📚 Universal Gravitation | 万有引力 考点精讲
Gravity is the fundamental force of attraction that exists between all objects with mass in the universe. Understanding it is essential for explaining everything from falling apples to the orbits of planets. In WJEC GCSE Physics, you are expected to distinguish between mass and weight, calculate gravitational forces, and link gravity to circular motion and free fall. This revision guide covers all key concepts, equations, and exam tips to boost your confidence.
引力是宇宙中所有具有质量的物体之间存在的普遍吸引力。理解它对于解释从下落的苹果到行星轨道的一切现象至关重要。在 WJEC GCSE 物理中，你需要能够区分质量与重量，计算引力，并将引力与圆周运动及自由落体联系起来。这篇复习指南涵盖了所有关键概念、方程和考试技巧，助你提升自信。
1. What is Gravity? | 什么是万有引力？
Gravity is a non-contact force that pulls any two objects with mass toward each other. The strength of this force depends on the masses involved and the distance between their centres.
引力是一种非接触力，它将任何两个具有质量的物体拉向彼此。这种力的大小取决于物体的质量以及它们中心之间的距离。
Unlike contact forces such as friction, gravity acts across empty space. This means the Sun exerts a gravitational pull on Earth even though they are separated by about 150 million kilometres of vacuum.
与摩擦力等接触力不同，引力可以跨越虚空作用。这意味着太阳对地球施加引力，尽管它们之间相距约1.5亿公里的真空。
Gravity is always attractive – it never pushes objects apart. On a cosmic scale, it is the force that governs the motion of moons, planets, stars, and galaxies.
引力总是吸引力——它从来不会将物体推开。在宇宙尺度上，它是支配卫星、行星、恒星和星系运动的力。
2. Weight vs Mass | 重量与质量的区别
Mass is the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity and does not change regardless of location.
质量是物体所含物质的多少，单位是千克（kg）。它是标量，无论位置如何都不发生变化。
Weight is the force due to gravity acting on an object's mass. It is measured in newtons (N) and is a vector quantity that always points toward the centre of the planet or moon.
重量是由于重力作用在物体质量上的力，单位是牛顿（N）。它是矢量，总是指向行星或月球中心。
Here is a helpful comparison table:
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Gravitational force on a mass |
| Unit | kilogram (kg) | newton (N) |
| Measured with | Balances | Newton meters or spring scales |
| Depends on location? | No | Yes (varies with gravitational field strength) |
| Type | Scalar | Vector |
Remember: an astronaut's mass stays the same on the Moon, but their weight becomes only about one-sixth of its Earth value because the Moon's gravity is weaker.
记住：宇航员在月球上的质量保持不变，但其重量变为地球上的约六分之一，因为月球的引力较弱。
3. Gravitational Field Strength (g) | 引力场强度
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 N/kg.
引力场强度（g）定义为放在引力场中的小测试质量所受到的每单位质量的力，单位是 N/kg。
Near Earth's surface, g is approximately 10 N/kg (more precisely 9.8 N/kg). This means every 1 kg of mass experiences a downward force of 10 N.
在地球表面附近，g 约为 10 N/kg（更精确为 9.8 N/kg）。这意味着每1千克质量受到10牛顿向下的力。
The direction of the gravitational field is always toward the centre of the Earth. Field lines are drawn pointing radially inward, showing the direction of force on a mass.
引力场的方向始终指向地心。场线被画成径向向内，表示作用于质量上的力的方向。
If you lift an object to a high altitude, g decreases slightly because you are farther from Earth's centre, but for most GCSE calculations we treat g as constant near the surface.
如果将物体提升到高海拔，g 会略微减小，因为你离地心更远，但在大多数 GCSE 计算中，我们将地表附近的 g 视为常数。
4. Newton's Law of Universal Gravitation | 牛顿万有引力定律
Sir Isaac Newton proposed that every particle in the universe 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.
艾萨克·牛顿爵士提出，宇宙中每个粒子都吸引其他每个粒子，吸引力的大小与它们的质量乘积成正比，与它们中心之间距离的平方成反比。
This relationship can be written as:
F = G m₁ m₂ / r²
This relationship can be written as:
F = G m₁ m₂ / r²
entres in metres, and G is the universal gravitational constant (6.674 × 10⁻¹¹ N m² kg⁻²).
