📚 GCSE OCR Physics: Gravitation Key Revision Notes | GCSE OCR 物理：万有引力 考点精讲
Welcome to your dedicated revision guide on gravitation for GCSE OCR Physics. Gravity is not just the force that keeps your feet on the ground; it governs the motion of planets, moons and artificial satellites. This article breaks down every key concept you need to master, from Newton’s law to orbits and weightlessness, all structured to match the OCR specification.
欢迎阅读专为 GCSE OCR 物理准备的万有引力考点精讲。引力不仅让你脚踏实地，它还支配着行星、卫星运行。本文拆解每个核心概念，从牛顿定律到轨道运动和失重，全部紧扣 OCR 考纲，助你精准复习。
1. What is Gravity? | 什么是万有引力？
Gravity is a non-contact force that attracts any two objects with mass towards each other. It is one of the four fundamental forces in nature and acts over infinite distances, although it weakens rapidly with separation.
引力是一种非接触力，任何两个有质量的物体之间都会相互吸引。它是自然界四种基本力之一，尽管随着距离增大迅速减弱，但作用范围无限远。
On Earth, gravity gives objects weight and causes them to fall towards the ground. It is also responsible for keeping the Moon in orbit around the Earth and the planets around the Sun.
在地球上，引力赋予物体重量并使它们落向地面。它也使月球绕地球运转、行星绕太阳运转。
2. Newton’s Law of Universal Gravitation | 牛顿万有引力定律
Newton’s law states that every particle attracts every other particle 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.
牛顿定律指出，任意两个质点之间的引力大小与它们质量的乘积成正比，与它们中心距离的平方成反比。
The equation is:
F = G × (m₁ × m₂) / r²
where F is the gravitational force in newtons (N), m₁ and m₂ are the masses in kilograms (kg), r is the distance in metres (m), and G is the gravitational constant, approximately 6.67 × 10⁻¹¹ N m² kg⁻².
其公式为：
F = G × (m₁ × m₂) / r²
F 是引力（牛顿 N），m₁ 和 m₂ 是质量（千克 kg），r 是距离（米 m），G 是万有引力常数，约 6.67 × 10⁻¹¹ N m² kg⁻²。
3. Gravitational Field Strength (g) | 重力场强度 (g)
Gravitational field strength, g, is defined as the force per unit mass experienced by a small test mass placed in a gravitational field. Its unit is newtons per kilogram (N/kg).
重力场强度 g 定义为放置在引力场中的小检验质量所受到的单位质量力。单位是牛顿每千克（N/kg）。
Near the Earth’s surface, g is approximately 9.8 N/kg. This means that every kilogram of mass experiences a downward gravitational pull of about 9.8 newtons. The value of g decreases with altitude and is weaker on the Moon.
地球表面附近 g 约为 9.8 N/kg。这表示每千克质量受到约 9.8 牛的向下引力。g 值随高度增加而减小，月球上的 g 更小。
4. Weight, Mass and the g Equation | 重量、质量和 g 的公式
Weight is the gravitational force acting on an object and is measured in newtons. It should not be confused with mass, which is the amount of matter and is measured in kilograms.
重量是作用在物体上的引力，单位为牛顿。切勿与质量混淆，质量是物体所含物质的多少，单位为千克。
The relationship is given by the equation:
W = m × g
Weight (W) equals mass (m) multiplied by gravitational field strength (g). Weight is a vector quantity, always directed towards the centre of the planet.
关系式如下：
W = m × g
重量 W 等于质量 m 乘以重力场强度 g。重量是一个矢量，方向始终指向行星中心。
5. Gravitational Field Lines | 重力场线
Gravitational fields can be represented by field lines. Around a spherical mass like the Earth, these lines point radially inwards towards the centre, showing the direction of the gravitational force on a mass.
引力场可以用场线表示。在地球这样的球形质量周围，场线径向指向中心，表明作用在质量上的引力方向。
Where the field lines are closer together, the gravitational field is stronger. Near the Earth’s surface the lines are almost parallel and equally spaced, indicating a nearly uniform field.
场线越密，引力场越强。在地球表面附近，场线几乎平行且等距，表明这是一个近似匀强场。
6. Free Fall and Acceleration Due to Gravity | 自由落体与重力加速度
If gravity is the only force acting on an object, the object is in free fall. In the absence of air resistance, all objects near the Earth’s surface fall with the same acceleration: approximately 9.8 m/s², which is numerically equal to g.
若只有引力作用，物体处于自由落体状态。在没有空气阻力时，地球表面附近所有物体下落的加速度相同，约为 9.8 m/s²，数值上等于 g。
This surprising result, demonstrated by dropping a feather and a hammer on the Moon, confirms that gravitational acceleration does not depend on mass.
这个令人惊讶的结果——在月球上同时释放羽毛和锤子的实验——证实了重力加速度与质量无关。
7. Factors Affecting Gravitational Force | 影响万有引力的因素
According to Newton’s law, the gravitational force doubles if one of the masses doubles, and it becomes four times stronger if both masses double. However, if the distance is doubled, the force decreases to one-quarter of its original value (an inverse square relationship).
