Next: Solar and Lunar Eclipses Up: Lunar-Solar Syzygies and Eclipses Previous: Determination of Lunar-Solar Elongation

Example Syzygy Calculations

Example 1: Sixth new moon in 2004 CE:

From Table 42, the date of first new moon in 2004 CE is 2453026.4 JD. Now, the lunar-solar elongation increases at the mean rate per day, or in days--the latter time period is known as a synodic month. Hence, a rough estimate for the date of the sixth new moon in 2004 CE is five synodic months after that of the first: i.e., JD. It follows that JD. Let us calculate the lunar-solar elongation at this date. From Table 40:
 (JD) +1000 +600 +20 +9 +.1 Epoch Modulus

Thus,

Table 41 yields

Hence,

Now, the actual new moon takes place when . Thus, a far better estimate for the date of the sixth new moon in 2004 CE is JD. This corresponds to 20:00 UT on June 17th.

Example 2: Third full moon in 1982 CE:

From Table 42, the fractional Julian day number of first new moon in 1982 CE is 2444994.7 JD, which corresponds to January 25th. Since there is more than half a synodic month between this event and the start of year, we conclude that the first full moon in 1982 CE took place before January 25th. Hence, a rough estimate for the date of the third full moon in 1982 CE is one and a half synodic months after that of the first new moon: i.e., JD. It follows that JD. Let us calculate the lunar-solar elongation at this date. From Table 40:
 (JD) -6000 -500 -6 Epoch Modulus

Thus,

Table 41 yields

Hence,

Now, the actual full moon takes place when . Thus, a far better estimate for the date of the third full moon in 1982 CE is JD. This corresponds to 20:00 UT on March 9th.

Next: Solar and Lunar Eclipses Up: Lunar-Solar Syzygies and Eclipses Previous: Determination of Lunar-Solar Elongation
Richard Fitzpatrick 2010-07-21