Gravitation – GCSE CIE Physics | GCSE CIE 物理：万有引力考点精讲

📚 Gravitation – GCSE CIE Physics | GCSE CIE 物理：万有引力考点精讲

Gravitation is a fundamental force of nature that attracts any two objects with mass. In GCSE CIE Physics, you need to understand how gravity acts on objects near the Earth’s surface, how it governs planetary motion, and how to calculate weight, gravitational potential energy, and the acceleration due to free fall. This topic bridges everyday experience with the laws that keep the Moon in orbit and the planets around the Sun. Mastering these concepts will not only prepare you for your exam but also deepen your appreciation of the physical world.

万有引力是自然界中一种基本的吸引力，任何有质量的两个物体之间都存在万有引力。在 GCSE CIE 物理课程中，你需要理解重力如何作用于地球表面附近的物体、如何支配行星运动，并掌握重量、重力势能以及自由落体加速度的计算方法。这一主题将日常经验与维持月球轨道和行星绕日运行的定律联系起来。掌握这些概念不仅有助于你应对考试，还会加深你对物理世界的理解。

1. What is Gravitation? | 什么是万有引力？

Gravitation, or gravity, is a non-contact force that pulls masses toward each other. The size of the gravitational force between two objects depends on their masses and the distance between their centres. On a planetary scale, gravity is responsible for the orbits of moons, planets, and satellites. Near the Earth’s surface, we experience gravity as the force that gives us weight and causes objects to fall downwards.

万有引力（或简称重力）是一种非接触力，会把有质量的物体互相拉近。两个物体之间引力的大小取决于它们的质量以及它们中心之间的距离。在行星尺度上，重力决定了月球、行星和人造卫星的轨道。在地球表面附近，我们感受到的重力表现为赋予我们重量的力，并使物体向下落。

2. Gravitational Field Strength (g) | 引力场强度 (g)

The gravitational field strength, symbol g, is the force per unit mass acting on a small test mass placed in the field. On Earth, the average value of g is approximately 9.8 N/kg. This means that a 1 kg mass experiences a gravitational force of about 9.8 N downwards. The exact value of g can vary slightly with altitude and latitude, but you can assume g = 9.8 m/s² for most calculations.

引力场强度，符号为 g，是指作用在场中一个较小的检验质量上的每单位质量的力。在地球上，g 的平均值约为 9.8 牛/千克。这意味着 1 千克的质量会受到大约 9.8 牛向下的引力。g 的精确值会随海拔和纬度的不同而略有变化，但在大多数计算中你可以取 g = 9.8 米/秒²。

3. Mass vs Weight | 质量与重量

Mass is the amount of matter in an object and is measured in kilograms (kg). It does not change with location. Weight is the gravitational force acting on a mass and is measured in newtons (N). The relationship is given by W = mg, where m is the mass and g is the gravitational field strength. An astronaut’s mass is the same on the Moon as on Earth, but their weight is about one-sixth because the Moon’s gravitational field strength is much lower.

质量是物体所含物质的多少，单位是千克 (kg)，它不随位置改变。重量是作用在质量上的引力，单位是牛顿 (N)。两者之间的关系为 W = mg，其中 m 是质量，g 是引力场强度。航天员在月球上的质量与在地球上相同，但他们的重量大约只有地球上的六分之一，因为月球的引力场强度小得多。

4. Acceleration due to Gravity | 重力加速度

Near the Earth’s surface, all objects fall with the same acceleration if air resistance is negligible. This acceleration is called the acceleration due to gravity, also denoted by g, and its value is 9.8 m/s². This means that in each second of free fall, the object’s downward velocity increases by 9.8 m/s. Because weight is the force causing this acceleration, the value of g connects force (N/kg) to acceleration (m/s²) seamlessly.

在地球表面附近，如果忽略空气阻力，所有物体都以相同的加速度下落。这一加速度称为重力加速度，同样用 g 表示，其值为 9.8 米/秒²。这意味着在自由落体中，物体的向下速度每秒增加 9.8 米/秒。由于重量正是产生这一加速度的力，g 的值自然地将力（牛/千克）与加速度（米/秒²）联系起来。

5. Free Fall | 自由落体

Free fall is the motion of an object where gravity is the only force acting on it. In the absence of air resistance, a feather and a hammer dropped from the same height hit the ground at the same time. This was famously demonstrated on the Moon by astronaut David Scott. In real life, air resistance opposes the motion of falling objects, eventually leading to a constant terminal velocity when the resistance force balances the weight.

自由落体是指只受重力作用的物体运动。在没有空气阻力的情况下，从同一高度同时释放一根羽毛和一把锤子，它们会同时落地。航天员大卫·斯科特在月球上著名的实验证明了这一点。在现实生活中，空气阻力会阻碍下落物体的运动，当阻力与重量平衡时，物体的速度最终会达到一个恒定的终极速度。

6. Gravitational Potential Energy | 重力势能

Gravitational potential energy (E_p) is the energy stored in an object because of its position in a gravitational field. Near the Earth’s surface, the change in gravitational potential energy is given by ΔE_p = mgΔh, where Δh is the change in height. This equation assumes g is constant. Lifting an object does work against gravity and increases its store of gravitational potential energy; when it falls, this energy is transferred to kinetic energy.