根据牛顿定律，若其中一个质量翻倍，引力翻倍；若两个质量都翻倍，引力变为四倍。但如果距离翻倍，引力减小到原来的四分之一（平方反比关系）。
These relationships explain why astronauts experience much weaker gravity on the Moon: the Moon’s mass is only about 1/81 of Earth’s, and its radius is about 1/4, which together make the surface gravity roughly 1/6 of Earth’s.
这些关系解释了为何宇航员在月球上感受到的引力弱得多：月球质量仅为地球的约 1/81，半径约为 1/4，叠加起来使月表重力约为地球的 1/6。
8. Orbit of Planets and Satellites | 行星与人造卫星的轨道
For a planet or satellite to stay in a circular orbit, gravity must provide the necessary centripetal force. The gravitational pull acts towards the centre of the orbit, continually changing the object’s direction without changing its speed in a uniform circular motion.
行星或卫星要维持圆周轨道，引力必须提供所需的向心力。引力指向轨道中心，不断改变物体的运动方向，而在匀速圆周运动中不改变其速率。
Satellites in lower orbits travel at higher speeds because the gravitational field strength is greater, requiring a larger centripetal force and thus higher orbital velocity. Geostationary satellites orbit at a specific altitude where their period matches Earth’s rotation.
低轨道卫星速度更快，因为那里引力场较强，需要更大的向心力，从而轨道速度更高。地球同步卫星在特定高度运行，其周期与地球自转一致。
9. Artificial Satellites and Gravity | 人造卫星与引力
Artificial satellites rely entirely on Earth’s gravity to stay in orbit. Their horizontal velocity is carefully chosen so that as they fall towards Earth, the curvature of the planet matches their curved trajectory, resulting in a continuous free-fall orbit.
人造卫星完全依靠地球引力维持轨道。精心设定的水平速度使得卫星在落向地球时，地面的弯曲程度恰好与其弯曲轨迹吻合，形成持续的自由落体轨道。
Applications include communication relays, GPS navigation, weather monitoring and scientific observation. In each case, engineers must calculate the precise altitude and speed using gravitational principles.
应用包括通信中继、GPS 导航、气象监测和科学观测。每种情形下工程师都必须利用引力原理精确计算高度和速度。
10. Gravity on Different Planets | 不同行星上的重力
The surface gravity of a planet depends on its mass and radius. Even if a planet has much more mass than Earth, its surface g could be lower if its radius is proportionally larger. For example, Jupiter’s mass is 318 times Earth’s, but its radius is about 11 times larger, giving a surface gravity of roughly 2.5g.
行星表面重力取决于其质量和半径。即使质量比地球大得多，如果半径比例更大，表面 g 也可能更小。例如木星质量是地球的 318 倍，但半径约为 11 倍，表面重力约为 2.5g。
An object’s mass stays the same throughout the universe, but its weight changes according to the local gravitational field strength. This is a common exam question requiring W = m × g calculations.
物体的质量在宇宙各处保持不变，但其重量随当地重力场强度改变。这是考试常见题，需要运用 W = m × g 计算。
11. Weightlessness and Free Fall | 失重与自由落体
Astronauts on the International Space Station appear weightless not because gravity is absent, but because they are in continuous free fall around the Earth. Gravity at the ISS altitude is still about 90% of its surface value.
国际空间站上的宇航员看似失重，并非因为引力消失，而是因为他们随空间站一起围绕地球持续自由落体。ISS 轨道高度处的引力仍约为地面值的 90%。
Both the astronaut and the spacecraft accelerate at the same rate, so there is no normal reaction force — the sensation we interpret as weight. This explains why objects float inside the cabin.
宇航员和航天器以相同的加速度运动，因此没有支持力——这就是我们感知的重量。这也解释了舱内物体漂浮的原因。
12. Solving Gravitation Problems | 解答万有引力问题
GCSE problems often require using W = m × g to find weight, mass or g. Always write down the equation, substitute the correct values with units, and check that your final answer is reasonable. Remember weight is in newtons, mass in kilograms.
GCSE 题目常要求使用 W = m × g 计算重量、质量或 g。务必写出公式，代入正确数值和单位，并检查答案是否合理。牢记重量单位是牛顿，质量是千克。
A typical extended question might describe a rover on Mars, giving its mass and Mars’ gravitational field strength. Calculate the rover’s weight on Mars and then compare it with its weight on Earth. Show every step and state the direction of the force.
典型大题可能描述火星上的火星车，给出质量和火星重力场强度。计算火星车在火星上的重量并与地球重量比较。展示每一步并说明力的方向。
For orbital topics, you may be asked to explain why a satellite stays in orbit or how a change in altitude affects speed. Use the idea that gravity provides the centripetal force and link to changes in field strength with distance.
对于轨道主题，可能会要求解释卫星为何维持在轨、高度变化如何影响速度。运用引力提供向心力的思想，并联系场强随距离变化。
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