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# Venus

The ecliptic latitude of Venus can be determined with the aid of Tables 58, 73, and 74. Table 58 allows the mean argument of latitude, , of Venus to be calculated as a function of time. Next, Table 73 permits the epicyclic latitude, , to be determined as a function of the true argument of latitude, . Finally, Table 74 allows the quantities , , and to be calculated as functions of the epicyclic anomaly, .

The procedure for using the tables is as follows:

1. Determine the fractional Julian day number, , corresponding to the date and time at which the ecliptic latitude is to be calculated with the aid of Tables 27-29. Form , where is the epoch.
2. Calculate the planetary equation of center, , ecliptic anomaly, , and interpolation parameters and using the procedure set out in Cha. 9.
3. Enter Table 58 with the digit for each power of 10 in and take out the corresponding values of . If is negative then the corresponding values are also negative. The value of the mean argument of latitude, , is the sum of all the values plus the value of at the epoch.
4. Form the true argument of latitude, . Add as many multiples of to as is required to make it fall in the range to . Round to the nearest degree.
5. Enter Table 73 with the value of and take out the corresponding value of the epicyclic latitude, . It is necessary to interpolate if is odd.
6. Enter Table 74 with the value of and take out the corresponding values of , , and . If then it is necessary to make use of the identities and .
7. Form the deferential latitude correction factor, .
8. The ecliptic latitude, , is the product of the epicyclic latitude, , and the deferential latitude correction factor, . The decimal fraction can be converted into arc minutes using Table 31. Round to the nearest arc minute.
One example of this procedure is given below.

Example: May 5, 2005 CE, 00:00 UT:

From Cha. 9, JD, , , , and . Making use of Table 58, we find: (JD) +1000 +900 +50 +.5 Epoch  Modulus Thus, It follows from Table 73 that Since , Table 74 yields so Finally, Thus, the ecliptic latitude of Venus at 00:00 UT on May 5, 2005 CE was .   Next: Mercury Up: Planetary Latitudes Previous: Determination of Ecliptic Latitude
Richard Fitzpatrick 2010-07-21