(114) | |||

(115) | |||

(116) | |||

(117) | |||

(118) | |||

(119) | |||

(120) | |||

(121) | |||

(122) | |||

(123) |

Here, and are the longitude and mean anomaly of the sun, respectively. Moreover, , , , , and are the eccentricity, longitude, mean longitude, mean argument of latitude, and th anomaly of the moon, respectively. The moon's first anomaly is due to the eccentricity of its orbit, and is very similar in form to that obtained from Keplerian orbit theory (see Cha. 4). The moon's second, third, and fourth anomalies are knows as

The ecliptic longitude of the moon can be calculated with the aid of Tables 36 and 37. Table 36 allows the lunar mean longitude, , mean anomaly, , and mean argument of latitude, , to be determined as functions of time. Table 37 specifies the lunar anomalies, -, as functions of their various arguments.

The procedure for using the tables is as follows:

- Determine the fractional Julian day number, , corresponding to the date and time at which the moon's ecliptic longitude is to be calculated with the aid of Tables 27-29. Form , where is the epoch.
- Calculate the ecliptic longitude, , and the mean anomaly, , of the sun using the procedure set out in Sect. 5.1.
- Enter Table 36 with the digit for each power of 10 in and take out the corresponding values of , , and . If is negative then the values are minus those shown in the table. The value of the mean longitude, , is the sum of all the values plus the value of at the epoch. Likewise, the value of the mean anomaly, , is the sum of all the values plus the value of at the epoch. Finally, the value of the mean argument of latitude, , is the sum of all the values plus the value of at the epoch. Add as many multiples of to , , and as is required to make them all fall in the range to .
- Form .
- Form the five arguments , , , , . Add as many multiples of to the arguments as is required to make them all fall in the range to . Round each argument to the nearest degree.
- Enter Table 37 with the value of each of the five arguments - and take out the value of each of the five corresponding anomalies -. It is necessary to interpolate if the arguments are odd.
- The moon's ecliptic longitude is given by . If necessary, convert into an angle in the range to . The decimal fraction can be converted into arc minutes using Table 31. Round to the nearest arc minute.