Using Ptolemy's Anomaly Table to Find the Time of Perigee

  As indicated in the last blog Ptolemy's anomaly table can be used to the time it takes to go from one longitude to another. To find the time interval between the autumnal equinox and perigee one can use linear interpolation. Ptolemy's anomaly table is found on page 167 of Toomer, Ptolemy's Almagest. The first two columns are mean motion, M below, and the third column is the anomaly, α below, in degrees. The apparent longitude is the sum of the sum M + α  and one looks for two longitudes in the table that straddle some arbitrary longitude, λ, then do the interpolation.

One gets essentially the same result found previously. Finding the time from perigee is a special case but the time between any two longitudes will be the difference of the individual times to/from perigee.