Is Hanukkah’s new moon always the darkest one?

My second child was born on the day of the new moon, closest to the winter solstice, in the darkest year in recent memory (that is, 2020). I remember there was a new moon because there was a solar eclipse that day.

In the year of her birth, her birthday fell during Hanukkah. Maybe the new moon that falls during Hanukkah – Rosh Chodesh Tevet – is always the new moon closest to the winter solstice?

Basic information about the Hebrew calendar that’s relevant for this post:

  • a year in the Hebrew calendar consists of 12 or 13 months – 12 in “common” years and 13 in leap years. Leap years are 7 years out of 19, following the Metonic cycle.
  • in theory these months start at the new moon;
  • but the beginning of the year can be postponed (not preponed) so that, for example, Yom Kippur (the tenth day of the year) doesn’t fall on a Friday or Sunday – the exact circumstances under which those adjustments are made are beyond the scope of this post;
  • the months alternate between 29 and 30 days, with the odd months having 30 and the even months having 29, summing to 59 x 6 = 354… except that if things work out so that the year should be lengthened by a day.then the second month (Cheshvan) is 30 days, and if they work out so that the year should be shortened by a day then the third month (Kislev) is 29 days.

So Hanukkah starts on the 25th of (the third month) Kislev, and ends on the 2nd or 3rd of (the fourth month) Tevet. Rosh Chodesh Tevet, the first day of the fourth month, is either the sixth night of Hanukkah (if Kislev is short) or the seventh (if Kislev is long).

To answer the original question – no, this post follows Betteridge’s law. Thinking through the theory:

  • Passover is always the first full moon after the spring equinox, so between 0 and 1 lunar months after the equinox
  • from Passover (15 Nisan, year N) to the following Rosh Chodesh Tevet (1 Tevet, year N+1) is 8.5 lunar months
  • so from the spring equinox to Rosh Chodesh Tevet is 8.5 to 9.5 lunar months
  • but from the spring equinox to the following winter solstice is 9 solar months (that is, three-quarters of a year), or about 9 x 235/228 = 9.28 lunar months – the 235 comes from the Metonic cycle embedded in the calendar, in which there are seven leap years out of 19.
  • so the new moon closest to the winter solstice is between 8.78 and 9.78 lunar months after the winter solstice‚Ķ so it’s usually Rosh Chodesh Tevet (i. e. the new moon during Hanukkah) but not always.

Alternately, it was a big deal when Thanksgivukkah happened in 2013, when the first day of Hanukkah fell on Thanksgiving, November 28, 2013 (the first night of Hanukkah was the night before). That proves that Rosh Chodesh Tevet can be at least as early as December 4 (if Kislev is long), which is about 17 days short of the winter solstice, more than half a lunar month – and remember that typically the Hebrew month begins after the new moon. In fact, in the winter of 2013-14:

Similarly, one might guess that Rosh Hashanah is the new moon closest to the fall equinox… but by the same sort of argument it should be 5.5 to 6.5 lunar months after the spring equinox, and you need it to be six solar months, so it doesn’t always work out. I have heard it said that it’s a good thing Yom Kippur, on which the observant fast from sunset to sunset, falls at the time of year when the days are getting shorter the fastest.