# 宇宙中的运动

> 物理 · 爱德思IGCSE 4PH1
> 来源: https://www.owlsprep.com/zh/study/edexcel-igcse-physics-s8-motion-in-the-universe/

本讲义覆盖爱德思IGCSE物理第8章8.2-8.6的全部核心内容：宇宙结构、引力场变化、轨道类型与轨道速度计算，完全贴合2017版4PH1考纲要求。

**先修:** [重力=质量×g的相关计算（对应「力与运动」模块S1_T02）](https://www.owlsprep.com/zh/study/edexcel-igcse-physics-s1-force-motion-weight/); 单位换算与科学记数法运算能力

## 学习目标

- 描述宇宙、银河系与太阳系的层级结构
- 解释不同天体表面引力场强度（g）的差异
- 将万有引力与天然卫星、行星、人造卫星及彗星的轨道运动建立关联
- 对比彗星、天然卫星与行星的轨道形状及速度变化规律
- 使用公式v = 2πr/T计算轨道速度，包含天文数值的正确单位换算

## 1. 宇宙结构与引力场强度

宇宙是由数十亿个星系组成的庞大集合。每个星系都是由数十亿颗恒星通过引力束缚形成的大型天体系统。我们的太阳系（包含太阳、行星、天然卫星、彗星、小行星）位于银河系中。

**引力场强度（g）** — 引力场中作用在物体单位质量上的力，单位为N/kg，数值上与以m/s²为单位的自由落体加速度相等。

*记法:* g

*例:* g on Earth is 10 N/kg, while g on the Moon is 1.6 N/kg.

天体表面的引力场强度由两个因素决定：天体的总质量和自身半径。质量越大、表面半径越小，g值就越高。考试题目中会给出其他行星或卫星的g值，无需自行记忆。

> **info**
>
> 除非题目明确给出其他数值，所有涉及地球的计算默认取g = 10 N/kg。

**例题:** 一台火星车的质量为185 kg，火星表面的引力场强度为3.7 N/kg。请使用重力=质量×g的公式计算该火星车在火星上的重量。

1. 步骤1：提取已知数值：质量m = 185 kg，火星表面g = 3.7 N/kg
2. 步骤2：将数值代入重力计算公式：W = m × g
3. $$W = 185 \times 3.7 = 684.5 N$$
4. 步骤3：保留2位有效数字（与题目给出的g值有效数字位数一致），得到结果680 N

## 2. 万有引力与轨道运动

两个天体之间的引力提供了维持物体稳定轨道运动的向心力，避免物体沿直线飞离中心天体。太阳系中所有的轨道运动都可以通过该引力作用解释。

- Moons orbiting planets: gravitational pull of the planet on the moon maintains its orbit
- Planets orbiting the Sun: gravitational pull of the Sun on planets keeps them on their orbital path
- Artificial satellites orbiting Earth: Earth's gravity pulls satellites to keep them circling the planet for communication, weather, or navigation use
- Comets orbiting the Sun: the Sun's gravity pulls comets back towards the inner solar system even when they are very far away at the edge of their orbit

**例题:** 解释为什么地球同步卫星可以停留在地球赤道上方的固定位置。

1. 步骤1：确定轨道运动的作用力来源：地球对卫星的引力吸引
2. 步骤2：建立力与运动的关联：该引力充当向心力，将卫星拉向地心，阻止卫星沿直线飞离地球
3. 步骤3：结合同步卫星特性说明：该卫星的轨道周期与地球24小时的自转周期完全相等，因此相对于赤道上的固定点，卫星看起来是静止的

## 3. 彗星、天然卫星与行星的轨道对比

并非所有轨道的形状都相同，受引力大小变化的影响，轨道速度会随着物体到中心天体的距离发生改变。

**轨道偏心率** — 用于衡量轨道偏离正圆的程度；偏心率越高，代表轨道越扁、椭圆特征越明显。

| Orbiting body | Orbit shape | Orbit speed pattern |
| --- | --- | --- |
| Planet | Nearly circular (very low eccentricity) | Almost constant speed, as orbital radius is almost uniform |
| Moon | Nearly circular (very low eccentricity, orbiting a planet) | Almost constant speed, similar to planets |
| Comet | Highly elliptical (very high eccentricity, stretches far from and close to the Sun) | Fastest when closest to the Sun (smaller orbital radius, stronger gravitational pull), slowest when farthest away |

> **warning**
>
> 考试题目经常要求对比不同轨道，因此请确保你能清晰说明三类天体的轨道形状和运行速度差异。

**例题:** 某颗彗星在靠近太阳时的运行速度为50 km/s，在轨道最远点时的运行速度为2 km/s。请解释这一速度差异。

1. 步骤1：回忆彗星的轨道形状：彗星拥有极扁的椭圆轨道
2. 步骤2：将距离与引力关联：当彗星靠近太阳时，太阳对它的引力作用远强于它远离太阳时的情况
3. 步骤3：将引力与速度关联：更强的引力会使彗星加速，因此它在最接近太阳的位置时运行速度快得多

## 4. 轨道速度计算

考试中你必须熟记轨道速度公式，因为该公式不会出现在任何公式表中。该公式将圆周轨道上物体的平均速度定义为轨道周长除以完成一整圈轨道运动所用的时间（轨道周期）。

**轨道速度（v）** — 沿圆周轨道运动的物体的平均速度，其中r为轨道半径（单位：m），T为轨道周期（单位：s）。

*记法:* v = \frac{2\pi r}{T}

*例:* A satellite orbiting Earth at radius 42,000 km with a 24 hour period has an orbital speed of ~3100 m/s.

