הלכה על ראש השנה 49:10

All astronomers agree that the lunar month begins at the moment when the moon and the sun are in conjunction in the same longitude. This is what our Rabbis called the “molad ” (birth, i.e., new moon). Our scholars calculated it for the mean orbit,³ This figure is given in the Talmud: 29 days, 12 hours, and 793 halaqim (Rosh haShana 25a), or 29 days, 12 hours, 44 minutes, and 3 and ⅓ seconds, approximately 29.5306 days. Such a month is known as a “synodic month” and is defined as the mean time between new moons. The current approximation for a synodic month is 29 days, 12 hours, 44 minutes, and 2.7 seconds, or 29.5306 days. and all astronomers did the same. Then they adjusted it.⁴ “Mean conjunction” is conjunction of the sun and the moon relative to their individual spheres. However, since the moon’s sphere, the sun’s sphere, and the earth are not concentric, conjunction relative to the zodiacal sphere may differ from conjunction relative to the individual spheres. Conjunction relative to the zodiacal sphere is called “true conjunction.” Thus our Rabbis, their memory should be a blessing, said: “Sometimes it comes by a long path and sometimes it comes by a short path” (Rosh haShanah 25a). Since conjunction involves two bodies, we must know with regard to each one when it is a long path or a short path. Sometimes both are long, or both short, or the sun long and the moon short, or vice versa. Also, sometimes the length or shortness is small, sometimes large, to the extent that the length or the shortness may be as much as thirteen hours. Thus at times there is a difference between our calculation of conjunction and true conjunction of these many hours, either earlier or later.