WISH LIST - Progressions

[Jim Eshelman]

I don't think this is an immediate priority. I've argued that we defer this until version 2. In any case, it's worthwhile to describe the requirements and methods and start thinking about infrastructure and other design elements. Knowing where we ultimately want to go is basic to being ready to go when we get there.

One important thread where I've gone over much of this - one of the most important threads on the forum for progression matters - is this one titled "Which Day? Which Year? How much difference?" https://www.solunars.com/viewtopic.php?t=6176

An examination of whether fixed mean rates are good enough, even though the length of a sidereal year varies slightly each year, is at the following link, going on for several posts. (Spoiler: They are.) https://www.solunars.com/viewtopic.php?p=53077#p53077

Everything below is about secondary progressions until I branch into other systems later in the thread. (I'll label those.)

[Jim Eshelman]

Secondary progressions are defined as moving planets at the rate of one day for each year. However, we have to define what kind of day and what kind of year.

All existing astrological software AFAIK calculates this as one mean solar day = one tropical year. If the software allows both Q2 and Q1 variations, this is the Q2 definition, while the Q1 definition is one sidereal day = one tropical year.

These are wrong. The type of year should be the sidereal year. The difference doesn't really show except in quotidians, and doesn't really show in quotidians until advanced age, but then it can make a lot of difference. The progressed MC varies at the same rate as precession, being 1° (RA) off in 72 years. With orbs being theoretically 1°, this variation can be a problem sometimes even in early adulthood.

Fagan felt the Q1 rate was correct (but late in life was using the Q2 more). Bradley did comparison tests and rejected the Q1, finding the Q2 reliable. I find Q2 rate reliable and am bugged by the occasional example that seems to say otherwise (but it wins heavily on balance). We should offer both Q1 and Q2 rates and set the Q2 as TM's default.

Q2 Rate
Rate: 1 mean solar day = 1 sidereal year. That is, what we call a conventional civil day (return to the same UT) equals one revolution of Earth about the Sun.

Experimentation shows that using mean lengths of the year is sufficient within the scope of a human life (1' or so error on quotidian angles) and only slightly off across centuries (a few more minutes of arc). One could always remove this error with an extra step or two. The question is how far is it necessary to go for the accuracy we are willing to accept. I'll give both the "good enough, nobody will notice" method and the "this is exactly right always" method.

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"). Differences exist from year to year but, in spot tests, it seems we can use this mean value.

The simple (fixed rate) way to calculate the Q2 is: ((JD event) - (JD birth)) / 365.256363004 = number of civil days after the birth moment that represents the progressed date. Add this to JD of birth to get the progressed epoch.

The more complicated way (maybe not necessary, but rigorous): Subtract birth JD from event JD to get age. The integer value is the whole number of (civil) days after birth for the progressions. For the parts of a day: A = subtract current SSR JD from upcoming SSR JD (length of the current sidereal year); B = event JD minus current SSR JD (time since last completion of a whole sidereal year). Multiply B/A times 24:00:00 to get the time increment.

Q1 Rate
Rate: 1 sidereal day = 1 sidereal year. That is, one exact rotation of Earth on its axis (return to the same Midheaven longitude) equals one revolution of Earth about the Sun.

This is also called the bija rate because Fagan created a bija ("correction") table to help calculate the Q1 by hand.

The sidereal day (one Earth rotation) is 86,164.0905 seconds (= 23:56:04.0905, or 0.997269566 civil days). This means the Q1's rate is 0.997269566 the rate of the Q2. Dividing the length of the sidereal year (365.256363004 civil days) by the length of the sidereal day (0.997269566 civil days) gives the new length of 366.2564019366.

Therefore, the simple (fixed rate) way to calculate the Q1 is: ((JD event) - (JD birth)) / 366.2564019366 = number of civil days after the birth moment that represents the progressed date. Add this to JD of birth to get the progressed epoch.

