從圓到橢圓：克卜勒行星定律的排序與軌道圖像之探討

From Circular to Elliptical: Exploring the Sequence and Related Illustrations of Kepler's Laws of Planetary Motion

邱韻如(Yun-Ju Chiu)

《物理教育學刊》 20卷1期 (2019/07) Pp. 1-13

https://doi.org/10.6212/CPE.201907_20(1).0001

摘要

克卜勒三大定律是物理課程重要的概念之一。在發展的過程中，克卜勒是先確定等時間掃過等面積的第二定律之後，才發現火星軌道其實是橢圓的，和目前教科書上的順序顛倒，也就是說，現行教科書把後發現的橢圓律稱為第一定律，先發現的面積律稱為第二定律。除了順序問題之外，在陳述克卜勒前兩定律時，為強調行星軌道是橢圓的，絕大部分的物理教科書所畫的橢圓軌道，離心率大都超過0.5以上，甚至是高達0.8的長橢圓，導致許多學生誤以為太陽系行星的軌道都是長橢圓。另一方面，講到第三定律時，許多教科書把軌道畫成圓的，但卻以哈雷彗星為例來說明此定律。本研究從科學典籍與圖像出發，探討教科書的繪圖表徵所引起的迷思概念，提出其對物理教與學的影響及相關問題。從三方面來探討：（一）從古希臘到十七世紀，行星軌道從圓到橢圓的演變歷程及其圖像表徵。（二）從克卜勒前兩定律的順序被翻轉，探討教科書的物理定律陳述與實際歷史發展之歧異。（三）從教科書中與橢圓軌道相關的繪圖表徵及其相關的迷思概念，提出適切的教學表徵教學建議。

關鍵字

橢圓軌道 ； 科學史 ； 科學圖像表徵 ； 迷思概念 ； 教科書

並列摘要

Kepler's three laws of planetary motion proposed in 1600s are famous and important in physics course. However, the sequence of the first two laws in physics textbooks is in reverse order, different from their historical context. The second law, about the equal area in the same time interval, was in fact arrived first. Then, Kepler found the orbit an ellipse, which is now called the first law. Additionally, most textbooks emphatically point out that planetary orbits are elliptical in the first two laws and illustrate elliptical orbits of large eccentricity to strengthen the concept. These exaggerated illustrations lead students to mistake that most planetary orbits are long ellipses. Actually, very different from the illustrations of elliptical orbits in textbooks, most planetary orbits are nearly circular. On the other hand, textbooks usually use circular orbits to state the third law. In an odd way, some textbooks use the orbit of Comet Halley as an example to interpret the third law. The aim of this study is to bring forth some enlightenment of teaching and learning from exploring the representation of improper scientific illustrations and related misconceptions on the concept of ellipse and the elliptic orbits. The study will discuss from several aspects:(1) to understand the historical development and the graphical representations about planetary orbits from ancient Greece to 17th century; (2) to explore the disambiguation between the sequence of the first two laws and their historical context; (3) to find out some improper illustrations from the modern textbooks and then design some questionnaires to probe further related misconceptions.

並列關鍵字

elliptical orbit ； history of science ； representation of scientific illustrations ； misconception ； textbooks