What is the value of the elongation when the Moons age is one day?
It varies, depending on several factors: (1) The elongation at New Moon. The Moon can pass directly in front of the Sun at New Moon (when a solar eclipse will occur) or can pass as far as five degrees away. That is, the Moon can start the month with an elongation ranging from zero to five degrees. A minor complicating factor involves the definition of New Moon in the almanacs. Astronomical New Moon is defined to occur when the Sun and Moon have the same geocentric ecliptic longitude, which may not occur precisely when the Sun and Moon are closest together in the sky. (2) The speed of the Moon in its orbit. The Moon’s orbit is elliptical, and its speed is greatest when it is near perigee, least near apogee. If perigee occurs near New Moon, the Moon will appear to be moving away from the Sun in the sky at a greater than average rate. (3) The distance of the Moon. Again, because of its elliptical orbit, the distance of the Moon varies, so even if the Moon moved with a constant speed, its