Halakhah for Rosh Hashanah 16:9

The Jubilee is “seven sabbaths of years” (Leviticus 25:8). The Jubilee begins on the Day of Atonement, as it is written “on the Day of Atonement you shall pass a Shofar throughout your land and sanctify the fiftieth year” (ibid. 25:9–10). So the beginning of the Sabbatical year is like the beginning of the Jubilee year. Do not be puzzled that the year did not begin with the Day of Remembrance (Rosh haShanah, the first of Tishre). For if we should calculate that the first of Nisan was exactly on the vernal equinox, then the true third season (autumn) needs to add approximately ten days, the excess of the the solar year over the lunar year.¹⁰² Spring and summer together comprise 187 days (see note 52), while six lunar months consist of 6 ׳ 29.5 = 177 days. Therefore, we must add 10 days to the six months from Nisan until Tishre for the beginning of autumn. This turns out to be close to the difference between a solar year (365 days) and a standard lunar year (354 days). Also, since the sun’s movement is slow.¹⁰³ The sun’s movement appears slower near its apogee, which is during the summer (see note 49). Therefore the year begins with the Day of Atonement or Tabernacles.