The Solar System | 太阳系

📚 The Solar System | 太阳系

Mathematics is the language of the universe. The Solar System provides a magnificent classroom for applying mathematical ideas, from standard form to geometry and trigonometry. In this article, we will explore the mathematics behind the planets, orbits, and distances in our cosmic neighbourhood.

数学是宇宙的语言。太阳系为我们提供了一个绝佳的课堂，让我们能够应用从科学计数法到几何与三角的数学思想。在这篇文章中，我们将探索行星、轨道以及我们宇宙家园中距离背后的数学。

1. Distances in the Solar System and Standard Form | 太阳系中的距离与科学计数法

The distances between planets and the Sun are enormous. To handle them, we use scientific notation (standard form). For example, 1 AU (astronomical unit) is about 1.496 × 10⁸ km, and Neptune is about 30.1 AU from the Sun.

行星与太阳之间的距离十分巨大。为了处理这些数值，我们使用科学计数法（标准形式）。例如，1天文单位（AU）约为1.496 × 10⁸ km，而海王星距离太阳约30.1 AU。

• Earth to Sun: 1 AU ≈ 1.496 × 10⁸ km
• Jupiter to Sun: 5.20 AU ≈ 7.78 × 10⁸ km
• Saturn to Sun: 9.58 AU ≈ 1.43 × 10⁹ km

When we multiply or divide numbers in standard form, we use the laws of indices. For instance, the ratio of Saturn’s distance to Earth’s distance is 9.58 : 1.

当我们对标准形式的数字进行乘除运算时，需要使用指数法则。例如，土星与地球到太阳距离之比为9.58 : 1。

2. Ratios and Proportions of Planetary Orbits | 行星轨道的比率与比例

Ratios help us compare the sizes of planets. If Earth’s radius is taken as 1 unit, Jupiter’s radius is about 11.2 units. Thus the ratio of Jupiter’s volume to Earth’s volume is not 11.2 : 1, but much larger because volume scales with the cube of the radius.

比率帮助我们比较行星的大小。如果把地球半径看作1个单位，木星半径约为11.2个单位。因此，木星与地球的体积之比不是11.2 : 1，而是大得多，因为体积与半径的立方成正比。

V ∝ r³

If r increases by a factor of k, then V increases by a factor

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）