PSN ("Progressed Sidereal Natal" - calculations

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PSN ("Progressed Sidereal Natal" - calculations

Post by Jim Eshelman » Sat Jun 03, 2017 4:36 pm

I have proposed a new progression method that might have something to it, and asked for assistance in testing it. Testing it is hard because getting an actual chart is hard.

Until a better name comes across, I call this Progressed Sidereal Natal (PSN), a name selected to draw attention to its inseparability from the Progressed Sidereal Solar Return (PSSR). The name is awkward, because the natal is already progressed by other, more famous and widely used methods, but I'll stick with it for now.

PREMISE: The PSSR has angles that move continuously, without interruption, from one Sidereal Solar Return to the next. The PSSR in the last moment of the old SSR has angles identical to those of the first moment of the new SSR, so that it continues to flow non-stop throughout life. This means that they have flowed non-stop from the moment of birth, the nativity being the first "solar return," and the only such chart that never expires throughout life. The theory tested was that the already familiar PSSR rate continues not only from each new SSR (and expires when the SSR expires), but also runs non-stop from birth. Whereas the popular Secondary Progressions advance the birth chart one day (24 hours) for every year of life, the PSSR rate (the PSN method) advances it at just over 30 hours per year of life - a bit more than 25% faster than secondaries.

A previous thread, introducing the PSN, is here: viewtopic.php?f=23&t=2

Calculation is difficult. We don't have the right software. Work-around tactics are awkward and time-consuming. I have a tool that should make it better; but first we should explore where we have come so far, because there is an easy way to estimate the PSN planets that is accurate enough for testing (as long as we don't involve the angles).

Calculating the Right Rate
A Sidereal Year is given by astronomers as 365.25636 days.

The PSSR is based on the overage of 1.25636 beyond the 365-day calendar year. This is 1.25636 Sidereal Days, which are 23:56:04 long in civil time, so this equates to 1.25287 civil days. This distributes across a Sidereal year, which is 365.25636 days long. Using numbers with a lot more decimal points, I got the ratio as 0.0034301142203677 and, experimenting in Solar Fire, found that the level of precision that works adequately is 0.003430114. (This means 0.003430114 years per year, in case you're wondering.)

As a very close approximation (but only an approximation), in Solar Fire, under Current Settings, go to the Progs/Dirs tab and put 0.003430114 in the "Rate for User Progs." Click OK, then save your settings (Ctrl+S or Preferences | Save Settings). You're now ready to go.

For anything further, download the spreadsheet attached here:
viewtopic.php?f=22&t=234
It helps calculate both the PSSR and PSN, and is the best tool I can recommend at the moment.
Jim Eshelman
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Re: PSN ("Progressed Sidereal Natal" - calculations

Post by Jim Eshelman » Sat Jun 03, 2017 4:45 pm

Because this is simply a method of progressing the natal chart (think of it as the same kind of critter as Secondary Progressions), the most important thing - and the only think that will distinguish it from the PSSR - will be the aspects formed by progressed planets to each other and to natal planets. As long as we ignore the angles, the estimation system above is good enough to get these progressed planets (only Moon being sometimes off a bit, and that only by a few minutes at most).

The angles will always be exactly those of the PSSR. Because of this, Derek Kinsolving has proposed the practical approach of (1) calculate an approximate PSN, (2) calculate the PSSR, and (3) edit the approximate PSN, using the Rectification button in Solar Fire, to match the angles of the PSSR. This, in fact, works perfectly - but with the emphasis on "work."
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Using the PSN spreadsheet

Post by Jim Eshelman » Sat Jun 03, 2017 4:53 pm

An estimated PSN is easy. Solar Fire makes it possible even to watch it dynamically, generate reports, etc. These are all approximations but, as long as angles are ignored, they are close enough.

The spreadsheet above makes it possible to get accurate PSN angles. You can put in a small amount of work and get approximately correct results, or more work and get better (more accurate) results. Here are the instructions, starting with a simple step, and then describing three corrections. You can use the three corrections at your option if you want to get more exacting results.

