📚 Motion in the Universe | 宇宙中的运动
From the graceful elliptical paths of planets to the rapid recession of distant galaxies, motion in the universe is governed by a handful of fundamental physical principles. Understanding these movements not only unveils the mechanics of our solar system but also reveals the origin, evolution, and ultimate fate of the cosmos itself.
从行星优雅的椭圆轨道到遥远星系的快速退行，宇宙中的运动受少数几条基础物理原理支配。理解这些运动不仅能揭示太阳系的力学机制，还能展现宇宙的起源、演化与最终命运。
1. Our Solar System and Planetary Motion | 我们的太阳系与行星运动
The solar system consists of the Sun, eight planets, dwarf planets, moons, asteroids, and comets. All planets orbit the Sun in roughly the same plane, known as the ecliptic plane, and their paths are slightly elliptical with the Sun positioned at one focus of the ellipse.
太阳系由太阳、八大行星、矮行星、卫星、小行星和彗星组成。所有行星大致在同一个平面（黄道面）上绕太阳运行，轨道略呈椭圆形，太阳位于椭圆的一个焦点上。
Planets closer to the Sun travel at higher average speeds. For example, Mercury completes an orbit in just 88 Earth days, whereas Neptune takes about 165 Earth years. The farther a planet is, the longer its orbital period and the slower its average orbital speed.
离太阳越近的行星平均运行速度越快。例如，水星仅用88个地球日就能完成一圈公转，而海王星大约需要165个地球年。行星离太阳越远，轨道周期越长，平均轨道速度越慢。
2. Kepler's Laws of Planetary Motion | 开普勒行星运动定律
Johannes Kepler formulated three laws that describe planetary orbits with remarkable accuracy. The first law states that each planet moves in an ellipse with the Sun at one focus. The second law, the law of equal areas, says that a line joining a planet to the Sun sweeps out equal areas in equal times; hence a planet moves faster when it is nearer the Sun (perihelion) and slower when it is farther away (aphelion).
约翰内斯·开普勒归纳了三条精确描述行星轨道的定律。第一定律指出，每颗行星沿椭圆轨道运动，太阳位于椭圆的一个焦点。第二定律（面积定律）表明，行星与太阳的连线在相等时间内扫过相等的面积；因此行星在靠近太阳时（近日点）运动较快，远离时（远日点）运动较慢。
The third law relates the orbital period T of a planet to the semi‑major axis r of its orbit. For circular orbits (a good approximation for many planets) the relationship is T² ∝ r³. This means the square of the period is proportional to the cube of the orbital radius.
第三定律将行星的轨道周期T与轨道半长轴r联系起来。对于圆轨道（许多行星的很好近似），关系为T² ∝ r³。这意味着周期的平方正比于轨道半径的立方。
3. Gravitational Force and Its Role | 引力及其作用
Isaac Newton showed that the force keeping planets in orbit is the same force that pulls an apple to the ground: gravity. The magnitude of the gravitational force F between two point masses M and m separated by a distance r is given by Newton's law of universal gravitation.
艾萨克·牛顿证明，使行星保持轨道运行的力与使苹果落地的力是同一种力——引力。两个点质量M和m相距r时的引力大小F由万有引力定律给出。
F = G M m / r²
引力公式：F = G M m / r²，其中G是引力常量。
This force is always attractive, acts along the line joining the centres of the masses, and decreases with the square of the distance. In the solar system, the Sun's enormous mass means it provides the dominant gravitational pull that keeps the planets in their bound orbits.
这个力总是吸引力，沿着两物体中心连线方向作用，并以距离的平方衰减。在太阳系中，太阳巨大的质量使其提供主要的引力，从而使行星保持在束缚轨道上。
4. Circular Orbits and Centripetal Force | 圆轨道与向心力
For a planet or satellite moving with constant speed v in a circular orbit of radius r, the acceleration is directed towards the centre of the circle. The centripetal force required to maintain this motion is provided entirely by gravity.
对于以恒定速率v在半径为r的圆轨道上运动的行星或卫星，加速度指向圆心。维持这一运动所需的向心力完全由引力提供。
centripetal force = m v² / r = G M m / r²
向心力 = m v² / r = G M m / r²
Equating the two expressions leads to a useful relation that shows how orbital speed depends on the radius and the mass of the central body. Notice that the mass m of the orbiting object cancels out, so all objects at the same distance from the Sun orbit with the same speed regardless of their mass.
