Gravitational Force | 万有引力考点精讲

📚 Gravitational Force | 万有引力考点精讲

Gravitational force is one of the fundamental interactions in the universe, governing the motion of planets, the falling of an apple, and the weight you feel on Earth. In IGCSE Edexcel Physics, mastering gravity involves understanding Newton’s law, calculating weight, distinguishing mass from weight, and applying the concept of gravitational field strength. This article breaks down every key point you need, with paired English and Chinese explanations to build rock-solid understanding.

万有引力是宇宙中的基本相互作用之一，支配着行星的运动、苹果的下落以及你在地球上感受到的重力。在IGCSE Edexcel物理中，掌握万有引力包括理解牛顿定律、计算重力、区分质量与重量，以及应用引力场强度概念。本文分解每个关键考点，配以中英双语讲解，帮助你建立扎实的理解。

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

Gravitational force is an attractive force that acts between any two objects with mass. The greater the masses and the closer they are, the stronger the force. It is always attractive, never repulsive, and it extends infinitely across the universe.

万有引力是任意两个具有质量的物体之间的吸引力。质量越大、距离越近，引力越强。它始终是吸引力，从不排斥，并且在宇宙中无限延伸。

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

Newton’s law states: 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：每个粒子都吸引其他每个粒子，引力的大小与它们质量的乘积成正比，与它们中心之间距离的平方成反比。

F = G m₁ m₂ / r²

where F is the gravitational force (N), m₁ and m₂ are the masses (kg), r is the distance between centres (m), and G is the gravitational constant: 6.67 × 10⁻¹¹ N m² kg⁻².

其中 F 是引力（牛顿），m₁ 和 m₂ 是质量（千克），r 是两物体中心之间的距离（米），G 是引力常数：6.67 × 10⁻¹¹ N m² kg⁻²。

In IGCSE, you are not required to perform calculations with G, but you must understand the proportionalities: F ∝ m₁ m₂, and F ∝ 1/r². If the distance doubles, the force becomes one quarter.

在IGCSE中，你不需要用 G 进行计算，但必须理解比例关系：F ∝ m₁ m₂，以及 F ∝ 1/r²。如果距离加倍，力将变为四分之一。

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

Gravitational field strength g is defined as the gravitational force per unit mass acting on a small test mass placed at that point. On Earth, g ≈ 9.8 N/kg, often rounded to 10 N/kg in IGCSE problems.

引力场强度 g 定义为作用在放置在该点的小检验质量上的每单位质量的引力。地球表面，g ≈ 9.8 N/kg，在IGCSE题目中常取10 N/kg。

g = F / m

It is a vector quantity pointing toward the centre of the Earth. On other planets or moons, g varies because it depends on the mass and radius of the celestial body.

它是一个矢量，指向地球中心。在其他行星或卫星上，g 会变化，因为它取决于天体的质量和半径。

Near Earth’s surface, g is approximately constant, allowing us to use the simple weight equation.

在地球表面附近，g 近似恒定，因此我们可以使用简单的重量公式。

4. Weight vs Mass | 重量与质量

Mass is the amount of matter in an object, measured in kilograms (kg). It is a scalar and does not change with location. Weight is the gravitational force on that mass, measured in newtons (N). Weight depends on the local gravitational field strength.

质量是物体所含物质的量，以千克（kg）为单位，是标量，不随位置改变。重量是作用在该质量上的引力，以牛顿（N）为单位，取决于当地的引力场强度。

W = m g

On Earth, with g = 10 N/kg, a 5 kg object has a weight of 50 N. On the Moon, where g ≈ 1.6 N/kg, the same 5 kg mass weighs only 8 N, but its mass remains 5 kg.

在地球上，g = 10 N/kg 时，一个 5 kg 的物体重 50 N。在月球上，g ≈ 1.6 N/kg，同样 5 kg 的质量仅重 8 N，但其质量仍是 5 kg。

Common exam trap: a balance measures mass (by comparing weight), but a spring scale measures weight. In space, an object may be weightless but still has full mass.

常见考试陷阱：天平测量的是质量（通过比较重量），而弹簧秤测量的是重量。在太空中，物体可能失重，但仍具有完整的质量。

5. Acceleration due to Gravity | 重力加速度

In free fall, all objects near Earth’s surface accelerate downward at g ≈ 9.8 m/s² (or 10 m/s² in exam papers) if air resistance is negligible. This acceleration is independent of mass – a feather and a hammer fall at the same rate in a vacuum (Apollo 15 experiment).

在自由落体中，如果空气阻力可忽略，地球表面附近所有物体都以 g ≈ 9.8 m/s²（试卷中通常取 10 m/s²）向下加速。这个加速度与质量无关——真空中羽毛和锤子以相同速率下落（阿波罗15号实验）。

Equations of motion (suvat) apply: v = u + a t, s = u t + ½ a t², v² = u² + 2 a s, with a = g for vertical motion. When an object is thrown upwards, g acts downwards, so we often take a = –g if upward is positive.

运动学方程（suvat）适用：v = u + a t, s = u t + ½ a t², v² = u² + 2 a s，其中垂直运动 a = g。当物体向上抛时，g 向下方向，若取向上为正则 a = –g。

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

In real situations, air resistance opposes motion. As an object falls faster, drag increases until it balances the weight. Then the net force is zero and the object falls at a constant terminal velocity.

在实际情况中，空气阻力阻碍运动。物体下落越快，阻力越大，直到与重力平衡。此时合力为零，物体以恒定的终端速度下落。

Skydivers demonstrate this: initial acceleration of g, then decreasing acceleration as drag grows, then zero acceleration at terminal speed (about 50 m/s in a spread-eagle position). Opening a parachute increases drag drastically, lowering terminal velocity to about 5 m/s.