As a working example: I was born October 10, 1954, 4:13 AM CST, Rochester, IN. An event occurred to me September 5, 2005, 3:00 AM, New York, NY. Open the spreadsheet and click on the "PSN Rate" tab at the bottom. (I have some sample data stored to help you see the format.)

Estimate 1: Solar Fire
The "User Progression Rate" method described above for Solar Fire gives (for my natal chart relocated to New York) gives MC 26°32' Taurus, Asc 27°48' Leo, and progressed Moon at 9°24' Cancer.

Estimate 2: From the spreadsheet
Do not edit or modify anything in the colored squares. Only change values in the white squares. If you are not going to use the three Corrections listed on the spreadsheet, all the (white square) values in the three lower Correction sections should be empty.

In the upper right corner, see my birth data. So that it is in Eastern Time (for New York City), make sure it reads 10/10/1954 5:13:00. Immediately under it, put the event information as 9/5/2005 3:00:00.

Immediately you see under "PSN Date/Time" 12/12/1954 23:50:08. Calculate a chart for this date and time, for New York City, to get the correct (first estimate, known to be slightly wrong) PSN. Notice that it gives MC 26°34' Taurus, Asc 27°51' Leo, and progressed Moon at 9°24' Cancer. The angles agree with the above estimate almost exactly. They are calculated on similar principles, and both are only estimates.

Correction 1: Adjustment for Current SSR
Every solar return year (the time between two consecutive solar returns) is slightly different. The estimates above are based on an average, and they can be slightly off. However, we can easily adjust this because, at the moment of each new Sidereal Solar Return, the PSN angles are exactly the same as the SSR angles.

See the section marked "Correction 1" on the spreadsheet. It asks for the difference in RAMC (Right Ascension of the Midheaven) between the new SSR and the estimated PSN. For the sample data, calculate my SSR prior to the event. For the chart October 10, 2004, 1:51:09 AM EDT, New York, NY, the RAMC (from the Reports button) is 32°58'. Calculate the estimated PSN for the same moment (10/10/2004, 1:51:09 AM EDT, NYC) and get an RAMC of 31°12'. Subtract the latter number from the former to get a difference of 1°46'. Put these values in the two blanks next to the yellow labels in the "Correction 1" section of the spreadsheet.

You can add this value for yourself once a year and save the value in the spreadsheet to save time. Notice that, automatically, the PSN Date/Time has changed to 12/12/1954 23:55:47 EST. A chart for this moment gives slightly different values than previously: MC 27°53' Taurus, Asc 28°58' Leo, and progressed Moon at 9°27' Cancer. The angles have been corrected 1-2°.

Correction 2: Apparent Solar Rate (opt.)
The next correction is optional, except that you cannot do only Correction 2 or Correction 3. If you do one of them, then you have to do both.

Regarding Correction 2: There is uncertainty as to whether these progressions (and the PSSR) should move at the rate of the apparent Sun (RAAS) or the mean Sun (RAMS). Historically the PSSR has been calculated by the apparent rate, though that would make it the only such "daily angles" (quotidian) method that works that way. I encourage side-by-side comparison. After applying Correction 2, the RAAS method results will appear in the purple box, and the RAMS results will still be in the "PSN Date/Time" area as before.

Under "Correct 2" on the spreadsheet, add (in degrees and minutes) the Right Ascension (RA) of the Sun at your last Sidereal Solar Return, and then of transiting Sun for the event. The RA Sun is available on the Reports page in Solar Fire. For the sample data, the prior SSR RA Sun was 195°55'. The RA Sun for the event was 164°10'. We add these numbers to the marked boxes.

We won't stop and calculate the results until we have done the final correction. (2 and 3 are both needed for either one of them to work.)

Correction 3: Correct for Irregular PSSRY
PSSRY means Progressed Sidereal Solar Return Year. It is the difference in Sidereal Time between two consecutive SSRs. This is the value that is spread out through the whole year. Though it averages about 30:09, it can be 10 minutes or so less than this or more than this. At the end of the birthday year, PSSR and PSN angles ca be off by 2-3° in extreme cases. It is a good idea to make this correction, and you can (for yourself) just fill out the spreadsheet once for the whole year.