The more complicated way (maybe not necessary, but rigorous): Subtract birth JD from event JD to get age. The integer value is the whole number of (civil) days after birth for the progressions. For the parts of a day: A = subtract current SSR JD from upcoming SSR JD (length of the current sidereal year); B = event JD minus current SSR JD (time since last completion of a whole sidereal year). Multiply B/A times 23.9344695833 hours to get the time increment.

[Jim Eshelman]

A separate question is whether the progression rate is even throughout the year or uneven. Secondary progressions traditionally are calculated at an even rate. At different times in the 1950s and '60s, it was thought that this time varied according to the speed of transiting Sun (which changes throughout the year). This would never be perceptible without quotidian angles to consider, since it isn't uneven enough to change planet motion so that people normally would notice.

This variable rate was referred to an RAAS argument: right ascension of the apparent Sun. In the early 1960's (because alpha is a symbol for right ascension), this was sometimes called the alpha-Q. By the late '60s, Fagan began attaching the prefix Neo- to any Q method that used RAAS (Neo-SNQ, Neo-SQ).

The invariable (even) rate was referred to an RAMS argument: right ascension of the mean Sun. The term "mean Sun" is based on the exact way of calculating this by hand (pre-computer) and makes a nice verbal contrast to "apparent Sun" of the other math. Also, because of historic usage, these terms were never changed and are still familiar. All RAMS means is that time flows evenly - at the same even, invariable rate - no matter what time of the year.

We can perhaps most simply call these the mean and apparent rate.

All the comparisons I have done favor the mean rate, not the apparent. Fagan favored the apparent rate at the end of his life and, if this was going to be a phase, he didn't live long enough to grow out of it. Bradley's research pointed to the mean rate, which is also the basis of the Capsolar quotidian that he used to rectify the boundaries of the zodiac. Duncan felt that we damn well better find out experimentally which was better because, if it turned out to be the apparent rate, then this would require significant revision of Bradley's rectification of the zodiac!

Don wrote me about this on January 4, 1971:

...your letter, again hitting onto the solar-anomaly question, calls for a quick and forthright reply. Virtually everybody who becomes swept up in technical astrology gets snared in this question and few are able to straighten themselves out alone. It is mainly a matter of semantics, not mathematics.

The term "fictitious time" is itself fictitious if you confuse revolutions with rotations! Even Cyril in his dotage couldn't separate the two logically, though of course he knew better in his brighter years. GET THIS STRAIGHT: What is called fictitious time in astronomy RUNS AT THE SAME PACE AS SIDEREAL TIME -- and by pace I MEAN LINEARLY. The Earth turns, for all practical purposes within one part in millionths, EXACTLY AT THE SAME RATE WHETHER IT IS AT APHELION OR PERIHELION. THE SIDEREAL ROTATION OF THE EARTH IS UNIFORM, AND IT IS SURELY THE SIDEREAL (THAT IS, CELESTIAL) SPHERE WHICH IS THE TRUE FRAME OF REFERENCE.

It is pitiably simple to establish whether the Q charts should be rotated sidereally or in terms of the solar anomaly. Study just a few cases (a lot aren't necessary) of events occurring in October-November for February-born people, and you have a big surprise coming. Reverse the process, studying progressed charts by both methods for autumn-born people with the events in February. The flow of time is uniform in astrology as well as in physics. [emphasis added]

Ken Bowser prefers the apparent rate at least for SQ (thus, the Neo-SQ). I've never noticed (and never asked him) whether he thinks the SNQ should be calculated this way as well. We have a mismatch. I could claim I've looked at it enough (but it's not really enough) or that my conclusion was Bradley's conclusion but, really, we need to do a LOT more day-to-day and special event looking. This just won't happen until we have the software tools to put in everybody's hands.

If a user picks apparent instead of mean, we need a different approach. Maybe you can think of a better one mine below; this is what I came up with on first try: It's the "more complicated" way mentioned on the last post (which may, therefore, be the best single-approach model for all of these). Remember, these might be progressions of both the natal Q (SNQ) and the SSR's Q (SQ).

