ans

2. Key Figures and Their Contributions

Ptolemy (2nd Century CE)

EN: Developed the most influential geocentric model of antiquity, using deferents and epicycles to predict planetary positions (especially retrograde motion). His system, recorded in works like the Almagest, dominated Western astronomy for over a millennium.

中文： 托勒密建立了古代最有影响力的地心模型，用*本轮与均轮（epicycle & deferent）*来解释并预测行星位置（尤其是逆行）。其体系（如《天文学大成》）主导西方天文学逾千年。

Nicolaus Copernicus (1473–1543)

EN: Proposed a heliocentric system in which Earth is a planet orbiting the Sun; this explains retrograde motion as an apparent effect when Earth overtakes another planet. He retained circular orbits, but his model fundamentally challenged Church-backed geocentrism.

中文： 哥白尼提出日心体系：地球也是绕太阳运行的行星；行星“逆行”是地球追越外行星造成的视运动。虽仍坚持圆轨道，但其理论从根本上挑战了教会支持的地心说。

Tycho Brahe (1546–1601)

EN: Produced the most precise pre-telescope astronomical observations of his era, creating data accurate enough to expose errors in circular-orbit models. His measurements of Mars were crucial for Kepler’s discoveries. (He also proposed a geoheliocentric “Tychonic” system.)

中文： 第谷·布拉赫在望远镜发明前做出了当时最精确的观测数据，精度足以暴露“圆轨道”理论的误差。他对火星的长期观测是开普勒发现行星定律的关键基础。（他也提出过“第谷体系”的地—日混合模型。）

Galileo Galilei (1564–1642)

EN: Used the telescope to gather decisive evidence against the old cosmos: the moons of Jupiter, phases of Venus, and imperfections like mountains on the Moon and sunspots. These observations strongly supported heliocentrism and the idea that “heaven” obeys physical laws like Earth.

中文： 伽利略用望远镜获得关键证据：木星卫星、金星盈亏，以及月面山脉、太阳黑子等“天界并不完美”的事实。这些观测强力支持日心说，并推动“天与地受同一物理规律支配”的观念。

3. Kepler’s Three Laws of Planetary Motion

The Law of Ellipses

EN: Planets move in elliptical orbits, with the Sun at one focus of the ellipse.

中文： 行星绕太阳运行的轨道是椭圆，太阳位于椭圆的一个焦点上。

The Law of Equal Areas

EN: A line joining a planet and the Sun sweeps out equal areas in equal times (so a planet moves faster near perihelion and slower near aphelion).

中文： 行星与太阳连线在相等时间内扫过的面积相等（因此行星近日点更快、远日点更慢）。

The Law of Harmonies

EN: The square of a planet’s orbital period is proportional to the cube of its average distance (semi-major axis) from the Sun: P² ∝ a³.

中文： 行星公转周期的平方与其到太阳平均距离（半长轴）的立方成正比：P² ∝ a³。

4. Key Concepts & Terms

Geocentric Model

EN: An Earth-centered model in which the Sun, Moon, planets, and stars revolve around Earth.

中文： 地心模型：认为太阳、月亮、行星与恒星都绕地球转。

Heliocentric Model

EN: A Sun-centered model in which Earth and the other planets revolve around the Sun.

中文： 日心模型：认为地球和其他行星都绕太阳转。

Retrograde Motion

EN: The apparent backward motion of a planet against the background stars, caused by changing viewing geometry (e.g., Earth overtaking an outer planet).

中文： 逆行：行星相对恒星背景出现的“向后走”的视运动，源于观测几何变化（如地球追越外行星）。

Epicycle & Deferent

EN: In the Ptolemaic system, a planet moves on a small circle (epicycle) whose center moves along a larger circle (deferent) around Earth, producing retrograde loops.

中文： 在托勒密体系中，行星在小圆（本轮）上运动，本轮中心又沿大圆（均轮）绕地球转，从而产生逆行“回环”。

Ellipse

EN: An oval-shaped curve in which the sum of distances from any point on the curve to two fixed points (the foci) is constant.

中文： 椭圆：一种卵形曲线，曲线上任一点到两个定点（焦点）的距离之和为常数。

Focus (pl. Foci)

EN: One of the two fixed points that define an ellipse; in planetary orbits, the Sun lies at one focus.

中文： 焦点：定义椭圆的两个定点之一；在行星轨道中，太阳位于其中一个焦点。

Astrology vs. Astronomy

EN: Astronomy is a scientific study of celestial objects and the laws governing them; astrology claims (without solid evidence) that celestial positions influence human personality and fate.

中文：****天文学是研究天体及其规律的科学；占星术则声称天体位置会影响人的命运与性格，但缺乏可靠证据，属于伪科学。

5. How has this chapter shaped or reshaped your understanding of science?

EN (sample response):

This chapter shows that science advances when careful observation meets courageous reasoning. It highlights how precise data (like Tycho’s) can force thinkers (like Kepler) to abandon elegant but incorrect beliefs, and how mathematical laws can reveal deep order behind confusing appearances. It also reshaped my view of science as a collaborative, international process that progresses by testing claims against evidence, distinguishing reliable knowledge (astronomy) from unsupported belief (astrology).

中文（参考翻译）：

这一章让我看到科学的推进来自“严谨观测”与“勇敢推理”的结合。它强调精确数据（如第谷的观测）如何迫使思想家（如开普勒）放弃优美但错误的观念，并说明数学定律能在表面混乱的现象背后揭示深层秩序。它也让我更清楚地理解：科学是一种跨文化协作的过程，核心在于用证据检验主张，并区分可靠知识（天文学）与缺乏证据的信念（占星术）。