Strictly speaking, the months appearing in a Tibetan almanac, called by us Tibetan calendar months, are not the same as lunar or synodic months ( " tshes zla " ), which can begin and end at any time of day.
42.
This allows the calculation of 12, 24, 36, 48, 54 and 57 synodic months in the lunar system and of 12, 18, 24, 36, 48, 54 and 57 sun months ( i . e . twelfths of a tropical year ).
43.
We need to approximate this ratio by common fractions : the numerators and denominators then give the multiples of the two periods draconic and synodic months that ( approximately ) span the same amount of time, representing an eclipse cycle.
44.
He argued that Naburimannu developed the Babylonian System A of calculating solar system ephemerides, and that later Kidinnu developed the Babylonian System B . A Greco-Roman tradition, mentioned above, attributes to Kidinnu the discovery that 251 synodic months equals 269 anomalistic months.
45.
The period of the mean synodic month can be approximated as 29 + 26 / 49 days ( a more accurate vulgar fraction is 29 + 451 / 850; the Hebrew calendar uses 29 + 12 hours + 793 / 1080 hours ).
46.
The Babylonian estimate for the synodic month was adopted for the greater part of two millennia by Hipparchus, Ptolemy and medieval writers ( and it is still in use as part of the basis for the calculated Hebrew ( Jewish ) calendar ).
47.
As seen from the Earth, the time it takes for the Moon to return to a node, the draconic month, is less than the time it takes for the Moon to return to the same ecliptic longitude as the Sun : the synodic month.
48.
The Metonic cycle has 19 tropical years and 235 synodic months in 6940 days . The Callippic cycle synchronizes days per orbit and rotations per orbit within the Metonic cycle, noting the difference of one after 4 Metonic cycles, a duration of 76 years.
49.
Eclipse cycles have a period in which a certain number of synodic months closely equals an integer or half-integer number of draconic months : one such period after an eclipse, a node of the Moon's orbit on the ecliptic, and an eclipse can occur again.
50.
The Variation has a period of half a synodic month and causes the Moon's ecliptic longitude to vary by nearly two-thirds of a degree, more exactly by + 2370 " sin ( 2D ) where D is the mean elongation of the Moon from the Sun.