将这两个表达式联立可得出一个有用的关系式，表明轨道速度如何依赖于轨道半径和中心天体的质量。注意轨道物体的质量m会消掉，因此与太阳相同距离的所有物体，无论质量大小，都以相同的速度绕行。
5. Deriving Orbital Speed | 推导轨道速度
From the equality m v² / r = G M m / r², we can solve for the orbital speed v:
由等式m v² / r = G M m / r²，我们可以解出轨道速度v：
v = √G M / r
轨道速度公式：v = √G M / r
This equation shows that the orbital speed decreases as the orbital radius increases. For example, Earth's orbital speed around the Sun is about 30 km/s, while Neptune's is only about 5.4 km/s. It also explains why satellites in low Earth orbit must travel faster than those in higher orbits.
该公式表明轨道半径越大，轨道速度越小。例如，地球绕太阳的轨道速度约为30 km/s，而海王星仅为约5.4 km/s。同时也解释了为什么低地球轨道的卫星必须比高轨卫星运行得更快。
We can also express the orbital period T in terms of radius using v = 2πr / T. Substituting gives T² = (4π² / GM) r³, which is the precise form of Kepler's third law for circular orbits.
我们还可以利用v = 2πr / T将轨道周期T用半径表示。代入后得到T² = (4π² / GM) r³，这正是圆轨道条件下开普勒第三定律的精确形式。
6. Satellite Orbits: Geostationary and Polar | 卫星轨道：地球同步与极地
Artificial satellites are placed into different orbits depending on their purpose. Two important types are geostationary orbits and polar orbits.
人造卫星根据用途被送入不同的轨道。两种重要的类型是地球同步轨道和极地轨道。
A geostationary satellite orbits Earth above the equator with a period of 24 hours, matching Earth's rotation. As a result, it appears stationary in the sky from the ground. These satellites orbit at an altitude of about 36 000 km and are widely used for communications and weather monitoring.
地球同步卫星在赤道上空绕地球运行，周期为24小时，与地球自转同步，因此从地面看它在天空中静止不动。这类卫星的轨道高度约为36 000 km，广泛用于通信和天气监测。
In contrast, a polar orbit passes over or near Earth's poles. As the satellite travels along its orbit, Earth rotates beneath it, allowing the satellite to scan the entire globe over time. Polar orbits are typically low-altitude (200–1000 km) and are ideal for Earth observation, mapping, and reconnaissance.
相比之下，极地轨道经过或接近地球两极。卫星沿轨道运行时，地球在下方自转，使卫星能够随时间推移扫描整个地球。极地轨道通常高度较低（200–1000 km），非常适合地球观测、测绘和侦察。
7. Orbital Period and Kepler's Third Law | 轨道周期与开普勒第三定律
Kepler's third law in its general form states that the square of the orbital period T is proportional to the cube of the semi‑major axis r. For circular orbits, this becomes T² ∝ r³.
开普勒第三定律的一般形式为轨道周期T的平方正比于半长轴r的立方。对于圆轨道，即T² ∝ r³。
We can test this relationship using data from the planets. The table below shows the mean orbital radius r (in AU) and period T (in Earth years) for four planets, along with the calculated value of T² / r³.
我们可以用行星数据验证这一关系。下表显示了四颗行星的平均轨道半径r（以天文单位AU计量）和周期T（以地球年计量），并计算了T² / r³的值。
| Planet | r (AU) | T (years) | T² / r³ |
|---|---|---|---|
| Mercury | 0.387 | 0.241 | 1.00 |
| Venus | 0.723 | 0.615 | 1.00 |
| Earth | 1.000 | 1.000 | 1.00 |
| Mars | 1.524 | 1.881 | 1.00 |
The near-constant value of T² / r³ confirms that the law holds throughout the solar system. Small deviations arise because actual orbits are slightly elliptical and planets interact gravitationally.
T² / r³的值接近常数，证实该定律在整个太阳系成立。微小的偏差来源于实际轨道的椭圆性以及行星间的引力相互作用。
8. The Expanding Universe: Redshift | 膨胀的宇宙：红移
When astronomers examine the light from distant galaxies, they find that the characteristic spectral lines are shifted towards the longer‑wavelength (red) end of the spectrum. This phenomenon is called redshift.
天文学家在观测遥远星系的光时，发现其特征谱线向长波（红）端移动。这种现象称为红移。
The redshift arises because the galaxies are moving away from us, stretching the light waves via the Doppler effect. A wave emitted by a receding source is stretched, so its wavelength increases and frequency decreases. The greater the speed of recession, the larger the redshift.