> **tip**
>
> 代入数值到公式前，请务必先统一单位：将千米转换为米（乘以1000），将天/小时/分钟转换为秒。对于较大的天文数值请使用科学记数法，避免出现计算错误。

**例题:** 月球绕地球运行的平均轨道半径为384000 km，完成一整圈轨道运动需要27.3天。计算月球的平均轨道速度，单位为m/s，结果保留2位有效数字。

1. 步骤1：将单位转换为国际单位制：半径r = 384000 km = 3.84 × 10⁸ m；周期T = 27.3 天 = 27.3 × 24 × 60 × 60 = 2.35872 × 10⁶ s
2. 步骤2：代入轨道速度公式：v = 2πr / T
3. $$v = \frac{2 \times \pi \times 3.84 \times 10^8}{2.35872 \times 10^6} \approx 1022 m/s$$
4. 步骤3：保留2位有效数字：1.0 × 10³ m/s（即1000 m/s）

**概念自测**

1. What is the correct unit for orbital period when using v = 2πr/T to calculate speed in m/s?

   - Hours
   - Days
   - Seconds
   - Years

   *解析:* All values must be in SI units for the speed to be calculated in m/s. Convert other time units to seconds first.

2. A planet orbits the Sun with a radius of 1.5 × 10¹¹ m, and a period of 3.15 × 10⁷ s. What is its orbital speed?

   - ~30 km/s
   - ~10 km/s
   - ~50 km/s
   - ~3 km/s

   *解析:* Calculation: v = (2 × π × 1.5e11) / 3.15e7 ≈ 30,000 m/s = 30 km/s

*计算器:* allowed

## 常见错误

- **错误做法:** Forgetting to convert km to m or hours/days to seconds in orbital speed calculations.
  - 原因: The formula requires SI units to give speed in m/s, the unit required for exam marks. Incorrect units lead to wildly wrong answers.
  - 正确做法: Always convert radius to metres and time period to seconds before substituting into v = 2πr/T. Use standard form for large values to reduce errors.
- **错误做法:** Stating that comets have circular orbits, or that planets have highly elliptical orbits.
  - 原因: Exam questions regularly test orbit shape differences, and mixing this up loses easy marks.
  - 正确做法: Remember: planets/moons = nearly circular, comets = highly elliptical.
- **错误做法:** Using out-of-scope formulas like F = Gm₁m₂/r² or centripetal force equations for orbit questions.
  - 原因: These concepts are not part of the IGCSE specification, and using them will not gain extra marks, and may lead to mistakes.
  - 正确做法: Only use qualitative descriptions of gravitational force causing orbits, and the v = 2πr/T formula for calculations.
- **错误做法:** Using g = 9.81 m/s² for Earth calculations when not specified.
  - 原因: The exam board explicitly states you should use g = 10 N/kg for all Earth-based questions unless told otherwise.
  - 正确做法: Write g = 10 N/kg at the start of any weight or free fall calculation unless the question gives a different g value.
- **错误做法:** Stating that comets travel slowest when closest to the Sun.
  - 原因: Questions about comet speed changes are common, and reversing the relationship loses marking points.
  - 正确做法: Smaller orbital radius = stronger gravitational pull = higher orbital speed, especially for comets with elliptical orbits.

## 速查表

| Concept | Key Facts / Formula |
| --- | --- |
| Cosmic structure | Universe → billions of galaxies; each galaxy → billions of stars; Solar System is in the Milky Way |
| g variation | Higher mass or smaller radius of a body → higher surface g; Earth g = 10 N/kg (default) |
| Gravitational force role | Causes orbits of moons, planets, artificial satellites, comets |
| Orbit shapes | Planets/moons: nearly circular; Comets: highly elliptical, fastest near Sun |
| Orbital speed formula | v = 2πr/T (must recall for exams); r in m, T in s, v in m/s |

## 下一步

Now you have mastered the core content for Motion in the Universe, you are ready to progress to the remaining topics in Edexcel IGCSE Physics Astrophysics. Next, you will learn about stellar evolution, including the life cycle of stars like our Sun, and how astronomers classify stars using the Hertzsprung-Russell (HR) diagram. Following that, you will cover cosmology, including the Big Bang theory, red-shift evidence, and the evolution of the universe. Make sure you practice past paper questions focused on orbital speed calculations and orbit comparison questions to reinforce your understanding, and confirm you can recall the orbital speed formula without a prompt, as it is not provided in exams. Pay close attention to unit conversion steps to avoid losing easy marks in calculations.

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