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

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

Gravitation is one of the fundamental forces in physics, and in the IGCSE CIE Physics syllabus, it links concepts of mass, weight, free fall, orbital motion, and the structure of the Universe. Understanding gravitation not only helps you solve calculation problems involving weight and acceleration but also explains why planets stay in orbit, why comets speed up near the Sun, and how satellites are placed to stay above a fixed point on Earth. This article breaks down every key point you need to master for the exam, with paired English–Chinese explanations and essential formulas in clear Unicode notation.

万有引力是 IGCSE CIE 物理中的基本力之一，它把质量、重量、自由落体、轨道运动和宇宙结构等概念联系在一起。理解万有引力不仅能帮助你解决有关重量和加速度的计算题，还能解释行星为何沿轨道运行、彗星靠近太阳时为何加速，以及如何让卫星固定在地球某点上方。本文以中英对照的方式梳理考试中必须掌握的每一个要点，并使用清晰的 Unicode 公式符号。

1. What is Gravitational Force? | 什么是万有引力？

Gravitational force is a force of attraction that acts between any two objects with mass. The larger the masses, the greater the gravitational pull between them. The force also depends on the distance between the centres of the two masses – as distance increases, the force decreases rapidly (inverse-square law). On the scale of everyday objects, this force is extremely small and can be ignored, but when one of the objects is a planet or a star, the force becomes significant.

万有引力是存在于任何两个有质量物体之间的吸引力。质量越大，引力越强。引力还与两个物体中心之间的距离有关——距离增大，引力迅速减小（平方反比定律）。在日常物体的尺度下，这个力极小，可以忽略不计；但当其中一个物体是行星或恒星时，引力就变得非常显著。

The force that holds us to the Earth is gravity. The Earth’s gravitational pull acts towards the centre of the Earth and gives objects weight. In the IGCSE course, we often treat the gravitational field near the Earth’s surface as uniform, meaning g is constant.

把我们束缚在地球上的力就是重力。地球的引力指向地心，并赋予物体重量。在 IGCSE 课程中，我们常把地球表面附近的引力场视为均匀场，即 g 为定值。

2. Mass vs Weight | 质量与重量的区别

Mass is the amount of matter in an object. It is a scalar quantity, measured in kilograms (kg), and does not change with location. Weight, on the other hand, is the gravitational force acting on an object’s mass. Weight is a vector quantity, measured in newtons (N), and depends on the gravitational field strength at the object’s location.

质量是物体所含物质的多少，是一个标量，单位是千克 (kg)，不随位置改变。重量则是作用在物体质量上的引力，是一个矢量，单位是牛顿 (N)，取决于物体所在位置的引力场强度。

A common exam pitfall is confusing mass and weight. For example, an astronaut in space is often said to be ‘weightless’, but their mass is still the same as on Earth. In orbit, they are actually in free fall, which creates the sensation of weightlessness while mass remains unchanged.

考试中常见的错误是混淆质量与重量。例如，常有人说宇航员在太空中“失重”，但他们的质量与在地球上相同。在轨道上，宇航员实际上处于自由落体状态，产生了“失重”的感觉，质量却未改变。

3. Gravitational Field Strength g | 引力场强度 g

Gravitational field strength (g) is defined as the gravitational force per unit mass. On the Earth’s surface, g ≈ 9.8 N/kg, but for most IGCSE calculations, we use 10 N/kg. The value of g decreases with altitude and is weaker on the Moon (about 1.6 N/kg) because the Moon has a smaller mass and radius.

引力场强度 (g) 定义为单位质量所受的引力。在地球表面，g ≈ 9.8 N/kg，但在 IGCSE 的大部分计算中我们使用 10 N/kg。g 的值随高度增加而减小；月球表面的 g 更小（约 1.6 N/kg），因为月球的质量和半径都较小。

The relationship between weight, mass and g is given by:

重量、质量和 g 的关系式为：

W = m × g

Where W is weight in newtons (N), m is mass in kg, and g is gravitational field strength in N/kg. Notice that g is numerically equal to the acceleration due to gravity, so the same symbol g is used in free‑fall calculations.

其中 W 是重量（牛顿），m 是质量（千克），g 是引力场强度（牛/千克）。注意 g 在数值上等于重力加速度，因此自由落体计算中也使用同一个符号 g。

4. Free Fall and Air Resistance | 自由落体与空气阻力

An object is in free fall when the only force acting on it is gravity. In a vacuum, all objects fall with the same acceleration g, regardless of their mass. This was famously demonstrated on the Moon where a hammer and a feather dropped together hit the surface at the same time.

