1,288. Equinoxes and Solstices

Hilchos Kiddush HaChodesh 9:3

The Nisan (i.e., vernal) equinox occurs at the hour and chalak that the sun enters the constellation of Aries. The Tammuz (summer) solstice occurs when the sun is in the beginning of Cancer. The Tishrei (autumnal) equinox occurs at the hour and chalak that the sun enters Libra. The Teves (winter) solstice occurs when the sun is in the beginning of Capricorn. Using these calculations, we see that the vernal equinox in the year of creation occurred seven days, nine hours, 642 chalakim before the molad of Nisan (7, 9, 642).

Hilchos Kiddush HaChodesh 9:4

The way to calculate the seasons is as follows. First, one must calculate how many 19-year cycles have passed until the cycle in question. Next, one adds one hour and 485 chalakim for each cycle that has passed. One then regroups chalakim into hours and hours into days. From the total, one subtracts seven days, nine hours, 642 chalakim. To this, one adds the time remaining until the molad of Nisan in the first year of the cycle in question. This will yield the hour and the date of the vernal equinox for the first year of the cycle. From there, one can calculate all subsequent seasons by adding 91 days, seven and a half hours per season.

To calculate the vernal equinox of a given year within a cycle, add one hour and 485 chalakim for each cycle. For every whole year of the cycle in question that has passed, add ten days, 21 hours, 204 chalakim. Regroup the result (chalakim into hours, hours into days, as above). Next, subtract seven days, nine hours, 642 chalakim and divide the result into lunar months of 29 days, 12 hours and 793 chalakim each. What remains beyond these lunar months is added to the molad of Nisan for the year in question. This will yield the date and the time of the vernal equinox for the year in question. Based on these calculations, the vernal equinox always occurs at sundown, midnight, sunrise or noon; the summer solstice always occurs at either seven and a half hours or at one and a half hours, either by day or by night. The autumnal equinox always occurs at nine hours or at three hours, either by day or by night; the winter solstice always occurs at ten and a half hours or at four and a half hours, either by day or by night. To calculate the day and hour of the equinox, count the number of whole years that have passed from creation until the year in question, then divide them into groups of 28, adding one day and six hours for each year remaining. [The years are divided into groups of 28 because every 28 years the equinox occurs on the same day and at the same hour as it did the very first time. For this reason, Birkas HaChamah – the blessing on the sun – is recited every 28 years.] After adding the hours and days, three days are added to the total. Divide the days into groups of seven then add the remaining days and hours to the start of Saturday night (i.e., at the start of the first day). This will yield the day and time of the vernal equinox. The reason three days are added is because the very first vernal equinox of creation occurred on a Tuesday night (i.e., at the start of the fourth day). We will see this process applied in the next halacha.