The Origin of Modern Astronomy Chapter 4: The Origin of Modern Astronomy

Ancient Greek Astronomy古希腊天文 Models were generally wrong because they were based on wrong “first principles”, believed to be “obvious” and not questioned:（所依据的“根本原理”是错误而不可质疑的，因而模型也是错误的。） Geocentric Universe（地心宇宙）: Earth at the Center of the Universe. “Perfect Heavens”（完美的天空）: Motions of all celestial bodies described by motions involving objects of “perfect” shape, i.e., spheres or circles. 天体及其运动是完美的球型或圆。

Ancient Greek Astronomers Aristotle 亚里士多德 (384 – 322 B.C.), major authority of philosophy until the late middle ages: Universe can be divided in 2 parts: （宇宙分成两部分） 1. Imperfect, changeable Earth （不完美的，可变的地球）, 2. Perfect Heavens (described by spheres)（完美的天空；球对称）

Issues of Ancient Astronomy (I) 古天文的问题 Fundamental argument for the geocentric universe 地心宇宙的依据: Motion of Earth should result in an observable parallax, which was not seen. 如果地球运动，应该有视差，但没看到。

Issues of Ancient Astronomy (II) 古天文的问题 The retrograde 退行 (westward) motion of the planets 行星相对于背景星空（天球）退行的现象 The “solution”: Epicycles! “解决办法”：本轮

Introduced by Ptolemy 托勒密 (ca. A.D. 140) The Ptolemaic system was considered the “standard model” of the universe until the Copernican Revolution. 在哥白尼革命之前，托勒密系统一直是标准模型

The Copernican Revolution 哥白尼革命 Nicolaus Copernicus (1473 – 1543): heliocentric universe 日心宇宙 (sun in the center)

哥白尼对行星退行现象的新的、正确的解释: 当地球超越行星时，产生退行现象 This made Ptolemy’s epicycles unnecessary 这样，本轮就没必要.

哥白尼对行星退行现象的新的、正确的解释: 2005.7－2006.2 火星

Tycho Brahe第谷·布拉赫 (1546 – 1601) Use of high-precision instruments for precise astronomical observations, reported in tables. 利用精密仪器的精确的天文观测的开端 Later used by Kepler 开普勒 to develop laws of planetary motion. 后来，开普勒利用这些数据找到了行星运动规律

A Quadrant designed by Brahe Used to precisely measure an object’s angular distance above the horizon 精确测量天体距地平线的角度。

Johannes Kepler开普勒 (1571 – 1630) 利用第谷·布拉赫的精确测量结果，用数学方法研究行星的运动， 发现了一致性，如果 放弃 Circular motion（圆周运动） Uniform motion（匀速运动）. Planets move around the sun on elliptical paths, with non-uniform velocities （行星绕太阳是椭圆轨道、非匀速运动）.

Kepler’s Laws of Planetary Motion 开普勒行星运动定律 The orbits of the planets are ellipses with the sun at one focus （轨道是椭圆，太阳在一个焦点上。） c Eccentricity椭率 e = c/a e的大小在0和1之间

Eccentricities of Ellipses椭圆的椭率 1) 2) 3) e = 0.02 e = 0.1 e = 0.2 5) 4) e = 0.4 e = 0.6

Eccentricities of planetary orbits 行星轨道和圆几乎无法区分。 最极端的例子: 冥王星: e = 0.248 地球: e = 0.0167 看着象圆，但中心可能偏离太阳很远。

行星和太阳的连线在相同的时间里扫过的面积相同 行星和太阳的连线在相同的时间里扫过的面积相同 行星轨道周期的平方正比于它到太阳距离的三次方: Pyear2 = aAU3 (Py = period周期, 单位年; aAU = distance距离, 单位AU)

例子：火星离太阳的平均距离是1.52AU，它的公转周期是多长？ P2 ＝ 1.523 ＝ 3.51 P = 1.87（年） 冥王星：a=39.44AU, P=247.7years 247.72 = 39.443 61355 ~ 61349 行星轨道周期的平方正比于它到太阳距离的三次方: Pyear2 = aAU3 (Py = period周期, 单位年; aAU = distance距离, 单位AU)

Galileo伽利略 Galilei (1594 – 1642) 1、引入了现代科学的观点，从以信仰为基础的科学，到以观测为基础的科学。 2、极大地改进了新发明的望远镜（但伽利略并没有发明望远镜） 3、第一个精确报告了用望远镜观测的天空，支持哥白尼的宇宙模型。

Major discoveries of Galileo (I): 伽利略的主要发现 Moons of Jupiter 木星的卫星 (4 Galilean moons) Rings of Saturn土星环 (What he really saw)

Major discoveries of Galileo (II): 伽利略的主要发现 sunspots 太阳黑子 (proving that the sun is not perfect!) 证明太阳不是完美的！

Major discoveries of Galileo (III): 伽利略的主要发现 Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not Earth! 观测到金星位相，证明金星绕太阳，而不是地球。

Historical Overview

Isaac Newton牛顿 (1643 - 1727) Major achievements: Building on the results of Galileo and Kepler Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: Invented calculus微积分 as a necessary tool to solve mathematical problems related to motion Discovered the three laws of motion运动定律 Discovered the universal law of mutual gravitation引力

The Universal Law of Gravity万有引力 Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance: Mm F = - G r2 (G is the gravitational constant 引力常数.)

Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons: Example: Dv Earth and moon attract each other through gravitation. v v’ Since Earth is much more massive than the moon , the moon’s effect on Earth is small. Moon F Earth’s gravitational force constantly accelerates the moon towards Earth. Earth This acceleration is constantly changing the moon’s direction of motion, holding it on its almost circular orbit.

Orbital Motion (II) In order to stay on a closed orbit, an object has to be within a certain range of velocities: 在闭合轨道上运动，物体运动必须在一定的速度范围内。 Too slow : Object falls back down to Earth Too fast : Object escapes the Earth’s gravity

轨道运动 Geosynchronous Orbits 地球同步轨道 轨道运动 Geosynchronous Orbits 地球同步轨道 轨道速度仅与轨道高度和中心体（地球）质量有关，与卫星（月亮或人造卫星）质量无关。太阳系也一样。

源于月球对地球上水的引力不同。近点引力大，远点引力小。 The Tides潮汐 源于月球对地球上水的引力不同。近点引力大，远点引力小。 同一地点，每天两次大潮，周期12个小时 月亮的影响远大于太阳

潮汐的增强和减弱 太阳的潮汐作用只有月亮的一半。叠加起来，可以增强或减弱潮汐。