IGCSE Physics: Gravitation Key Concepts | IGCSE 物理：万有引力考点精讲

📚 IGCSE Physics: Gravitation Key Concepts | IGCSE 物理：万有引力考点精讲

Gravitation is a fundamental force that shapes the universe – from an apple falling to the ground to the Moon orbiting Earth. In IGCSE Physics, you need to understand Newton’s law of universal gravitation, the relationship between mass and weight, free fall, and orbital motion. This guide breaks down every key concept, formula, and common exam question to help you build confidence and accuracy.

万有引力是塑造宇宙的基本力——从苹果落地到月球绕地球运行，都离不开它。在 IGCSE 物理中，你需要掌握牛顿万有引力定律、质量与重量的关系、自由落体以及轨道运动。本篇指南剖析每一个核心概念、公式和常见考题，帮助你建立信心并提高答题准确性。

1. What is Gravitation? | 什么是万有引力？

Gravitation, or gravity, is a force of attraction that acts between any two masses in the universe. It is always attractive and never repulsive. The force is extremely weak for small objects but becomes significant when at least one object has a large mass, such as a planet or a star.

万有引力是宇宙中任意两个物体之间的吸引力。它始终是吸引的，从未排斥。对于小物体，引力极弱，但当至少一个物体质量很大（如行星或恒星）时，引力就变得显著。

The concept of gravity was revolutionized by Isaac Newton in the 17th century. He proposed that the same force causing an apple to fall also keeps the Moon in orbit around the Earth. This idea unified celestial and terrestrial mechanics.

艾萨克·牛顿在17世纪革新了引力的概念。他提出，使苹果落地的力正是使月球绕地球运行的力。这一思想统一了天体和地面力学。

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

The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The formula is:

两个质点间的引力与质量的乘积成正比，与它们中心距离的平方成反比。公式为：

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 universal gravitational constant: 6.67 × 10⁻¹¹ N m² kg⁻².

其中 F 是引力（牛，N），m₁ 和 m₂ 是质量（千克，kg），r 是距离（米，m），G 是万有引力常量：6.67 × 10⁻¹¹ 牛·米²/千克²。

This law applies to all objects in the universe. For a person standing on Earth, m₁ is Earth’s mass and m₂ is the person’s mass. The distance r is approximately the radius of Earth. That gravitational pull is what we feel as weight.

该定律适用于宇宙中一切物体。站在地球上的人，m₁ 是地球质量，m₂ 是人的质量，距离 r 约等于地球半径。这个引力就是我们感受到的重量。

The force is always along the line joining the two centres.
引力方向总是沿着两物体中心的连线。
Doubling one mass doubles the force; doubling the distance reduces the force to one quarter.
一个质量加倍，力加倍；距离加倍，力减为原来的四分之一。

3. Gravitational Field and g | 引力场与重力加速度 g

A gravitational field is a region where a mass experiences a force. The strength of the field, g, is the gravitational force per unit mass. On Earth’s surface, g is approximately 9.8 N/kg or 9.8 m/s². This is often called the acceleration of free fall.

引力场是质量受到力的区域。场强 g 是单位质量所受的引力。在地球表面，g 约等于 9.8 牛/千克或 9.8 米/秒²，常被称为自由落体加速度。

The value of g can be derived from Newton’s law: g = G M / r², where M is the mass of the planet and r is its radius. This shows that g is independent of the mass of the object experiencing the field – a crucial concept in free fall.

g 的值可由牛顿定律推导：g = G M / r²，其中 M 是行星质量，r 是其半径。这表明 g 与受力物体的质量无关——这是自由落体的关键概念。

Because Earth is not a perfect sphere and rotates, g varies slightly: about 9.78 N/kg at the equator and 9.83 N/kg at the poles. In IGCSE problems, you can use 10 N/kg for simplicity unless told otherwise.

由于地球不是正球体且自转，g 略有变化：赤道约 9.78 牛/千克，两极约 9.83 牛/千克。IGCSE 题目中，若无特别说明可使用 10 牛/千克简化计算。

4. Mass vs Weight | 质量与重量的区别

A very common exam pitfall is confusing mass and weight. Mass is a measure of the amount of matter in an object; it is a scalar quantity and is measured in kilograms (kg). Mass does not change with location.

考试中常见的陷阱是混淆质量与重量。质量是物体所含物质的多少，是标量，单位为千克（kg）。质量不随位置变化。

Weight is the gravitational force acting on an object. It is a vector quantity and is measured in newtons (N). Weight depends on the local gravitational field strength: W = m × g. On the Moon, your mass remains the same, but your weight is only about one-sixth of that on Earth because g is smaller.