当物体只受重力作用时，便处于自由落体状态。在真空中，所有物体无论质量大小，均以相同的加速度 g 下落。这一点曾在月球上得到经典验证：一把锤子和一片羽毛同时落地。

In the Earth’s atmosphere, air resistance opposes the motion. As an object falls, its speed increases until the upward air resistance equals the downward weight. At this point, the net force is zero, and the object falls at a constant terminal velocity. A skydiver, for example, reaches a terminal velocity of about 50–60 m/s before opening the parachute.

在地球大气中，空气阻力会阻碍运动。物体下落时速度不断增加，直到向上的空气阻力等于向下的重力。此时合力为零，物体以恒定的终极速度下落。比如跳伞者在开伞前的终极速度约为 50–60 m/s。

In the IGCSE exam, you may be asked to describe how terminal velocity is reached or to interpret a velocity–time graph showing acceleration decreasing to zero.

在 IGCSE 考试中，可能会要求描述终极速度的形成过程，或解读速度-时间图中加速度减小至零的情形。

5. Projectile Motion | 抛体运动

A projectile is any object that is launched into the air and then moves under the force of gravity alone (ignoring air resistance). The motion can be analysed as two independent components: horizontal motion at constant velocity, and vertical motion with constant acceleration g downwards. The path is a parabola.

抛体是指被发射到空中后只在重力作用下运动的物体（忽略空气阻力）。其运动可以分解为两个独立分量：水平方向以恒定速度运动，竖直方向以恒定加速度 g 向下加速。轨迹为抛物线。

For exam purposes, you need to understand that the horizontal velocity stays constant because there is no horizontal force, while the vertical velocity changes by 10 m/s every second. The time of flight depends only on the vertical motion. At the highest point, vertical velocity is zero, but horizontal velocity is unchanged.

考试中需要理解：水平速度保持不变，因为没有水平力；而竖直速度每秒变化约 10 m/s。飞行时间仅取决于竖直运动。在最高点，竖直速度为零，但水平速度不变。

6. Orbital Motion: Planets and Satellites | 轨道运动：行星与人造卫星

Planets orbit the Sun, and satellites orbit planets, due to the gravitational force. For a satellite in a circular orbit, the gravitational force provides the necessary centripetal force to keep it moving in a circle. The direction of the velocity is constantly changing, so the satellite is accelerating even if its speed is constant.

行星绕太阳运行，卫星绕行星运行，都源于万有引力。对于处在圆轨道上的卫星，引力提供了保持其圆周运动所需的向心力。速度的方向不断改变，因此即使速率不变卫星也在加速。

Key points to remember:

The force of gravity always points towards the centre of the Earth (or the planet).
The orbital speed is higher for satellites closer to the Earth.
Geostationary satellites have an orbital period of 24 hours.

需要记住的要点：

引力始终指向地球（或行星）的中心。
轨道越靠近地球，卫星的轨道速度越大。
地球同步卫星的轨道周期为 24 小时。

7. Geostationary Satellites | 地球同步卫星

A geostationary satellite orbits the Earth directly above the equator with a period of exactly 24 hours, matching the Earth’s rotation. From the ground, it appears to stay at the same point in the sky. This makes geostationary satellites ideal for telecommunications and weather monitoring, because ground receivers can point at a fixed position.

地球同步卫星在赤道正上方的轨道上运行，周期恰好为 24 小时，与地球自转同步。从地面看，它仿佛静止在天空中的同一点。这使得地球同步卫星非常适合通信和气象监测，因为地面接收器可以固定指向某一位置。

Conditions for a geostationary orbit:

Orbit must be equatorial (above the equator).
Period must be 24 hours.
The satellite must travel from west to east (same direction as Earth’s rotation).
Altitude is about 36 000 km above the Earth’s surface.

地球同步轨道的条件：

轨道必须在赤道所在的平面内。
周期必须为 24 小时。
卫星必须由西向东运行（与地球自转方向相同）。
高度约为地表上方 36 000 公里。

8. Comets and Elliptical Orbits | 彗星与椭圆轨道

Comets are small Solar System bodies that travel in highly elliptical orbits around the Sun. Unlike planets, whose orbits are nearly circular, comets spend most of their time far from the Sun and move very slowly. As a comet approaches the Sun, the gravitational force does work on it, causing its speed to increase dramatically near perihelion (closest approach). After rounding the Sun, the comet slows down again as it travels back to the outer Solar System.

