[8] Variation from Astronomical New Moon to Full Moon; Variation from New Crescent to Full Moon

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Someone may imagine that since the day immediately following the moment of the full moon could be known by the method described above, perhaps the day of the conjunction could be known from the day of the full moon.

This conjecture is now discussed.

On the bottom of page 6 of Parker 1950, he wrote, “The necessary time for full moon varies from 13.73 to 15.80 days after conjunction.” This is a swing of 2.07 days, which is about 49 hours 41 minutes. This shows that the conjunction (i. e., astronomical new moon) does not have to be exactly opposite the full moon.

By examining a few cases near these extremes in the 20th century we may compare the day of the lunar month based upon whether one considers the first day of the lunar month to be the day on which the conjunction occurs or the day on which the new crescent is seen. Let us consider three cases in which the computation for visibility of the new crescent is made from
Jerusalem, and the boundary for a new day is computed as sunset.

For those who wish to check with other software, I am considering the latitude of Jerusalem to be 31.80 N and the longitude of Jerusalem to be 35.22 E, which are the coordinates I have seen for an official weather station of Jerusalem.

The abbreviation UT stands for “universal time”, and is intended to refer to the time zone based upon Greenwich, England.

Case 1: Conjunction on July 7, 1967 at 17:01 UT and sunset 16:48 UT The full moon occurred on July 21, 1967 at 14:39 UT. The time from conjunction to full moon is 13.90 days (a little over the minimum of 13.73).

Note that the conjunction occurred shortly after sunset, close to the beginning of a new day. For a month that is considered to begin on the day of the conjunction, the full moon occurs on the 14th day of the month in this example. On the evening that ends July 9, 1967 the new crescent will be theoretically visible. For a month that is considered to begin on the day beginning with
the new crescent, the full moon occurs on the 12th day of the month.

Case 2: Conjunction on December 12, 1966 at 3:15 UT and sunset 14:35 UT The full moon occurred on December 27, 1966 at 17:45 UT. The time from conjunction to full moon is 15.60 days (a little under the maximum of 15.80 days). For a month that is considered to begin on the day of the conjunction, the full moon occurs on the 15th day of the month in this example.

On the evening that ends December 13, 1966 the new crescent will be theoretically visible. For a month that is considered to begin on the day beginning with the new crescent, the full moon occurs on the 13th day of the month.

Case 3: Conjunction on September 26, 1973 at 13:54 UT and sunset 15:32 UT The full moon occurred on October 12, 1973 at 3:11 UT. Note that the conjunction occurred shortly before sunset, close to the end of a new day.

The time from conjunction to full moon is 15.55 days (a little under the maximum of 15.80 days). For a month that is considered to begin on the day of the conjunction, the full moon occurs on the 17th day of the month in this example!!

On the evening that ends September 28, 1973 the new crescent will be theoretically visible. For a month that is considered to begin on the day beginning with the new crescent, the full moon occurs on the 14th day of the month.

Conclusion from these Examples

In these examples, for a conjunction month, the full moon occurs from the 14th to the 17th day of the month. The 17th is very rare.
In these examples, for a new crescent month, the full moon occurs from the 12th to the 14th day of the month. In the most extreme case for a new crescent month, the full moon can occur on the 16th day of the month, but this is very rare. Typically the full moon occurs on the 13th, 14th, and 15th for the new crescent month.