Q2 Rate

• Subtract birth JD from event JD to get age: Take the integer for whole years. (For the SQ, the answer will always be zero.) - You won't use the non-integer part of this age.
• Calculate the epochs of the current and next SSRs. Subtract to get the length of the current sidereal year.
• Calculate RA of transiting Sun and RA of SSR Sun. Subtract and divide by 360° to get the percentage of the current year that has elapsed per the apparent solar rate. Multiply by 24:00:00 to get the part of a day that has elapsed (time increment). (Shorter form: Dividing by 360 and multiplying by 24 can, of course, be squeezed into one step.)
• Add the age (whole years treated as days) and the time increment to the birth epoch to get the progressed epoch. (Technical note: I have left a possible error in this that will never exceed 3.35 time-seconds, i.e., less than 0°01' on angles.)

Q1 Rate
Same as the method recommended for Neo-Q2 right above, with one modification (bold below):

• Subtract birth JD from event JD to get age: Take the integer for whole years. (For the SQ, the answer will always be zero.) - You won't use the non-integer part of this age.
• Calculate the epochs of the current and next SSRs. Subtract to get the length of the current sidereal year.
• Calculate RA of transiting Sun and RA of SSR Sun. Subtract and divide by 360°... then multiply by 24:00:00 to get the part of a day that has elapsed (time increment).
• Multiply age + time increment by 0.997269566 to convert Q2 rate to Q1 rate.
• Add the result (treated as days) to the birth epoch to get the progressed epoch.

[Jim Eshelman]

Though a pure Q2 at mean rate could be done more simply, I know it would be useful to invoke a single process that covers all variations the same way. Here is an attempt at that. (In case it isn't obvious, the most recent SSR is used to mark the exact moment a full sidereal year ended, and thus the exact time a progressed day last ended.)

• For Q2 vs. Q1: DayLength = 1.0 (for Q2) or 0.997269566 (for Q1).
• Age = event JD minus birth JD.
• YearsOld = integer part of (Age/365.256363004). [There are awkward spots very near the SSR where this could {rarely} screw up. All we need here is the number of completed years alive, i.e., one's age. You may have an easy way. The absurdly long way is current SSR JD minus birth JD divided by 365.256363004, rounded to a whole number.]
• Calculate elapsed time within the current year (for mean rate): YrElapsed = (event JD minus current SSR JD)/(next SSR JD minus current SSR JD)
• Calculate elapsed time within the current year (for apparent rate): YrElapsed = (RA of transiting Sun minus RA of SSR Sun)/360.0139583333 (= 360°00'50.25") [360°00'50.25" includes the amount of precession transiting Sun will accrue over the course of the year.]
• Age = YearsOld + Time Increment
• Age = Age x DayLength
• JD of base chart (whether natal, solar, or other) + Age = progressed epoch (progressed JD).

I think that's right. Please point out any places my brain got twisted in that.

[Jim Eshelman]

Whereas the Solar Quotidian is a straight secondary progression of the SSR, the Progressed Sidereal Solar Return (PSSR) is at a different rate about one-fourth faster.

The PSSR is based on the fact that each sidereal year is a bit more than 365.25 days long with the Sidereal Time (RAMC) of each SSR being just a bit more than six hours ahead of its predecessor.

The value called SSRY in historic Sidereal ephemerides - Sidereal Solar Return Year - is a precalculated next SSR's ST minus current SSR's ST + 24 hours. That is, Fagan realized that the difference is not 6+ hours (as assert in Wynn's Key Cycle) but 30+ hours: a day and a quarter.

This 30+ hours is spread out over the year either by the even mean rate or uneven apparent rate. Fagan asserted (and Bradley accepted) that the PSSR worked in terms of the apparent rate - that it was always a Neo-PSSR (to use Fagan's end of life language). Neither Ken Bowser nor I currently think so. We could be wrong, of course.

