📚 GCSE CCEA Physics: Gravitation | GCSE CCEA 物理：万有引力
In GCSE CCEA Physics, gravitation is a fundamental topic that explains how objects with mass attract each other. Understanding gravitational force is crucial for distinguishing between mass and weight, analyzing free-fall motion, and explaining the motion of planets, moons, and artificial satellites. This revision guide summarises all key points needed for your exam.
在GCSE CCEA物理课程中，万有引力是一个基本主题，解释有质量的物体如何相互吸引。理解引力对于区分质量与重量、分析自由落体运动以及解释行星、卫星和人造卫星的运动至关重要。这篇复习指南总结了考试所需的所有关键点。
1. What is Gravitational Force? | 什么是万有引力？
Gravitational force is a non-contact force of attraction that exists between any two objects that have mass. The larger the masses involved, the stronger the gravitational pull between them. This force acts over enormous distances, holding planets in orbit around the Sun and moons around planets.
万有引力是一种非接触吸引力，存在于任何两个有质量的物体之间。质量越大，它们之间的引力就越强。这种力的作用范围极大，将行星保持在绕太阳运行的轨道上，并将卫星保持在绕行星运行的轨道上。
On Earth, the gravitational attraction of the planet pulls objects towards its centre. This pull gives objects weight and causes them to accelerate downwards when dropped.
在地球上，行星的引力将物体拉向地心。这种拉力使物体具有重量，并导致它们在落下时向下加速。
2. Mass versus Weight | 质量与重量
One of the most common exam questions is to compare mass and weight. Mass is a measure of the amount of matter in an object and is a scalar quantity. It is measured in kilograms (kg) and does not change regardless of location. Weight, on the other hand, is the gravitational force acting on an object's mass. It is a vector quantity and is measured in newtons (N).
最常见的考题之一是比较质量和重量。质量是物体所含物质的量度，是一个标量。它的单位是千克（kg），无论位置如何都不变。而重量是作用在物体质量上的引力，是一个矢量，单位是牛顿（N）。
The weight of an object can change if it is taken to a different planet or to a high altitude where the gravitational field strength is different.
如果一个物体被带到不同的行星或高海拔地区，在那里重力场强度不同，其重量会改变。
A quick comparison:
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Gravitational force on mass |
| SI Unit | kilogram (kg) | newton (N) |
| Scalar or Vector | Scalar | Vector (acts downwards) |
| Does it vary with location? | No | Yes |
| Instrument | Top-pan balance | Spring balance / newton meter |
中文对照：定义—物质的量 vs 引力；单位—千克 vs 牛顿；标量与矢量—标量 vs 矢量（向下）；是否随地点变化—否 vs 是；测量工具—托盘天平 vs 弹簧秤/牛顿计。
3. The Weight Equation: W = mg | 重量公式：W = mg
Weight, gravitational field strength and mass are linked by the equation:
W = m × g
where W is weight in newtons (N), m is mass in kilograms (kg), and g is the gravitational field strength in newtons per kilogram (N/kg). On the surface of the Earth, g is approximately 9.8 N/kg, but for GCSE CCEA calculations it is often taken as 10 N/kg.
重量、重力场强度和质量之间的关系由公式表示：W = m × g。其中W是重量（牛顿，N），m是质量（千克，kg），g是重力场强度（牛每千克，N/kg）。在地球表面，g约为9.8 N/kg，但在GCSE CCEA的计算中常取10 N/kg。
a key skill: calculating g from a weight measurement, or finding weight given mass and g.
变换公式，重力场强度可通过 g = W / m 求得。这是一项关键技能：通过重量测量计算g，或根据质量和g求重量。
4. Gravitational Field Strength (g) | 重力场强度 (g)
Gravitational field strength is defined as the gravitational force per unit mass experienced by a small object placed at that point. It is a vector quantity directed towards the centre of the planet. The field lines point radially inwards towards the centre of mass.