重量是作用于物体的引力，是矢量，单位为牛（N）。重量取决于当地的引力场强：W = m × g。在月球上，你质量不变，但重量仅为地球上的六分之一左右，因为 g 较小。

IGCSE questions often ask you to calculate weight on different planets or to explain why astronauts feel weightless in orbit (they are in free fall, not because there is no gravity).

IGCSE 题目常要求计算不同行星上的重量，或解释为什么宇航员在轨道中感觉失重（他们处于自由落体状态，并非因为没有引力）。

5. Free Fall | 自由落体

An object is in free fall when the only force acting on it is gravity. In the absence of air resistance, all objects near Earth’s surface fall with the same constant acceleration g, regardless of their mass.

当物体只受重力作用时，它处于自由落体状态。如果没有空气阻力，地表附近所有物体都以恒定加速度 g 下落，与其质量无关。

The classic demonstration of this is dropping a feather and a hammer in a vacuum; they hit the ground simultaneously. In the real world, air resistance opposes motion, causing lighter or larger surface area objects to fall more slowly.

经典演示是在真空中释放羽毛和锤子，它们同时落地。现实世界中，空气阻力阻碍运动，使轻或表面积大的物体下落较慢。

For vertical free fall, the equations of uniformly accelerated motion apply: v = u + a t, s = u t + ½ a t², v² = u² + 2 a s, with a = g. These equations are often used in paper calculations.

对于竖直自由落体，匀加速运动方程适用：v = u + a t，s = u t + ½ a t²，v² = u² + 2 a s，其中 a = g。这些方程常用于试卷计算。

6. Projectile Motion | 抛体运动

A projectile is any object thrown into the air and moving under gravity. IGCSE typically considers objects launched horizontally or at an angle, but analysis is usually limited to horizontal and vertical components separately, assuming no air resistance.

抛体是抛到空中并在重力作用下运动的物体。IGCSE 通常考察水平发射或以一定角度发射的物体，但分析通常限于分别考虑水平和竖直分量，并假设无空气阻力。

The horizontal component of velocity remains constant, while the vertical component accelerates downwards at g. The path is a parabola. Important quantities include time of flight, maximum height, and range.

速度的水平分量保持不变，而竖直分量以加速度 g 向下加速。路径为抛物线。重要的量包括飞行时间、最大高度和射程。

In many IGCSE syllabuses, you will be asked to sketch the trajectory or determine the vertical drop of a horizontally fired bullet over a distance, using the fact that vertical and horizontal motions are independent.

在许多 IGCSE 课程大纲中，你会被要求画出轨迹，或利用竖直和水平运动独立的事实，确定水平发射子弹在一段距离内的竖直下落。

7. Orbital Motion and Satellites | 轨道运动与卫星

Satellites, including the Moon and artificial ones, remain in orbit due to a balance between their velocity and the gravitational pull of the central body. The gravitational force provides the necessary centripetal force to keep them moving in a curved path.

包括月球和人造卫星在内的卫星之所以保持在轨道上，是因为它们的速度与中心天体的引力达成了平衡。引力提供了必要的向心力，使其沿曲线运动。

For a circular orbit, the speed is constant but the direction changes continuously. The closer a satellite is to Earth, the stronger the gravity and the faster it must move to stay in orbit. Geostationary satellites orbit at a specific height where their orbital period matches Earth’s rotation, making them appear fixed in the sky.

对于圆形轨道，速率不变但方向不断改变。卫星离地球越近，引力越强，它必须移动得越快才能留在轨道上。地球同步卫星在特定高度运行，轨道周期与地球自转周期一致，因此看起来高悬于天空的某一点。

The concept of apparent weightlessness in orbiting spacecraft is a classic topic: astronauts float not because gravity is zero, but because they are in continuous free fall towards Earth, falling at the same rate as their spacecraft.

轨道飞行器中的视重失重现象是一个经典话题：宇航员漂浮不是因为重力为零，而是因为他们与航天器一起，持续向地球自由落体。

8. Gravity on the Moon and Planets | 月球和行星上的重力

Different celestial bodies have different surface gravities depending on their mass and radius. Using g = G M / r², we can compare g values. For example, the Moon’s mass is about 0.0123 Earth masses and its radius is 0.273 Earth radii, giving g_moon ≈ 1.6 N/kg, about 1/6 of Earth’s.