Although the calculations were always historically done in Sidereal Time, they could as well be done in clock time since ST and UT are linear against each other but with ST moving at a stable faster rate. Therefore, for TM's purposes, we can use calculate the PSSR chart by adding one line to the above procedural outline:

• For Q2 vs. Q1: DayLength = 1.0 (for Q2) or 0.997269566 (for Q1).
• For PSSR: DayLength = (Next SSR JD minus current SSR JD) minus 364
• Age = event JD minus birth JD.
• YearsOld = integer part of (Age/365.256363004). [There are awkward spots very near the SSR where this could {rarely} screw up. All we need here is the number of completed years alive, i.e., one's age. You may have an easy way. The absurdly long way is current SSR JD minus birth JD divided by 365.256363004, rounded to a whole number.]
• Calculate elapsed time within the current year (for mean rate): YrElapsed = (event JD minus current SSR JD)/(next SSR JD minus current SSR JD)
• Calculate elapsed time within the current year (for apparent rate): YrElapsed = (RA of transiting Sun minus RA of SSR Sun)/360.0139583333 (= 360°00'50.25") [360°00'50.25" includes the amount of precession transiting Sun will accrue over the course of the year.]
• Age = YearsOld + Time Increment
• Age = Age x DayLength
• JD of base chart (whether natal, solar, or other) + Age = progressed epoch (progressed JD).

[Jim Eshelman]

Tertiary progressions are based on the theory: one day = one month. Of course, we have to sort out what kind of day and what kind of month. In this case we mean one mean solar day (civil day) = one sidereal month. (Troinski conceived of this in tropical months, which are an absurd measurement idea and barely any different.)

Sidereal months average 27.321661 days. It's not at all clear that much refinement is expected, although Solar Fire does have variants of "true tertiary" vs. "mean tertiary." There is almost no difference: If I run mine for the minute I'm typing this, Moon longitudes are 0°05' apart (and Moon positions are rarely thought to be too important in terts).

Therefore, while the procedure could be forced into the general protocol above, what is most warranted is probably much simpler:

• Age = event JD minus birth JD.
• Time Increment = Age/27.321661
• Natal JD + Time Increment = progressed JD.

However, with terts we need a new way to calculate the angles. The historic ways are the dual options of Naibod's arc in right ascension or solar arc in longitude. I need to explain these.

The easiest way to explain Naibod's arc is Sun's mean daily increment in right ascension (expressed as time). To get all the decimals we might want, let's derive it freshly. Since a tropical year averages 365.24219 (Sun goes through 360° of RA in that time), each day Sun averages 0.9856474131° (we should probably truncate that to 0.985647° to give significant digit parity) each day. This is the same as 0°59'08.33". Multiply this 0.985647° value by Time Increment calculated above, and add the result to the RAMC of the natal chart (for birth or a location - whichever is selected) to get the RAMC of the tertiary progressed chart.

The other method is "solar arc in longitude." This means: subtract natal Sun from tert progressed Sun to get the solar arc, then add this to natal MC (in longitude). This gives the progressed MC. Then find the RAMC that gives that that Midheaven and use it to calculate everything else.

Quaternary Progressions
Elbert Benjamine's "minor progressions" (named in contrast to secondary or "major" progressions) were called by me - and have been called by others - quaternary progressions. They're valid enough but, I think, quite minor. Most likely nobody needs them. though some may want them.

I mention them only because, once one has tertiaries programmed, quaternaries require nothing more than changing a single number. Quats are one sidereal month = one sidereal year. (Church of Light used tropical months and years but this is an unlikely reality. Fortunately, there is essentially no difference in the results.) With a sidereal month 27.321661 days and a sidereal year 365.256363004 days (these are averages), the time increment is age in days times (27.321661/365.256363004) = age in days x 0.074801328.

As hinted, I'm not sure these are worth it. (I'm not actually sure terts are worth it, though I do suspect there will be demand for them.