红移的产生是因为星系正在远离我们，通过多普勒效应拉伸了光波。远离的光源发出的波被拉长，因此波长增加、频率降低。退行速度越大，红移越大。
Observations show that almost all galaxies exhibit redshift, and more distant galaxies show greater redshifts. This tells us that the universe is expanding, with galaxies moving apart from each other in all directions.
观测表明，几乎所有的星系都呈现红移，而且越远的星系红移越大。这说明宇宙正在膨胀，星系彼此之间在各个方向上都在相互远离。
9. Hubble's Law and Cosmic Distances | 哈勃定律与宇宙距离
Edwin Hubble discovered a simple relationship between the recessional speed v of a galaxy and its distance d from Earth:
埃德温·哈勃发现，星系的退行速度v与它到地球的距离d之间存在简单的关系：
v = H₀ d
哈勃定律：v = H₀ d，其中H₀是哈勃常数。
Hubble's law indicates that the universe is expanding uniformly. The constant H₀ is approximately 70 km/s per megaparsec (Mpc). By measuring a galaxy's redshift and using Hubble's law, astronomers can estimate its distance and map the large‑scale structure of the cosmos.
哈勃定律表明宇宙在均匀膨胀。哈勃常数H₀约为70 km/s每百万秒差距（Mpc）。通过测量星系的红移并运用哈勃定律，天文学家可以估计其距离并绘制宇宙的大尺度结构。
An important consequence is that if we trace the expansion backwards in time, all matter must have originated from an extremely hot and dense point about 13.8 billion years ago — the Big Bang.
一个重要的推论是，如果追溯时间反演膨胀过程，所有物质必定源于约138亿年前一个极热极密的点——即大爆炸。
10. The Big Bang Theory and CMB | 大爆炸理论与宇宙微波背景
The Big Bang theory states that the universe began from an infinitely small, hot, and dense singularity and has been expanding ever since. Two major pieces of evidence support this theory: galactic redshift and the cosmic microwave background (CMB) radiation.
大爆炸理论认为，宇宙始于一个无限小、炽热、致密的奇点，此后一直在膨胀。支持这一理论的两大证据是星系红移和宇宙微波背景（CMB）辐射。
The CMB is a faint glow of microwave radiation that fills the universe uniformly in all directions. It has a temperature of about 2.7 K and is interpreted as the afterglow of the Big Bang, released when the universe first became transparent around 380 000 years after its birth.
CMB是充满宇宙各处的微弱微波辐射辉光，温度约为2.7 K，被解释为大爆炸的余晖，释放于宇宙诞生后约38万年首次变得透明之时。
The existence of CMB was predicted by the Big Bang theory and later discovered accidentally by Penzias and Wilson. Its nearly perfect blackbody spectrum and tiny temperature fluctuations provide strong confirmation of the model.
CMB的存在由大爆炸理论预言，后来被彭齐亚斯和威尔逊偶然发现。其近乎完美的黑体谱和微小的温度涨落为该模型提供了强有力的证实。
11. Dark Matter and Dark Energy | 暗物质与暗能量
Observations of the rotation speeds of galaxies and the motions of galaxy clusters suggest that there is much more mass in the universe than we can see. This invisible mass, called dark matter, does not emit, absorb, or reflect electromagnetic radiation but exerts gravitational pull on visible matter.
对星系旋转速度和星系团运动的观测表明，宇宙中存在远多于可见物质的质量。这种不可见质量称为暗物质，它不发射、吸收或反射电磁辐射，但对可见物质施加引力作用。
In addition, measurements of distant supernovae have shown that the expansion of the universe is accelerating. This acceleration is attributed to a mysterious form of energy known as dark energy, which appears to oppose gravity on cosmic scales and makes up about 68% of the total energy content of the universe.
此外，对遥远超新星的测量显示，宇宙膨胀正在加速。这种加速被归因于一种神秘的能量形式——暗能量，它在宇宙尺度上似乎对抗引力，约占宇宙总能量组成的68%。
While dark matter and dark energy remain poorly understood, they are essential components of modern cosmology and help explain why the motions of galaxies and the expansion history of the universe do not match predictions based solely on ordinary matter.
尽管暗物质和暗能量目前仍知之甚少，但它们是现代宇宙学的基本组成部分，有助于解释为何星系的运动以及宇宙膨胀历史与仅基于普通物质的预言不符。
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