如何用R绘制太阳、地球、月亮的运行轨迹。 最初的动机有三个，1）要向两岁的澹澹展示星球的运动，2） 嫦娥5号登月背给人家解释月球自转， 3）数学推理中国农历。暂时都是根据已知的星球周期和轨道特征绘制的图，写好了R代码，就发布到CRAN让大家使用。 因为澹澹还喜欢那首歌“The wheels on the bus go round and round”，所以开发包的名字就叫“RoundAndRound"。

等我研究研究天体力学，就发布一个具有物理意义的天体运行算法的R开发包。

先发简单的二维版本绘制的内容。  博文同时在我的英文博客发布，leleshu.wordpress.com.

I planed to write an R package and submit on CRAN, that can plot the planets orbiting in Solar System, or satellite/moon orbiting around earth. That package must plot the moving planets, the moon, moon phase and satellite in 2D or 3D canvas. In future, it may calculate the orbit based on orbit mechanics.

My son loves the song “The wheels on the bus go round and round“, and he has an obsession on planets. He asks mommy play the solar system documentary every night when we ask him to brush his teeth.  So I decided to plot the moving planets in solar system for him with the scientific knowledge I know.

Another motivation is from the Chinese lunar exploration, Chang-E 5 landing on far-side of the moon.  Lots of people discussed it and were fuddled on the rotation of moon and relation between the earth and the moon.

Furthermore, I kept thinking the Chinese semi-lunar calendar for many years, I know the founder mental logic and algorithm of the calendar in my mind, but never scratched the equations and numbers in paper yet.  This calendar is determined by the moon phase and the position of the earth in orbit. Definitely the solver in papers are more rousted in my brain.

Let’s see what I got, by now.

The idea of the Moon and the Sun are moving around the Earth, when we assume the earth is the center of system. The orbital period of the moon is 27.321 day, but the synodic period is 29.53 day, that because the sun moves 27.321/365.25 in its sun’s orbit when the moon moves in the moon’s orbit. It requires 2.2 days to let the sun and the moon to face-to-face again.

The position of the Moon and the Sun in an earth year (365 day). The right legend shows the moon phase in 30 days. The concentric orbits are numbers of the moon periods.

They are so beautiful, aren’t they

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贴一个中文版的图。

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