其中 F 是引力，单位为牛顿；m₁ 和 m₂ 是两个物体的质量，单位为千克；r 是它们中心之间的距离，单位为米；G 是万有引力常数（6.674 × 10⁻¹¹ N m² kg⁻²）。
Although you do not need to perform calculations with G at GCSE WJEC, understanding the proportionality helps you explain how changing mass or distance affects the force. Double one mass, force doubles. Double the distance, force becomes one quarter.
虽然在 GCSE WJEC 中不需要用 G 进行计算，但理解比例关系有助于解释改变质量或距离如何影响力。将一个质量加倍，力加倍；将距离加倍，力变为四分之一。
5. The Inverse Square Law | 距离平方反比定律
The fact that gravitational force follows an inverse square law means that if the distance between two objects is multiplied by a factor, the force is divided by the square of that factor. Mathematically:
引力遵循平方反比定律，这意味着如果两个物体之间的距离乘以一个因子，则力要除以该因子的平方。数学上表示为：
F ∝ 1 / d²
For example, if the distance is tripled (d becomes 3d), the force becomes 1/9 of its original value. This rapid drop-off explains why astronauts in the International Space Station experience microgravity – they are still under Earth's gravity, but the force is slightly weaker 400 km above the surface, though the main reason for apparent weightlessness is free fall around the Earth.
例如，如果距离变为原来的三倍，力就变为原来的 1/9。这种快速衰减解释了为什么国际空间站中的宇航员会体验微重力——他们仍然受地球引力作用，但在400公里高处力略微减弱，不过表观失重的主要原因是绕地球自由落体。
In WJEC exams, you may be asked to use this idea to predict how the weight of an object would change if it were moved to a different altitude, or to compare forces between two planets.
在 WJEC 考试中，可能会要求你利用这一概念预测物体移动到不同高度时重量如何变化，或者比较两个行星之间的引力。
6. Gravity on Earth and Other Planets | 地球与其他行星上的重力
Different planets have different gravitational field strengths (g) because they have different masses and radii. For instance, g on the Moon is about 1.6 N/kg, on Mars about 3.7 N/kg, and on Jupiter about 25 N/kg. This means you would weigh more on Jupiter and less on the Moon.
不同行星具有不同的引力场强度（g），因为它们的质量和半径不同。例如，月球上的 g 约为 1.6 N/kg，火星上约为 3.7 N/kg，木星上约为 25 N/kg。这意味着你在木星上会更重，在月球上会更轻。
The gravitational field strength at the surface of a planet is determined by the planet's mass and radius. A planet with a larger mass or smaller radius will have a higher surface g.
行星表面的引力场强度由行星的质量和半径决定。质量更大或半径更小的行星，其表面 g 值会更高。
ut with a different g. Always ensure you use the correct value of g given in the question.
WJEC 试题经常要求你使用同样的 W = mg 方程，但用不同的 g 值计算在其他行星上的重量。务必确保使用题目给出的正确 g 值。
7. Orbits: How Gravity Provides Centripetal Force | 轨道：引力如何提供向心力
For a planet orbiting the Sun, or a satellite orbiting Earth, gravity is the centripetal force that keeps the object moving in a curved path. Without gravity, the object would move off in a straight line at a tangent.
对于绕太阳运行的行星或绕地球运行的卫星，引力是使物体沿曲线路径运动的向心力。如果没有引力，物体将沿切线方向做直线运动远离。
The gravitational pull is always directed toward the centre of the more massive body. It constantly changes the direction of the orbiting object's velocity without necessarily changing its speed, resulting in circular (or elliptical) motion.
引力始终指向较大质量天体的中心。它不断改变轨道物体速度的方向，而不一定改变速率，从而产生圆周（或椭圆）运动。
In WJEC physics, you are not required to calculate centripetal force numerically, but you must be able to explain that gravity is the force responsible for the curved orbit. A smaller orbital radius generally means a stronger gravitational force and a higher orbital speed for stable orbit.
在 WJEC 物理中，你不需要定量计算向心力，但必须能够解释引力是负责曲线轨道运动的力。较小的轨道半径通常意味着更强的引力和更高的轨道速度以维持稳定轨道。
8. Satellites: Natural and Artificial | 卫星：天然与人造
A satellite is any object that orbits a planet. The Moon is Earth's only natural satellite. Artificial satellites are human-made objects launched into orbit for communication, weather monitoring, GPS, and scientific research.
