Mathematics of the Jewish Calendar/The prayer for rain and the blessing of the sun

The prayer for rain and the blessing of the sun

Two Jewish rituals appear to be fixed by the civil calendar rather than the Jewish calendar. These are the insertion of the words Tal umatar ("dew and rain") in the Amidah prayer recited three times every day, and the Blessing of the Sun made every 28 years. The former is done every day "from Ma'ariv (evening service) on 4th December (and in years preceding a civil leap year, 5th December)" up to and including Erev Pesach. The latter is done on 8th April. What is special about those rituals?

The reason is that they are fixed by reference to the tekufot (solstices and equinoxes). These are calculated from rules due to Rabbi Mar Samuel (3rd century CE). They assume that the length of the year is always 365¼ days, rather than varying between 12 and 13 lunar months, hence the fixed dates in the Gregorian calendar. Of course, 365¼ days is slightly too long (the same as the error in the Julian calendar). Thus the date for starting Tal umatar and for saying the Blessing of the Sun in the 20th and 21st centuries are both a day later than they were in the 19th century, and they will get later in the Gregorian calendar by three days every four centuries.

The date of Tal umatar
In Israel, this prayer is said from 7th Cheshvan, following the Jewish calendar (following the ruling of Rabban Gamliel, Mishnah Ta'anit 1:3). However, the Gemara on that Mishnah (Ta'anit 10a) says that outside Israel, it should not be said until the 60th day from Tekufat Tishri (the autumnal equinox).

The date of the Blessing of the Sun
Mar Samuel said that the world was created in Nisan. Every 28 years by his calculation, the Spring equinox falls on a Wednesday as it did at the time of creation. There is a custom to say a blessing on the Sun when this happens, "... who makes the work of creation". This contradicts the tradition of BeHaRaD, which assumes that the world was created in Tishri, or to be precise at the end of Ellul. Following this view, the Rosh Hashana prayers include the phrase: "the World was created today".

The same date is used both inside and outside Israel.