跳伞者演示了这一点：初始加速度为 g，随着阻力增大加速度减小，最终在终端速度时加速度为零（四肢伸展姿势下约 50 m/s）。打开降落伞会大幅增加阻力，将终端速度降低到约 5 m/s。

Velocity–time graphs for falling objects show a curve starting at zero, steepening, then levelling off. IGCSE questions frequently ask you to interpret such graphs.

下落物体的速度-时间图显示一条从零开始、先陡后平的曲线。IGCSE 经常要求你解读这类图形。

7. Orbits and Satellites | 轨道与人造卫星

A satellite stays in orbit because the gravitational force provides the centripetal force required for circular motion. This force keeps the satellite accelerating towards the Earth’s centre, but its tangential velocity prevents it from falling straight down.

卫星之所以停留在轨道上，是因为引力提供了圆周运动所需的向心力。这个力使卫星不断向地球中心加速，但其切向速度阻止了它直接坠落。

Geostationary satellites orbit above the equator with a period of 24 hours, so they appear fixed in the sky. They are used for communications and weather monitoring. Their orbital radius is about 42,000 km from Earth’s centre.

地球同步轨道卫星位于赤道上方，运行周期为24小时，因此看起来固定在天空某一点。它们用于通信和天气监测。轨道半径距地心约42000公里。

Planets orbiting the Sun follow elliptical orbits (Kepler’s first law), but in IGCSE we treat them as approximately circular. The gravitational pull of the Sun acts as the centripetal force.

绕太阳运行的行星遵循椭圆轨道（开普勒第一定律），但在IGCSE中我们近似为圆形。太阳的引力充当向心力。

8. Circular Motion and Gravity | 圆周运动与引力

For an object moving in a circle at constant speed, the velocity is constantly changing direction – there is an acceleration towards the centre (centripetal acceleration). The resultant force causing this is the centripetal force, given by:

对于匀速圆周运动的物体，速度方向不断改变——存在指向中心的加速度（向心加速度）。导致这一加速度的合力即为向心力，公式为：

F = m v² / r

where m is mass, v is orbital speed, r is radius. For a satellite, this centripetal force is supplied by gravity, so we can relate v, r, and the central mass.

其中 m 是质量，v 是轨道速率，r 是半径。对于卫星，这个向心力由引力提供，因此我们可以将 v、r 和中心质量联系起来。

Although full derivations are not always required, you should know that a lower orbit means higher speed (because gravity is stronger) and a shorter orbital period. The Moon, far from Earth, has a period of about 27 days.

虽然不总要求完整推导，但你应该知道轨道越低、速度越快（因为引力更强），轨道周期更短。离地球很远的月球，周期约为27天。

9. Gravitational Potential Energy (near Earth’s surface) | 引力势能（近地表面）

When lifting an object near Earth’s surface, work is done against gravity. The gravitational potential energy (GPE) gained is:

在地球表面附近举起物体时，反抗引力做功。增加的引力势能（GPE）为：

ΔEₚ = m g Δh

where Δh is the change in height. This formula assumes g is constant, which is valid for small height changes. The unit is the joule (J).

其中 Δh 是高度变化量。此公式假设 g 恒定，适用于高度变化不大的情况。单位是焦耳（J）。

Beyond IGCSE, GPE is considered negative at large distances, but you only need the mgh form. Always link this with energy conservation: GPE lost becomes kinetic energy (KE) in a falling object (ignoring air resistance).

超出IGCSE范围的大距离下GPE被视为负值，但你只需掌握 mgh 形式。始终将其与能量守恒联系：在忽略空气阻力时，失去的GPE变为下落物体的动能（KE）。

10. Common Misconceptions and Exam Tips | 常见误区与应试技巧

1. Mass and weight are not the same. Mass is measured in kg, weight in N. In everyday language people say ‘weight in kg’ – do not get confused. Exam questions often test this distinction.

1. 质量和重量不同。质量单位是kg，重量单位是N。日常生活中人们说“重量多少公斤”——不要混淆。考试常考这个区别。

2. In free fall without air resistance, all objects have the same acceleration g regardless of mass. Heavier objects do not fall faster.

2. 在没有空气阻力的自由落体中，所有物体加速度均为g，与质量无关。更重的物体不会下落更快。

3. Gravity is a force, measurable in newtons. Gravitational field strength g is not a force; it is force per unit mass (N/kg).

3. 引力是一种力，以牛顿为单位。引力场强度 g 不是力；它是每单位质量的力（N/kg）。

4. In orbit, astronauts are not in ‘zero gravity’; they are in free fall around the Earth, experiencing weightlessness because they are accelerating at g towards Earth along with their spacecraft.

4. 在轨道上，宇航员并非处于“零重力”；他们绕地球自由坠落，因为与航天器一起以g向地球加速，从而体验到失重。

5. When using equations of motion, set your sign convention clearly. If upward is positive, then a = –g.

5. 使用运动方程时，明确设定正负号。若向上为正，则 a = –g。

Always write the formula, substitute values with units, and check your answer makes sense. In IGCSE Edexcel Physics, questions on gravity often mix calculations with graph interpretation or explanation of satellite motion, so master the concepts, not just the maths.

始终写出公式，代入带单位的数值，并检查答案是否合理。在IGCSE Edexcel物理中，万有引力题目常混合计算、图形解读或卫星运动的解释，因此要掌握概念，而不仅仅是数学。

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Gravitational Force | 万有引力考点精讲