“月上柳梢头”天文现象的数学建模

Mathematical Modeling of Astronomical Phenomenon “Moon on the Willow Head”

研究著名诗句"月上柳梢头,人约黄昏后"所蕴含的天文现象。按太阳高度角定义"黄昏后"的时间段,利用天文学知识得到该时段的数学运算模型;引入与月亮有关的天文参数,建立月亮高度角的计算公式;计算出诗人写诗当日"黄昏后"时段所对应的月亮高度角范围,以此定义"月上柳梢头";对于北京及其他地区,利用所建模型计算黄昏后的月亮高度角,并依据"月上柳梢头"的定义进行筛选,得到"月上柳梢头,人约黄昏后"这一情景的发生日期与时间段。

This paper studies the astronomical phenomenon contained in the famous poem ＂moon on the willow head and people liaison after dusk＂. According to solar elevation angle to define ＂after dusk＂ period, the mathematical model of the period is obtained by using the knowledge of astronomy. The astronomical parameters related to the moon are introduced and the calculation formula of moon elevation angle is established. The range of the moon elevation angle is calculated in the corresponding ＂after dusk＂ period of the day when the poet wrote the poem, to determine ＂moon on the willow head＂. For the Beijing and other regions, the model is used to calculate the moon elevation angles after dusk and on the basis of the definition of ＂moon on willow head＂ the angles are selected, then the date and the period of the scene ＂moon on the willow head and people liaison after dusk＂ are obtained.