不同天体的表面重力取决于其质量和半径。利用 g = G M / r² 可比较 g 值。例如，月球质量约为地球的 0.0123 倍，半径约为地球的 0.273 倍，得出 g_月 ≈ 1.6 牛/千克，约为地球的 1/6。

This lower gravity explains why astronauts can jump higher on the Moon and why objects fall more slowly. IGCSE questions might ask you to calculate weight on Mars (g ≈ 3.7 N/kg) or Jupiter (g ≈ 24.7 N/kg) given mass and radius data.

重力较小解释了为什么宇航员在月球上能跳得更高、物体下落更慢。IGCSE 题目可能要求你根据质量和半径数据计算在火星（g ≈ 3.7 牛/千克）或木星（g ≈ 24.7 牛/千克）上的重量。

9. Measuring g in the Laboratory | 实验室测量 g

A common practical investigation to determine g involves using a pendulum or a free-fall apparatus. For a simple pendulum, the period T is related to length L by T = 2π √(L/g). By measuring T for various L and plotting T² against L, the gradient is 4π²/g, from which g can be calculated.

测定 g 的常见实验包括使用单摆或自由落体装置。对于单摆，周期 T 与摆长 L 的关系为 T = 2π √(L/g)。通过测量不同 L 下的 T，绘制 T²-L 图，斜率为 4π²/g，由此可算出 g。

With a free-fall method, a small dense object is dropped from a known height, and the time of fall is measured electronically (e.g., using a trap door and timer). Then g = 2s / t². Repeat for different heights to improve accuracy.

使用自由落体法，从已知高度释放小密度物体，用电子方式测量下落时间（如用活板门和计时器）。则 g = 2s / t²。重复不同高度以提高准确性。

Sources of error include reaction time, air resistance, and parallax. IGCSE exam questions frequently assess understanding of these experiments and the interpretation of data.

误差来源包括反应时间、空气阻力和视差。IGCSE 考题常评估对这些实验的理解和数据分析。

10. Common Misconceptions and Pitfalls | 常见误区和陷阱

Misconception 1: Heavier objects fall faster. In the absence of air resistance, all objects fall with the same acceleration g. A brick and a penny dropped from a height will hit the ground together in a vacuum.

误区一：重物下落得更快。没有空气阻力时，所有物体以相同加速度 g 下落。真空中，一块砖和一枚硬币从同一高度释放会同时落地。

Misconception 2: There is no gravity in space. In orbit, gravity is still significant – it provides the centripetal force. The sensation of weightlessness arises from free fall, not from a lack of gravity.

误区二：太空中没有重力。在轨道上，引力仍然显著——它提供向心力。失重感源于自由落体，而非没有引力。

Misconception 3: Mass and weight are the same. Mass is measured in kg and is invariant; weight is a force in N and depends on g. Always use W = mg in calculations.

误区三：质量和重量是一回事。质量以 kg 为单位，恒定不变；重量是力，以 N 为单位，取决于 g。计算时务必使用 W = mg。

Misconception 4: Gravitational force is always strong. G is very small, so the force between everyday objects is negligible unless at least one mass is huge.

误区四：引力总是很强。G 极小，日常物体间的引力微乎其微，除非至少一个质量极大。

11. Exam Techniques and Key Tips | 考试技巧与要点

Always write the formula first: F = Gm₁m₂/r² or W = mg. Substitute values with units, and give your final answer with the correct unit (N for force, kg for mass). For g, use 10 N/kg if the question allows, or 9.8 N/kg for precision.

答题时先写公式：F = Gm₁m₂/r² 或 W = mg。代入数值带单位，最终答案给出正确单位（力用 N，质量用 kg）。如题目允许，g 取 10 牛/千克，或取 9.8 以求精确。

When explaining satellite motion, use the phrase ‘gravitational force provides the centripetal force’ to earn full marks. For free-fall problems, state that acceleration is constant and equals g. In graphing questions, pay attention to labelling axes and calculating slopes correctly.

解释卫星运动时，使用“引力提供向心力”这一表达以获得满分。对于自由落体问题，声明加速度恒定且等于 g。在图表题中，注意正确标注坐标轴和计算斜率。

Revision summary: know the difference between mass and weight; be able to calculate g on other planets; understand why astronauts float; and practise pendulum and free-fall data analysis. Gravitation topics interconnect with forces, energy, and motion – linking concepts will boost your overall physics score.

复习总结：分清质量与重量；能计算其他行星上的 g；理解宇航员为何漂浮；练习摆和自由落体数据分析。引力主题与力、能量、运动相互联系——将概念联系起来会提升你的整体物理成绩。

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IGCSE Physics: Gravitation Key Concepts | IGCSE 物理：万有引力 考点精讲