The procedure for using the tables is as follows:

- 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.
- Calculate the planetary equation of center, , ecliptic anomaly, , and interpolation parameters and using the procedure set out in Cha. 8.
- Enter Table 46 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.
- 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.
- Enter Table 67 with the value of and take out the corresponding value of the deferential latitude, . It is necessary to interpolate if is odd.
- Enter Table 68 with the value of and take out the corresponding values of , , and . If then it is necessary to make use of the identities and .
- Form the epicyclic latitude correction factor, .
- The ecliptic latitude, , is the product of the deferential latitude, , and the epicyclic latitude correction factor, . The decimal fraction can be converted into arc minutes using Table 31. Round to the nearest arc minute.

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

From Cha. 8,
JD,
,
,
, and
.
Making use of
Table 46, we find:

(JD) | |

+1000 | |

+900 | |

+50 | |

+.5 | |

Epoch | |

Modulus | |

Thus,

It follows from Table 67 that

Since , Table 68 yields

so

Finally,

Thus, the ecliptic latitude of Mars at 00:00 UT on May 5, 2005 CE was .