卫星是任何围绕行星运行的天体。月球是地球唯一的天然卫星。人造卫星是为通信、气象监测、全球定位和科学研究等目的而发射到轨道上的人造物体。
Geostationary satellites orbit Earth at a special altitude (about 36,000 km) where their orbital period equals Earth's rotation period (24 hours). They appear stationary in the sky, which is useful for TV broadcasting.
地球静止轨道卫星运行在特定高度（约36,000公里），其轨道周期等于地球自转周期（24小时）。它们看起来在天空中静止，这对电视广播很有用。
Low Earth orbit (LEO) satellites circle at altitudes of a few hundred kilometres and have much shorter orbital periods, about 90 minutes. They are used for imaging and the International Space Station.
近地轨道（LEO）卫星在几百公里高度飞行，轨道周期短得多，大约90分钟。它们用于成像和国际空间站。
In all these cases, gravity provides the necessary centripetal force. The higher the satellite, the weaker the gravitational pull and the slower its orbital velocity to stay in orbit.
在所有这些情况下，引力提供必要的向心力。卫星越高，引力越小，其保持轨道所需的轨道速度越慢。
9. Free Fall and Terminal Velocity | 自由落体与终端速度
An object is in free fall when gravity is the only force acting on it. In a vacuum, all objects free fall with the same acceleration g, regardless of their mass. This was famously demonstrated by Galileo's thought experiment and by the hammer-feather drop on the Moon.
当只有重力作用在物体上时，物体处于自由落体状态。在真空中，所有物体无论质量大小，都以相同的加速度 g 自由下落。伽利略的思想实验以及月球上锤子和羽毛同时下落的实验都著名地证明了这一点。
On Earth, air resistance opposes the motion of falling objects. This upward force increases with speed. Eventually, the resultant force becomes zero when air resistance equals weight, and the object falls at a constant maximum speed called terminal velocity.
在地球上，空气阻力会阻碍下落物体的运动。这个向上的力随速度增加而增大。最终，当空气阻力等于重量时，合力为零，物体将以恒定的最大速度下落，这个速度称为终端速度。
A skydiver experiences terminal velocity twice: first in a spread-eagle position (around 55 m/s) and then again at a higher speed after closing the parachute, when the increased air resistance balances weight at a much lower terminal velocity (roughly 5 m/s).
跳伞者会经历两次终端速度：首先在四肢展开姿势下（约55米/秒），然后在打开降落伞后再次达到终端速度，此时增大的空气阻力与重量在低得多的终端速度（约5米/秒）下平衡。
WJEC questions may ask you to interpret velocity-time graphs for a falling object, showing acceleration reducing until the graph levels off at terminal velocity.
WJEC 试题可能会要求你解读下落物体的速度-时间图像，显示加速度逐渐减小，直到图像在终端速度处持平。
10. WJEC Exam Tips and Calculations | WJEC 考试技巧与计算
The most important equation in this topic is W = m g mass and gravitational field strength, and also to rearrange it to find mass (m = W / g).
本主题最重要的方程是 W = m × g。你必须能够用它根据给定的质量和引力场强度计算重量，也能够将其变形以求出质量（m = W / g）。
Example calculation: An astronaut' ht becomes 120 × 1.6 = 192 N. This shows how weight changes even though mass is unchanged.
计算示例：一名宇航员的航天服和背包总质量为 120 kg。在地球上（g = 10 N/kg），其重量为 W = 120 × 10 = 1200 N。在月球上（g = 1.6 N/kg），重量变为 120 × 1.6 = 192 N。这表明尽管质量不变，重量却发生了变化。
Common pitfalls:
Confusing mass and weight – always check units; weight in newtons, mass in kilograms.
混淆质量和重量——务必检查单位；重量用牛顿，质量用千克。
Forgetting that g on Earth is approximately 10 N/kg, not 9.8 unless specified.
忘记地球上的 g 大约为 10 N/kg，除非题目特别说明，不要使用 9.8。
Using incorrect distance when discussing inverse square law – use centre-to-centre distance, not surface gap.
讨论平方反比定律时使用了错误的距离——应使用中心间距离，而非表面间隙。
When explaining orbits, always state that gravity provides the centripetal force. Use keywords like 'centre-seeking force' and 'constant change of direction' to secure full marks.
在解释轨道运动时，始终指出引力提供向心力。使用诸如“指向中心的力”和“方向不断改变”等关键词以获得满分。
Published by TutorHao | Physics Revision Series | aleveler.com
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