1,289. Calculating Seasons Forever

Hilchos Kiddush HaChodesh 9:5

Based on the instructions given in the previous halacha, if one wants to know the day and time of the vernal equinox for the year 4930 from creation, divide 4930 by 28; this leaves one year left over, which gives us the result of one day and six hours. By adding three days to this, we see that the vernal equinox will occur at midnight on the night of the fifth day (i.e., the midnight in between Wednesday and Thursday). By adding seven and a half hours to this figure, we calculate that the summer solstice will occur on Thursday, an hour and a half into the day. By adding seven and a half hours to that, we see that the autumnal equinox will occur on Friday at nine hours of the day. By adding seven and a half hours to that, we see that the winter solstice will occur on the night of the sixth day (i.e., Thursday night), four and a half hours into the night. By adding seven and a half hours to this, we see that the vernal equinox of the next year will occur at the start of the day on Friday. In this way, one could calculate the seasons forever.

Hilchos Kiddush HaChodesh 9:6

If one wants to know the day of the month on which the vernal equinox will occur in the current year, one must first figure out the day of the week on which it will occur. Next, one calculates the day of the week that will be Rosh Chodesh Nisan and how many complete years of the current 19-year cycle have passed. One adds 11 days for each of these years, and then add seven days to the total. This number is then divided by 30, from which one counts the days remaining from Rosh Chodesh Nisan. If the resulting date is the same as the day of the week on which the equinox is already known to occur, you’re done. Otherwise, add one, two or three days to reach the day of the week on which the equinox will occur. If the year is a leap year, start counting from Rosh Chodesh of Adar II. When a day is calculated by using this process, that’s the date on which the equinox will occur.