彗星是太阳系中以高度扁长的椭圆轨道绕太阳运行的小天体。与轨道接近圆形的行星不同，彗星大部分时间在远离太阳的地方缓慢移动。当彗星接近太阳时，引力对其做功，使其在近日点附近速度急剧增加。绕过太阳后，彗星在返回太阳系外围的过程中再次减速。

The changing speed of a comet illustrates the conservation of energy – gravitational potential energy is converted into kinetic energy and vice versa. This is a favourite IGCSE exam topic, often linked to questions about why the comet’s tail points away from the Sun due to solar wind, though the tail is not a gravitational effect.

彗星变速的过程体现了能量守恒——引力势能转化为动能，反之亦然。这是 IGCSE 考试中常见的考点，常与“为何彗尾因太阳风而背离太阳”的问题联系，不过彗尾并非引力效应。

9. The Solar System and Galaxies | 太阳系与星系

The Solar System consists of one star (the Sun), eight planets, their moons, dwarf planets, asteroids, and comets. All planets orbit the Sun in elliptical paths that are nearly circular. The order of the planets from the Sun outwards is: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

太阳系由一颗恒星（太阳）、八大行星、它们的卫星、矮行星、小行星和彗星组成。所有行星以接近圆形的椭圆轨道绕太阳运行。从太阳向外行星的顺序是：水星、金星、地球、火星、木星、土星、天王星、海王星。

On a larger scale, the Sun is one of billions of stars in the Milky Way galaxy, which is a spiral galaxy. The Universe contains countless galaxies. The gravitational force holds stars together in galaxies and holds galaxies in clusters. Understanding this hierarchical structure is part of the IGCSE syllabus and is often assessed through multiple‑choice or short‑answer questions.

在更大尺度上，太阳是银河系数十亿颗恒星中的一颗，银河系是一个旋涡星系。宇宙包含无数星系。引力将恒星聚集在星系内，也将星系聚集为星系团。理解这种层级结构是 IGCSE 大纲的一部分，常以选择题或简答题形式考查。

10. Key Formulas and Calculations | 核心公式与计算

Below is a summary of the most important quantitative relationships involving gravitation in the IGCSE course:

以下是 IGCSE 课程中涉及万有引力的最重要定量关系总结：

Relationship	Equation
Weight, mass and g	W = m × g
Acceleration due to gravity	g = 10 m/s² (near Earth)
Centripetal force (qualitative)	Provided by gravity: F_gravity = F_centripetal

Always remember to use consistent units: mass in kg, weight in N, g in N/kg (or m/s²). When calculating weight on the Moon, use g = 1.6 N/kg. In free‑fall calculations, you can apply SUVAT equations with a = g, taking the downward direction as positive or negative depending on your sign convention.

始终注意统一单位：质量用 kg，重量用 N，g 用 N/kg（或 m/s²）。计算月球上的重量时，使用 g = 1.6 N/kg。在自由落体计算中，可以使用匀加速运动公式 (SUVAT)，令 a = g，根据你所选的正方向规定向下为正或负。

11. Exam Tips and Common Misconceptions | 备考技巧与常见误区

1. Mass is not weight. Never say ‘a mass of 100 N’ – mass is measured in kg, weight in N.

1. 质量非重量。绝不要说“质量为 100 N”——质量的单位是 kg，重量的单位是 N。

2. On the Moon, your weight changes but your mass stays the same. g is smaller because the Moon is smaller, not because there is ‘no gravity’ in space.

2. 在月球上，你的重量会变但质量不变。g 较小是因为月球本身较小，而不是因为太空中“没有重力”。

3. In orbit, astronauts appear weightless because they are in continuous free fall towards the Earth, but gravity is still acting on them. If there were no gravity, they would fly off in a straight line.

3. 在轨道上，宇航员看似失重是因为他们持续向地球自由落体，但重力仍然作用在他们身上。如果没有重力，它们会沿直线飞离。

4. Air resistance always opposes motion. Terminal velocity is reached when air resistance equals weight, not when the object stops accelerating – it keeps falling at constant speed.

4. 空气阻力始终阻碍运动。终极速度在空气阻力等于重量时达到，并非物体停止加速之时——此后物体以恒定速度继续下落。

5. For orbits, remember that gravitational force provides the centripetal force. An object moving in a circle at constant speed is still accelerating because its direction changes.

5. 涉及轨道时，记住引力充当向心力。速率不变的圆周运动仍在加速，因为方向在变化。

6. Practice drawing and interpreting velocity–time graphs for falling objects, distinguishing between free fall (no air resistance) and fall with air resistance. Learn to identify the constant acceleration stage and the terminal velocity stage.

6. 练习绘制和解读下落物体的速度-时间图，区分自由落体（无空气阻力）和有空气阻力的下落。学会识别匀加速阶段和终极速度阶段。

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