📚 Celestial Motion in the Universe | 宇宙中的天体运动
Every object in the universe is in motion. Planets race around the Sun, moons circle their parent planets, comets sweep through the Solar System on long elliptical paths, and entire galaxies drift apart from one another. In this article, we will explore the physics behind these celestial motions, focusing on the IGCSE Edexcel specification.
宇宙中的每一个天体都在运动。行星绕着太阳飞驰，卫星环绕其母行星运转，彗星沿细长的椭圆轨道掠过太阳系，甚至整个星系都在彼此远离。在本文中，我们将围绕 Edexcel IGCSE 考纲，深入探讨这些天体运动背后的物理原理。
1. The Structure of the Solar System | 太阳系的结构
The Solar System is centred on the Sun, a massive star that contains about 99.9% of the total mass of the Solar System. Eight planets orbit the Sun in a relatively flat plane, along with dwarf planets, asteroids, comets and moons.
太阳系以太阳为中心。太阳是一颗巨大的恒星，占据了太阳系总质量的约99.9%。八大行星在相对平坦的平面上绕太阳运行，此外还有矮行星、小行星、彗星和卫星。
The eight planets can be divided into two groups. The four inner planets — Mercury, Venus, Earth and Mars — are small, dense, rocky worlds. The four outer planets — Jupiter, Saturn, Uranus and Neptune — are much larger gas giants, composed mainly of hydrogen and helium.
八大行星可分为两类。四颗内行星——水星、金星、地球和火星——体积较小、密度较高，是岩石质世界。四颗外行星——木星、土星、天王星和海王星——体积大得多，是主要由氢和氦组成的巨大气态行星。
Moons are natural satellites that orbit planets. For example, the Moon orbits the Earth once every lunar month (about 27.3 days). In addition, asteroids are irregular rocky bodies mostly found in the asteroid belt between Mars and Jupiter, while comets are icy bodies that travel in highly stretched elliptical orbits around the Sun.
卫星是绕行星运转的自然天体。例如，月球约每27.3天（一个恒星月）绕地球一周。此外，小行星是形状不规则的岩石天体，大多位于火星与木星之间的小行星带中；彗星则是沿极度拉长的椭圆轨道绕太阳运行的天体。
2. Gravity — The Universal Force | 引力——宇宙中的通用力
Gravity is the force of attraction that acts between any two objects that have mass. It is the fundamental force that controls the motion of all celestial bodies. Without gravity, planets would not stay in orbit around the Sun, and the Moon would not circle the Earth.
引力是存在于任何两个有质量物体之间的吸引力。它是支配所有天体运动的基本力。如果没有引力，行星将无法保持在绕太阳的轨道上，月球也不会环绕地球。
The gravitational force between two masses depends on two factors: the size of the masses and the distance between them. The larger the masses, the greater the force. The greater the separation, the weaker the force. Mathematically, the force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centres:
两个质量之间的引力取决于两个因素：质量的大小和它们之间的距离。质量越大，引力越大；距离越远，引力越弱。在数学上，引力与两个质量的乘积成正比，与它们质心之间距离的平方成反比：
F ∝ m₁m₂ / r²
This is the inverse square law. If the distance r between two objects is doubled, the gravitational force falls to one quarter of its original value. If the distance is tripled, the force falls to one ninth. This weakening of gravity with distance explains why the outer planets, which are far from the Sun, experience a much weaker gravitational pull than the inner planets.
这就是平方反比定律。如果两个物体之间的距离 r 加倍，引力将减小到原来的四分之一；如果距离变为三倍，引力将减小到原来的九分之一。引力随距离增大而减弱的特性，解释了为什么远离太阳的外行星所受到的引力比内行星弱得多。
3. Circular Orbits and Centripetal Force | 圆形轨道与向心力
Many celestial bodies, such as planets and artificial satellites, follow approximately circular orbits. Why do they keep going around instead of flying off into space? The answer lies in the combination of the body’s forward velocity and the gravitational force pulling it sideways.