重力势能 (E_p) 是物体由于在引力场中的位置而储存的能量。在地球表面附近，重力势能的变化由公式 ΔE_p = mgΔh 给出，其中 Δh 是高度的变化。这一公式假设 g 保持不变。提升一个物体会克服重力做功，增加其重力势能的储存；当它下落时，这部分能量转化为动能。

7. Measuring g Experimentally | 实验测量 g

In the laboratory, you can determine g by measuring the time it takes for a freely falling object to drop a known distance. Using a trapdoor and an electromagnet, you can time a steel ball’s fall and apply the equation of motion s = ½gt² (if initial velocity is zero). Rearranging gives g = 2s / t². Another method uses a pendulum: by measuring the period T for small oscillations, you can find g from T = 2π√(L/g).

在实验室中，你可以通过测量自由下落物体经过已知距离所需的时间来测定 g。用一个陷阱门和电磁铁，你可以记录一个钢球下落的时间，并应用运动学公式 s = ½gt²（当初速度为零时）。整理可得 g = 2s / t²。另一种方法使用单摆：测量小角度摆动时的周期 T，然后通过 T = 2π√(L/g) 计算出 g。

8. Factors Affecting g | 影响 g 的因素

The value of g is not exactly the same everywhere on Earth. It is slightly higher at the poles than at the equator because the Earth is not a perfect sphere; the poles are closer to the Earth’s centre. Altitude also matters: g decreases as you move away from the Earth’s surface. Furthermore, the Earth’s rotation causes a slight reduction in apparent g at the equator. For the GCSE exam, you only need to know that g can vary slightly, and on other planets g is very different.

在地球上不同地方，g 的值并不完全相同。由于地球不是一个完美的球体，两极的 g 略高于赤道，因为两极更靠近地心。海拔高度也有影响：离地球表面越远，g 越小。此外，地球的自转使得赤道处的视在 g 略微减小。在 GCSE 考试中，你只需知道 g 可能会有微小变化，而在其他行星上 g 的值则完全不同。

9. Weightlessness and Orbits | 失重与轨道

Astronauts in orbit around the Earth appear to be weightless, but this does not mean that gravity is absent. The spacecraft and the astronauts are in free fall towards the Earth, but they also have a large tangential velocity that makes them fall around the Earth rather than directly into it. This continuous free-fall state creates the sensation of weightlessness. The same principle governs the Moon’s orbit around the Earth and the Earth’s orbit around the Sun.

在环绕地球轨道上的航天员似乎处于失重状态，但这并不表示重力已经消失。航天器与航天员都在朝着地球自由下落，但同时又具有足够大的切向速度，使得他们围绕地球下落，而不是直接坠入地球。这种持续的自由落体状态造成了失重的感觉。同样的原理支配着月球绕地球的运动以及地球绕太阳的运动。

10. Gravity on the Moon and Planets | 月球与行星上的重力

The gravitational field strength on the surface of a planet or moon depends on its mass and radius. The Moon’s surface gravity is about 1.6 N/kg, roughly one-sixth that of Earth. On Jupiter, the giant planet, g is about 24.8 N/kg. Because weight is mg, an object would weigh far more on Jupiter than on Earth. Understanding how g varies across celestial bodies helps explain why astronauts can leap higher on the Moon and why planets have different atmospheres.

行星或月球表面的引力场强度取决于其质量和半径。月球表面的重力约为 1.6 牛/千克，大约是地球的六分之一。在巨大的木星上，g 约为 24.8 牛/千克。由于重量为 mg，一个物体在木星上的重量会比在地球上大很多。了解 g 如何在不同天体间变化，有助于解释为什么航天员在月球上能跳得更高，以及为什么各行星拥有不同的大气层。

11. Projectile Motion and Gravity | 抛体运动与重力

A projectile is any object that is thrown or launched and moves under the influence of gravity. Near the Earth’s surface, the horizontal and vertical components of motion can be treated independently. The horizontal velocity remains constant (ignoring air resistance), while the vertical velocity changes at a rate of 9.8 m/s² downwards. This combination gives the parabolic path characteristic of a projectile. Gravity is the only force acting on the projectile after launch, making it accelerate towards the ground.

抛体是指任何被抛出或发射、并在重力作用下运动的物体。在地球表面附近，运动的水平分量和竖直分量可以独立分析。水平速度（忽略空气阻力）保持不变，而竖直速度以 9.8 米/秒² 的速率向下变化。这两种运动的结合使得抛体轨迹呈抛物线形。抛出后，重力是唯一作用在抛体上的力，使它加速向地面坠落。

12. Summary of Key Equations | 关键公式总结

Here are the essential equations related to gravitation for your GCSE Physics exam. They should be memorised and applied with the correct units: weight W = mg (newtons, kilograms, N/kg); gravitational potential energy change ΔE_p = mgΔh (joules, kilograms, metres); for an object starting from rest, distance fallen s = ½gt² (metres, seconds). Remember that g is 9.8 m/s² on Earth unless stated otherwise, and always check that your answer makes physical sense.

以下是 GCSE 物理考试中与万有引力相关的关键公式。你需要记忆这些公式，并使用正确的单位：重量 W = mg（牛顿、千克、牛/千克）；重力势能变化 ΔE_p = mgΔh（焦耳、千克、米）；对于从静止开始下落的物体，下落距离 s = ½gt²（米、秒）。请牢记，除非另有说明，地球上的 g 取 9.8 米/秒²，并且要始终检查你的答案在物理上是否合理。

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