到卫星轨道，掌握引力概念对 IB 和 OCR A Level 物理至关重要。本文梳理每一个考点、公式和考试技巧，助你高效备考。

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

Newton’s law 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 the distance between their centres. The magnitude is given by:

牛顿万有引力定律指出：任何两个质点之间都存在相互吸引力，力的大小与它们的质量乘积成正比，与它们中心间距离的平方成反比。其大小为：

F = G m₁ m₂ / r²

where G = 6.67 × 10⁻¹¹ N m² kg⁻² is the universal gravitational constant. The force acts along the line joining the centres of the two masses and is always attractive.

式中 G = 6.67 × 10⁻¹¹ N m² kg⁻² 为万有引力常量。力沿两质点连线方向，且始终为引力。

Note that the law applies strictly to point masses, but it can be applied to spherical objects with uniform density as if their mass were concentrated at the centre. The force on each mass is equal in magnitude and opposite in direction (Newton’s third law).

注意，定律严格适用于质点，但对于质量均匀分布的球体，可视为质量集中于球心进行计算。两物体所受引力大小相等、方向相反，符合牛顿第三定律。

2. Gravitational Field Strength | 引力场强度

A gravitational field is a region of space where a mass experiences a force. The gravitational field strength g at a point is the gravitational force per unit mass acting on a small test mass placed at that point:

引力场是空间中任何具有质量的物体都会受到力的作用的区域。某点的引力场强度 g 定义为作用在该点单位质量测试物体上的引力：

g = F / m

For a point mass M (or a spherical body), the field strength at a distance r from its centre is:

对于点质量 M（或球体），距其中心 r 处的引力场强为：

g = G M / r²

On the Earth’s surface, g ≈ 9.81 N kg⁻¹ (m s⁻²). The direction of g is towards the centre of the mass causing the field. g is a vector quantity, and for a uniform spherical shell, the field inside the shell is zero.

在地球表面，g ≈ 9.81 N kg⁻¹（m s⁻²）。g 的方向指向引力源质量中心。g 是矢量，对于均匀球壳，球壳内部引力场强为零。

3. Gravitational Potential & Potential Energy | 引力势与引力势能

Gravitational potential V at a point is defined as the work done per unit mass to bring

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