许多天体，如行星和人造卫星，都沿近似圆形的轨道运行。为什么它们一直绕行而不会飞入太空？答案在于天体自身的向前速度与把它拉向侧方的引力之间的结合。
An object moving in a circle is continuously changing direction. Whenever a body changes direction, it is accelerating, even if its speed is constant. An acceleration requires a resultant force to act on the body. For an orbiting object, this resultant force is gravity, which acts as a centripetal force — it pulls the object constantly toward the centre of the orbit. In the case of a planet around the Sun, gravity pulls the planet toward the Sun. Because the planet also has a forward velocity, it keeps “falling” around the Sun rather than straight into it.
作圆周运动的物体在不断地改变方向。每当物体改变方向时，即使速度大小不变，它也在加速。加速度需要合外力作用于物体。对于轨道上的天体，这个合外力就是引力，它充当向心力——将物体持续拉向轨道的中心。以行星绕太阳为例，引力将行星拉向太阳。由于行星同时具有向前速度，它不断地”下落”绕太阳运转，而不是径直坠入太阳。
It is important to remember that if the gravitational force suddenly disappeared, the orbiting body would continue moving in a straight line at a constant velocity, in accordance with Newton’s first law of motion.
务必记住，如果引力突然消失，根据牛顿第一运动定律，轨道上的天体将沿直线做匀速运动。
4. Orbital Speed and Period | 轨道速度与周期
The orbital speed of a body moving in a circular orbit can be calculated using the equation:
沿圆形轨道运行的天体的轨道速度可以使用以下公式计算：
v = 2πr / T
where v is the orbital speed in metres per second (m/s), r is the orbital radius in metres (m), and T is the orbital period in seconds (s). This equation is one of the most important in the IGCSE astrophysics topic.
其中 v 是轨道速度，单位米每秒（m/s）；r 是轨道半径，单位米（m）；T 是轨道周期，单位秒（s）。这个公式是 IGCSE 天体物理学中最重要的公式之一。
Worked example: The Moon orbits the Earth at an average radius of 3.84 × 10⁸ m, and its orbital period is 27.3 days. Calculate its orbital speed.
例题：月球绕地球运行的平均轨道半径为 3.84 × 10⁸ m，轨道周期为 27.3 天。求月球的轨道速度。
First, convert the period into seconds. T = 27.3 × 24 × 3600 = 2.36 × 10⁶ s. Then apply the equation: v = 2π × 3.84 × 10⁸ / 2.36 × 10⁶ ≈ 1020 m/s. So the Moon travels at roughly 1.02 km/s around the Earth.
首先将周期转换为秒：T = 27.3 × 24 × 3600 = 2.36 × 10⁶ s。然后代入公式：v = 2π × 3.84 × 10⁸ / 2.36 × 10⁶ ≈ 1020 m/s。因此月球绕地球运行的速度约为 1.02 km/s。
A useful tip for exams: always check whether the orbital radius and period are given in the correct SI units. Convert kilometres to metres and days or hours to seconds before substituting into the equation.
考试中一个有用的技巧：始终检查轨道半径和周期是否已换算为正确的 SI 单位。代入公式前，应将千米换算为米，将天或小时换算为秒。
5. Orbital Period and Distance from the Sun | 轨道周期与距日距离
The farther a planet is from the Sun, the longer it takes to complete one orbit. Mercury, for example, orbits the Sun in just 88 days, whereas Neptune takes about 165 Earth years. There are two reasons for this. First, the circumference of a wider orbit is larger. Second, because the gravitational attraction from the Sun is weaker at greater distances, the planet’s orbital speed is slower.
行星离太阳越远，完成一圈轨道所需的时间就越长。例如，水星绕太阳运行仅需88天，而海王星大约需要165个地球年。这有两个原因。第一，更大轨道的周长更长。第二，由于距离太阳越远，太阳引力越弱，行星的轨道速度也越慢。
This relationship is described by Kepler’s third law. In its precise form, it states that the square of the orbital period is proportional to the cube of the average orbital radius:
这一关系由开普勒第三定律描述。其精确表述为：轨道周期的平方与平均轨道半径的立方成正比：
T² ∝ r³
For IGCSE, you are not required to use this law in calculations, but you should be able to interpret it: the outermost planets have much longer orbital periods than the innermost planets.
