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When researching an article on Chinese New Year I found a few websites that predict the dates of Chinese New Year (CNY) tens - or sometimes even hundreds - of years in advance. I´m wondering how many years in advance the date of CNY can be predicted.

As the date of CNY is based on the phases of the moon, my question is:

Up to how many years in advance can the dates of new moon be predicted with 100% accuracy?

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There isn't any 100% accuracy in the real world. But if you want to be sure that the error is less than 12 hours, half a day, it's almost surely at least millions of years in advance. Those things are obeying Newton's equations rather meticulously and the dependence on detailed initial conditions is limited because of the approximate periodicity of all the processes. Even with Newton's mechanics, it would be lots and lots of thousands of years, and even before Newton's mechanics was known, astronomers knew quite something that allowed them to predict such things for millenniums rather well. – Luboš Motl Nov 28 '12 at 9:45
up vote 5 down vote accepted

According to this paper the Sun-Earth-Moon system is predictable for about 50Ma.

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