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历法的置闰原理

天象观星 昌达空间 1851℃ 0评论

阳历及闰年
  阳历是当今国际通用的历法,也叫公历。
  阳历依据地球绕太阳转一周的时间,定为一年。地球绕太阳转一周,叫一个回归年,总长度365.2422天,也就是365天5小时48分46秒。
  阳历规定一年12个月。其中,1、3、5、7、8、10、12为大月,每月31天;4、6、9、11为小月,每月30天;平年的2月28天,闰年2月29天。
  我们习惯以整数365天作为一年。事实上,从1月1日,到12月31日,日历撕完了,地球还没有围着太阳绕完一圈,还差一些尾数。就是说,阳历一年,差的尾数是5小时48分46秒。四年,就差了5小时48分46秒×4=23小时15分4秒,接近一整天。因此,人们规定:第一年、第二年、第三年都是365天,叫平年;第四年366天,叫闰年。闰年多出来的一天放在2月里。所以,阳历的平年的2月是28天,闰年的2月是29天。多出来的这一天,也叫闰日。
  为了计算简便,人们规定:4年一闰,公元年数凡是能被4除尽的,就是闰年。
  然而,新的问题又来了。4年积累的多余时间,只有23小时15分4秒,闰年加了一天之后,又少了44分56秒,相当于0.0312天。时间一长,这一不足就凸显出来了。
  于是,每4年有一个闰年,但在400年必须减去3个闰年。规定逢百年份的最后一年不设闰年。例如,2100年、2200年、2300年等等,虽然能被4除尽,也不算作闰年。只有逢百的年份既能被4除尽,也能被400除尽,例如,2000年、2400年、2800年,才算做闰年。
  这样,每4个逢百年份中只有一个闰年,其余3个就不是闰年。因为4年少0.0312天,隔了400年就少了3.12天。即使如此,400年仍然产生0.12天的误差。

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农历及闰年
  所谓的农历,实际就是阴历和阳历的结合历。它不但要观察月亮的运转轨迹,又要察看太阳的视位置。
  月亮运行绕地球一圈,大约29天。29天内,恰好是月亮盈亏的整个过程。
  地球绕太阳一圈,大约365天。太阳视位置不同,地球气温就不同,节气也跟着交替变化。这也是一年二十四节气的来由。
  农历,对于老百姓日常的生活和劳动,帮助是很大的。但也比较复杂。
  地球围着太阳转一圈,是一个回归年,总长度为365.2422日;365.2422÷12个月=30.43685(一个月的天数)
  月亮围着地球转一圈,是一个朔望月,长度为29.5306日。12个月×29.5306天=354.3672天(一年的日数)。两者相差将近11天。
  一年相差11天,三年就相差33天,十年就相差330天,这就出现天时与历法不合的怪现象。
  农历置闰,就是为了弥补月亮和太阳运行的时间差。那么,如何弥补呢?
  为了有效地协调太阳和月亮的运行时间,使他们统一起来,我们祖先找出了“闰月”的办法。累积三年,相差33天,只有逢三年设置一个闰年。然而,农历的大月只有30天,小月才29天,闰年之后仍然还余3天无法安排。
  最好的办法是,求出回归年日数与朔望月的日数的最小公倍数。我们希望,m个回归年的天数与n个朔望月的天数相等,等式如下:
  m×365.2422=n×29.5306
  在这个等式中,不能直接求出m和n,但可以求出它们比例的大约值,即:
  m/n=1/12 2/25 5/37 8/99 11/136 19/235
  在这些分式中,分子表示回归年的数目,分母表示朔望月的数目。例如,第六个分数式表示19个回归年中必须加7个闰月。
  19个回归年中加7个闰月的结果比较:
  19个回归年=19×365.2422=6939.6018(天)
  一个朔望月有29.5306天,235个朔望月=235×29.5306=6939.6910(天)
  19个回归年中加7个闰月后,只差:6939.6910-6939.6018=0.0892(天),即2小时9分多,这已经够精确的了。
  所以,农历采用了19年加7个闰月的办法,即“十九年七闰法”。这样,春节总是在冬末春初。月亮最圆的时候,总是在十五。
  具体在哪个月份置闰,这与太阳视位置有关。
  在两个冬至之间,仅有12个月则不置闰。若有13个月,即置闰。置闰的月从“冬至”开始,当出现第一个没有“中气”的月份,就在这个月置闰。由此得知,中气决定了农历在哪个月置闰。
  二十四节气在农历中是逐月推迟的,于是有的农历月份,中气落在月末,下个月就没有中气。
  一般每过两年多就有一个没有中气的月,这正好和需要加闰月的年头相符。所以农历规定,把没有中气的那个月作为闰月。

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