在 IGCSE 中，不要求使用这一定律进行计算，但你应该能够理解其含义：最外层的行星比最内层的行星具有长得多的轨道周期。
6. Artificial Satellites | 人造卫星
Artificial satellites are human-made objects placed into orbit around the Earth for practical purposes. They obey exactly the same physics as natural satellites: gravity provides the centripetal force that keeps them in their circular orbits.
人造卫星是人类制造并送入地球轨道的物体，用于各种实际用途。它们遵循与自然卫星完全相同的物理规律：引力提供使它们保持在圆形轨道上的向心力。
Artificial satellites can be placed at different distances from the Earth’s surface, depending on their purpose. Low Earth orbit satellites, at altitudes of roughly 200 to 2000 km, are used for imaging, scientific studies and the International Space Station. Medium Earth orbit satellites, at an altitude of about 20,000 km, are used for navigation systems such as GPS. Geostationary satellites, which we will examine next, orbit at around 36,000 km above the equator.
人造卫星可根据其用途放置在距地球表面不同的距离上。低地球轨道卫星，高度大约在200至2000 km，用于成像、科学研究和国际空间站。中地球轨道卫星，高度约20,000 km，用于全球定位系统（GPS）等导航系统。地球同步卫星，我们接下来会详细讨论，在赤道上方约36,000 km的轨道上运行。
The closer a satellite is to the Earth, the stronger the gravitational pull and the greater the orbital speed required to prevent it from falling back to Earth. Therefore a low-flying satellite must move faster than one in a higher orbit.
卫星离地球越近，受到的引力越强，防止其坠落回地球所需的轨道速度也越大。因此，低轨道卫星必须比高轨道卫星运动得更快。
7. Geostationary Satellites | 地球同步卫星
A geostationary satellite is a special type of satellite that orbits the Earth once every 24 hours, moving in the same direction as the Earth’s rotation (west to east), in an orbit directly above the equator. As a result, the satellite appears to remain fixed at the same point above the Earth’s surface.
地球同步卫星是一种特殊的卫星，它每24小时绕地球一周，并且与地球自转方向一致（自西向东），轨道位于赤道正上方。因此，从地球表面看，该卫星似乎固定在某一点静止不动。
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Orbital period: T = 24 hours = 86,400 seconds
轨道周期：T = 24 小时 = 86,400 秒
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Orbit directly above the equator in the equatorial plane
轨道位于赤道正上方的赤道平面内
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Direction of motion: same as the Earth’s rotation
运动方向与地球自转方向一致
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Altitude: approximately 36,000 km above the Earth’s surface
高度：距地球表面约 36,000 km
Because a geostationary satellite stays above the same point on the Earth’s surface, it is ideal for telecommunications and broadcasting. Satellite dishes on the ground can point at a fixed position in the sky and never need to adjust their direction to track the satellite.
由于地球同步卫星始终位于地球表面同一点的正上方，它非常适合用于电信和广播电视。地面上的卫星天线可以指向天空中一个固定的位置，无需不断调整方向来追踪卫星。
A common examination point is to state that the satellite’s period must be exactly 24 hours and that its orbit must lie in the equatorial plane, otherwise it would not appear stationary from the Earth’s surface.
一个常见的考点是：该卫星的周期必须恰好为24小时，且其轨道必须位于赤道平面内，否则从地球表面看它将不是静止的。
8. Comets — Elliptical Orbits | 彗星——椭圆轨道
Not all celestial bodies move in circular orbits. Comets, for example, travel in highly elliptical orbits around the Sun. Gravity still controls their motion, but because the distance between the comet and the Sun changes continuously, the gravitational force and the comet’s speed are not constant.
并非所有天体都沿圆形轨道运动。例如，彗星绕太阳运行在高度椭圆的轨道上。引力仍然控制着它们的运动，但由于彗星与太阳之间的距离不断变化，引力和彗星的速度也在不断变化。
When a comet is near the Sun — at a point called perihelion — the gravitational pull is strong, and the comet moves at its fastest speed. When the comet is far from the Sun — at a point called aphelion — the gravitational pull is weak, and the comet slows down. This is a key difference between circular and elliptical orbits: in a circular orbit the speed is constant, but in an elliptical orbit the speed varies.