Under "Correction 3," you will need the hour, minute, and second of the Sidereal Time of the current SSR and the next SSR. This is on the Reports page. For the sample, the first value is 2:11:50, and the second is 8:18:35. Their difference (6:06:45) is automatically calculated and processed in various ways.

This slightly adjusts both the RAMS and RAAS versions of the calculations. The slightly earlier time calculated is 12/12/1954 23:53:35 for the Mean Sun calculation, and this gives MC 27°22' Taurus, Asc 28°32' Leo, and progressed Moon at 9°26' Cancer. The angles are about half a degree earlier than last time we calculated them.

In the purple box, we see that the corrected value if Apparent Sun is used is 12/13/1954 0:08:47, which a bit different from the foreground. MC 0°52' Gemini, Asc 1°33' Virgo, and progressed Moon at 9°35' Cancer. This is several degrees different from the foregoing, hence the need to determine by observation whether the mean or apparent solar rate should be used. In theory (if our successive estimates haven't knocked us off course), this should exactly match the angles of the PSSR calculated for apparent solar rate.

For some reason, in this sample, the value overshoots the PSSR. Using Tab 1 of the spreadsheet to calculate an exact PSSR, I get a derived data and time of October 11, 2014, 5:14 AM with MC 29°54' Taurus, Asc 0°35' Virgo.
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Re: PSN ("Progressed Sidereal Natal" - calculations

Post by Jim Eshelman » Mon Jun 19, 2017 10:13 am

I ran another test, to see the accuracy of the PSSR-PSN spreadsheet. The bottom line (from the individual tests I've run so far) is that the spreadsheet does accurately calculate the PSN within small errors (easily correctly with Derek's trick, reviewed below) if you use all the correction options offered.

This post won't make much sense unless you've at least read the first post at the top of this thread.

I was born October 10, 1954, 4:13 AM, Rochester, IN. I currently live in Los Angeles at 34N03'46", 118W18'47", and all charts below are calculated with Solar Fire for those coordinates. Other calculation methods may produce slightly different results.

I used my chart to look at an upcoming event July 5, 2017, 1:00 PM PDT, my residence.

The test results
The final correct result we want is MC 28°53' Aquarius. Let's step through the various ways of estimating this.

First, the approximation method of using a "User Rate" progression from Solar Fire. Run from my natal chart, I get MC 21°19' Aquarius. (This is Mean rate, rather than Apparent rate, and that makes up most of the difference.) If I run it from my SSR, I get 23°02' Aquarius.

If, instead of the "User Progression" rate, I use the spreadsheet, applying all available corrections on the PSN tab, I get Midheaven 23°09' Aquarius for the mean rate. (Notice that this closes the gap between the two numbers above.) However - more interesting to us if, as Fagan thought, the PSSR should be calculated by the apparent solar rate... the PSN tab, in the purple box, applies the final adjustment and gives MC 28°44' Aquarius.

Notice this is within 0°09' of the carefully calculated full Neo-PSSR above (28°53'). If the small difference matters to you, use Derek's trick: Calculate a PSN chart (which will give the 28°44' Aquarius MC), click the Rectify button, and edit the MC to end in 53' (matching the fully calculated PSSR). That gives a perfect result.

Therefore...
Using the PSN spreadsheet with all corrections will get you within a few minutes of the correct MC, which, if you want, you can adjust by comparing it to the PSSR. Notice that the spreadsheet gives you what you want regardless of whether the PSSR/PSN work on mean or apparent solar rate. If you want to use mean rate, use the value at the top of the page under "PSN Date/Time." If you want to use the apparent rate, use the value in the purple box. Either will be correct (within a few minutes) according to its own theory, and could even serve as a basis for you to do both charts and compare the results. (At least, according to all tests I've run so far, the difference is only a few minutes.)

I recommend populating the spreadsheet pages with data from your natal and Solar Return charts, so that it only takes a few seconds to adjust it to a given date you want to check. If you want to study many events across time, I suggest copying the PSN tab to new tabs, one for each year you want to check.
Jim Eshelman
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