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To compensate for this drift, the Jewish calendar uses a 12-month lunar calendar with an extra month occasionally added.
The month of Nissan occurs 11 days earlier each year for two or three years, and then jumps forward 30 days, balancing out the drift.
Years are either 12 or 13 months, corresponding to the 12.4 month solar cycle.
The lunar month on the Jewish calendar begins when the first sliver of moon becomes visible after the dark of the moon.
For a fascinating (albeit somewhat defensive) article by a nuclear physicist showing how Einstein's Theory of Relativity sheds light on the correspondence between the Torah's age of the universe and the age ascertained by science, see The Age of the Universe. The names are actually Babylonian month names, brought back to Israel by the returning exiles.
These three phenomena are independent of each other, so there is no direct correlation between them.
On average, the moon revolves around the Earth in about 29½ days.
The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.
The civil calendar used by most of the world has abandoned any correlation between the moon cycles and the month, arbitrarily setting the length of months to 28, 30 or 31 days.