重力场强度定义为放置在该点的小物体所受的单位质量引力。它是一个矢量，方向指向行星中心。场线沿径向指向质心。
This value decreases slightly with altitude and varies slightly with latitude, but for GCSE purposes we treat it as constant near the Earth's surface.
在地球表面附近，g约为10 N/kg。这个值随海拔略减小，随纬度略有变化，但在GCSE考试中，我们将其视为在地表附近恒定的值。
The same gravitational field strength is numerically equal to the acceleration of free fall, 10 m/s². This is because a mass of 1 kg weighing 10 N will accelerate at 10 m/s² under this net force (ignoring air resistance).
同一重力场强度在数值上等于自由落体加速度 10 m/s²。这是因为质量为 1 kg、重量为 10 N 的物体在该净力作用下（忽略空气阻力）将获得 10 m/s² 的加速度。
5. Measuring Weight and g | 测量重量与重力场强度
In the lab, weight is measured using a newton meter or calibrated spring balance. Mass is measured using a top-pan balance or beam balance; these devices compare the gravitational force on a known mass, but they are calibrated to read mass in kg and are independent of g.
在实验室中，重量用牛顿计或校准的弹簧秤测量。质量用托盘天平或杠杆天平测量；这些设备比较已知质量所受的重力，但它们被校准为以千克为单位读取质量，并且与g无关。
/m. Alternatively, measure the acceleration of free fall using a light gate and a falling object.
要在实验中确定重力场强度，你可以在牛顿计上悬挂已知质量，记录重量，然后计算 g = W/m。或者，利用光门和落体测量自由落体加速度。
6. Free Fall and the Acceleration due to Gravity | 自由落体与重力加速度
In the absence of air resistance, all objects falling near the Earth' rate: the acceleration due to gravity, g = 10 m/s². This is true regardless of the object's mass. A heavy stone and a light feather would hit the ground simultaneously in a vacuum.
在没有空气阻力的情况下，所有靠近地球表面下落的物体都以相同的速率向下加速：重力加速度 g = 10 m/s²。这与物体的质量无关。在真空中，一块重石头和一片轻羽毛会同时落地。
When air resistance is present, it opposes the motion. As a falling object speeds up, air resistance increases until it balances the weight. At this point, the resultant force is zero and the object falls at a constant speed called terminal velocity.
当存在空气阻力时，它会阻碍运动。随着落体加速，空气阻力增大，直到与重量平衡。此时合力为零，物体以恒定速度下落，即终端速度。
Vectors are important here: weight acts downwards; air resistance acts upwards. The net force determines acceleration.
这里的矢量很重要：重量向下作用；空气阻力向上作用。净力决定加速度。
7. Gravity on the Moon and Other Planets | 月球及其他行星上的重力
The gravitational field strength on the Moon is about 1.6 N/kg, much smaller than Earth's. Therefore, an astronaut's weight on the Moon is only about 1/6 of their weight on Earth, even though their mass remains the same.
月球上的重力场强度约为 1.6 N/kg，远小于地球。因此，宇航员在月球上的重量只有其在地球上重量的约六分之一，尽管他们的质量不变。
On Jupiter, g is approximately 25 N/kg, so a person would feel much heavier. The table below compares g on different bodies:
| Celestial Body | Approx. g (N/kg) |
|---|---|
| Earth | 10 |
| Moon | 1.6 |
| Mars | 3.7 |
| Jupiter | 25 |
中文对照：天体—地球（约10 N/kg），月球（约1.6 N/kg），火星（约3.7 N/kg），木星（约25 N/kg）。
8. Universal Gravitation: Attraction Between Any Two Masses | 万有引力：任意两质量间的吸引
Newton's law of universal gravitation 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. In GCSE, you do not need to use the full equation, but you must understand that:
牛顿万有引力定律指出，每个粒子都吸引其他粒子，力的大小与两者质量的乘积成正比，与它们中心之间距离的平方成反比。在GCSE中，不需要使用完整
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