Which Day? Which Year? How much difference?
Posted: Fri Apr 29, 2022 7:31 am
(Adapted and repurposed from another tread elsewhere on the forum.)
Precis: The correct theoretical rate of secondary progressions is 1 sidereal day = 1 sidereal year for the Q1 and 1 mean solar day = 1 sidereal year for the Q2.
The length of the year varies in tiny amounts from year to year and throughout the year. For example, the ST between two consecutive Sidereal Solar Returns is about 6h 9m, but from year to year can vary from this by about 10-12 minutes either side.
In terms of rates, though, this remains small. One could always get the exact length of the sidereal year at any point just by calculating the next SSR. Something I've never seen mentioned - which is probably useless information in an age when nobody calculates secondaries by hand from a printed ephemeris - is that in the day=year formula the progressed chart date comes back to your exact birth time (one day later) exactly the moment of your solar return each year. (As I said, useless information in practice but something strangely never mentioned.)
The sidereal year for epoch 2000.0 was 365.256363004 ephemeris days (days measured in ET which, within a second or two, are nearly the same as "clock time"). The tropical year for the same epoch was 365.242190402 ephemeris days. These differ by 0:20:24.5 UT.
Therefore, dealing with averages that seem to vary in only tiny amounts, progressions unfolding one mean solar day conclude 0:20:24.5 days later each year when equated to a sidereal year than when equated to a tropical year. Ignoring, for this purpose, the miniscule difference between ET and UT, and using a rate of 1 mean solar day = 1 sidereal year,
0:20:24.5 UT = 0.0141724537037037 mean solar day
0.0141724537037037 days / 365.256363004 days = 3.880138757103185e-5 (which is the part of "year" the progressions are delayed per year, and thus the part of one mean solar day that the timing of secondaries need to be retarded) = 3.35 seconds/year
This is tiny. It's about the time it takes MC to move 0°01' of arc. However, that means that about age 60, it aggregates to the amount of time it takes an angle to move 60' or 1° of arc. (It's actually at age 72, but the way I just wrote it makes the point more understandably.) During the same time, progressed Moon only moves about 0°02', so one isn't likely to notice (one is more likely to think a 2' difference in progressed Moon's orb isn't a big deal), but it would throw an exact progressed Moon aspect off by about a day. With the progressed angles, though, since the orb is only 1° (or at most 2°), a 1° difference is significant.
Precis: The correct theoretical rate of secondary progressions is 1 sidereal day = 1 sidereal year for the Q1 and 1 mean solar day = 1 sidereal year for the Q2.
The length of the year varies in tiny amounts from year to year and throughout the year. For example, the ST between two consecutive Sidereal Solar Returns is about 6h 9m, but from year to year can vary from this by about 10-12 minutes either side.
In terms of rates, though, this remains small. One could always get the exact length of the sidereal year at any point just by calculating the next SSR. Something I've never seen mentioned - which is probably useless information in an age when nobody calculates secondaries by hand from a printed ephemeris - is that in the day=year formula the progressed chart date comes back to your exact birth time (one day later) exactly the moment of your solar return each year. (As I said, useless information in practice but something strangely never mentioned.)
The sidereal year for epoch 2000.0 was 365.256363004 ephemeris days (days measured in ET which, within a second or two, are nearly the same as "clock time"). The tropical year for the same epoch was 365.242190402 ephemeris days. These differ by 0:20:24.5 UT.
Therefore, dealing with averages that seem to vary in only tiny amounts, progressions unfolding one mean solar day conclude 0:20:24.5 days later each year when equated to a sidereal year than when equated to a tropical year. Ignoring, for this purpose, the miniscule difference between ET and UT, and using a rate of 1 mean solar day = 1 sidereal year,
0:20:24.5 UT = 0.0141724537037037 mean solar day
0.0141724537037037 days / 365.256363004 days = 3.880138757103185e-5 (which is the part of "year" the progressions are delayed per year, and thus the part of one mean solar day that the timing of secondaries need to be retarded) = 3.35 seconds/year
This is tiny. It's about the time it takes MC to move 0°01' of arc. However, that means that about age 60, it aggregates to the amount of time it takes an angle to move 60' or 1° of arc. (It's actually at age 72, but the way I just wrote it makes the point more understandably.) During the same time, progressed Moon only moves about 0°02', so one isn't likely to notice (one is more likely to think a 2' difference in progressed Moon's orb isn't a big deal), but it would throw an exact progressed Moon aspect off by about a day. With the progressed angles, though, since the orb is only 1° (or at most 2°), a 1° difference is significant.