当彗星靠近太阳时——这个点称为近日点——引力较强，彗星运行速度最快。当彗星远离太阳时——这个点称为远日点——引力较弱，彗星速度减慢。这是圆形轨道与椭圆轨道之间的一个关键区别：在圆形轨道中速度恒定，而在椭圆轨道中速度是变化的。
Although comets are not covered extensively in calculations at IGCSE, understanding their elliptical motion helps you explain the periodic nature of comets, such as Halley’s Comet, which returns to the inner Solar System roughly every 76 years.
虽然 IGCSE 考试中不要求对彗星进行大量计算，但理解其椭圆运动有助于你解释彗星的周期性，例如哈雷彗星大约每76年回归内太阳系一次。
9. Stars, Galaxies and the Universe | 恒星、星系与宇宙
Beyond our Solar System lies an enormous universe containing countless stars and galaxies. The Sun itself is a star — a giant ball of hot, glowing gas that produces energy through nuclear fusion, in which hydrogen is converted into helium.
在太阳系之外，是一个包含无数恒星和星系的广袤宇宙。太阳本身就是一颗恒星——一个炽热发光的气体巨球，通过核聚变（氢转化为氦）产生能量。
A galaxy is a massive collection of billions of stars, along with dust and gas, all held together by gravitational attraction. Our own galaxy is called the Milky Way. The universe is the largest structure we know: it is everything that exists — all space, all matter, all energy, and all time. It contains billions of galaxies, each containing billions of stars.
星系是数十亿颗恒星以及尘埃和气体在引力作用下聚集而成的庞大集合体。我们所在的星系叫作银河系。宇宙是我们所知的最大结构：它是存在的一切——所有的空间、所有的物质、所有的能量和所有的时间。宇宙包含数十亿个星系，每个星系又包含数十亿颗恒星。
For IGCSE, you should be able to state the hierarchy clearly: stars are clumped together into galaxies, and galaxies cluster together to form the universe.
对于 IGCSE，你应该能够清晰地表述层级关系：恒星聚集形成星系，星系共同构成宇宙。
10. Redshift and Cosmic Expansion | 红移与宇宙膨胀
One of the most important pieces of evidence about the motion of the universe comes from the study of light from distant galaxies. When a light source moves away from an observer, its wavelengths are stretched, and the light appears redder. This effect is known as redshift.
关于宇宙运动最重要的证据之一，来自对遥远星系发出的光的研究。当光源远离观察者时，其波长被拉长，光看起来偏红。这一效应被称为红移。
Astronomers observe that the light from virtually all distant galaxies shows a redshift. This tells us that these galaxies are moving away from us. Furthermore, the more distant a galaxy is, the larger its redshift and the faster it is receding. This observation suggests that the entire universe is expanding. It is important to note that this is not because galaxies are moving through space in a fixed framework; rather, the space between galaxies itself is stretching.
天文学家观察到，几乎所有遥远星系的光都显示红移。这告诉我们这些星系正在远离我们。更进一步，星系越远，红移越大，远离的速度越快。这一观测表明整个宇宙正在膨胀。需要指出的是，这并不是因为星系在固定框架中穿越空间运动，而是星系之间的空间本身在被拉伸。
This expanding-universe observation is a key piece of evidence supporting the Big Bang theory, which states that the universe began from an extremely hot, dense point approximately 13.8 billion years ago and has been expanding ever since.
宇宙膨胀的观测证据是支持大爆炸理论的关键依据。该理论认为，宇宙大约在138亿年前从一个极热、极密的点开始，并一直膨胀至今。
11. Key Equations Summary | 关键公式总结
The table below summarises the most important equations and facts for the IGCSE celestial motion topic.
下表总结了 IGCSE 天体运动主题中最重要的公式和事实。
| Quantity / Quantity | Equation / Formula | Notes / Notes |
| Orbital speed 轨道速度 |
v = 2πr / T | r in metres, T in seconds r 单位为米，T 单位为秒 |
| Gravitational force 引力 |
F ∝ m₁m₂ / r² | Inverse square law 平方反比定律 |
| Kepler’s third law 开普勒第三定律 |
T² ∝ r³ | Qualitative understanding 定性理解 |
| Geostationary period 地球同步卫星周期 |
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