Astrological Calendar

[mikestar13]

One feature in version 0.2 will be the ability to create a day by day listing for a given period of time (example January 2022) of transits to the nativity (or any other chart in future releases for example SSR or progressed chart). The user will be able to chose:

• Which transiting aspects to list (example conjuctions, opposition, squares, and octiles)
• How close to exact in order to list the transit (example 1 degree) per aspect type (for example 30 minutes for octiles).
• Which transiting planets to list (default all)

In future releases, similar ability to list progressions and directions in the same calendar.

I need this feature for myself, I have reason to believe it will be popular .

[Jim Eshelman]

This will be a great, popular feature. Here's an example of a similar feature in Solar Fire. (I happened to have Charlie Sheen's chart open, so these are his transits for September. There's a bug, though, because it is labelled as my radix when I export it, but radix of Charlie Sheen when I view it on my screen. Bizarre.)

Mike, I know this is looking farther down the road, and I'm about to mention a feature I've never chosen to use: SF has the option to export the calendar contents to a personal calendar - either Outlook, iCalendar, or vCalendar formats. Some people might like to dump all of this right into their calendar so they always have it handy. (It would crowd my calendar WAY too much.) Possibly this export would be easy.

[Illustration removed]

[mikestar13]

Jim, what would you suggest as the default aspects and orbs for transits? (Default for use by learners, advanced uses can pick whatever they like.)
If you care to, same question for Quotations and Solar Arcs (for future reference).
Are contacts by the Q-angles ecliptical or mundane? I'm assuming ecliptical for solar arc angles (correct me if I'm wrong).
Radix or relocated angles or both?

[mikestar13]

...
Mike, I know this is looking farther down the road, and I'm about to mention a feature I've never chosen to use: SF has the option to export the calendar contents to a personal calendar - either Outlook, iCalendar, or vCalendar formats. Some people might like to dump all of this right into their calendar so they always have it handy. (It would crowd my calendar WAY too much.) Possibly this export would be easy.
...

I will investigate that possibility, it will depend on how to do this within the program--once I understand the formats involved, export should be easy. Maybe even import directly into the target program (as opposed to merely exporting a file and letting the user open Outlook or ... and import the file there)--I will need some study. I won't be working on this right away, but this is a high value feature that should be in version 1.0.

BTW, one of my hopes is the existence of freeware with features of interest to Fagan-Bradley Siderealists that Solar Fire doesn't have will prompt SF to meet those interests (example: single wheel showing both zodiacal and mundane positions.)

[Jim Eshelman]

Jim, what would you suggest as the default aspects and orbs for transits? (Default for use by learners, advanced uses can pick whatever they like.)

1° orb, 8th harmonic. BTW I think the calendar should have the option of displaying only exact hits, in addition to an option to show "time in aspect."

If you care to, same question for Quotations and Solar Arcs (for future reference).

Same answer.

Are contacts by the Q-angles ecliptical or mundane?

In the past, I would have said Q angle contacts were mundane - I spend a decade from the mid-70s scrupulously calculating these every month. But the work with SMA, especially the Capsolar Quotidian, has shown me undeniably that these are ecliptical. (I was quite surprised at that.) I can't imagine that personal quotidians behave radically differently, so I have to give the option that it's ecliptical. - Some will want the other, or want to experiment with the other, so if the calculations are doable it would be nice to have an eventual user-selectable option.

Radix or relocated angles or both?

My view (which differs from Firebrace): Quotidians occur in the present, and occur where you are. So: current location.

[Jim Eshelman]

BTW, one of my hopes is the existence of freeware with features of interest to Fagan-Bradley Western Siderealists that Solar Fire doesn't have will prompt SF to meet those interests (example: single wheel showing both zodiacal and mundane positions.)

That would be a wonderful outcome!

[mikestar13]

User selection shouldn't be a problem, and with software I can easily calculate either and present the one the user wants. When I do progressions/directions, I will offer Q1 as an option but Q2 will be the default. Also I can offer as choice between mean rate PSSR and apparent rate PSSR, with mean rate as the default. When I am working on the progressions module (probably version 0.4) I may be asking for some equations.

[Jim Eshelman]

No problem with equations (or the rest). One line to sort out is how much precision is really needed. Here's what I mean:

Secondary progressions (on which other things also depend) should [for Q2] be the rate of 1 mean solar day = 1 sidereal year. Problem: The sidereal year isn't exactly the same from year to year. Does the exact length of the current sidereal year have to be calculated? Or can a mean be used for all cases and still have a precision nobody will notice. [NOTE 4/26/24: Subsequent testing, which I think is posted here somewhere, showed that the mean is sufficient.]

Wikipedia gives the length of the sidereal year for epoch 2000.0 as 365.256363004 ephemeris days. (If you read the Wikipedia article, what it then calls a "solar year" is a tropical year - for comparison. They differ by about 20 minutes/year, which sounds like a lot but even in advanced age doesn't amount to more than a day's timing on progressed aspects.)

How precise and accurate does the sidereal year length have to be? Well, the smallest secondary progression an astrologer is likely to notice would be 0°01' on a quotidian angle. It takes 4s of Sidereal Time (on average, and nearly always within a second or so of that) to change an angle 0°01' Four seconds of time is 4.62962962962963e-5 of a day (a very tiny bit). This fraction of the sidereal year's length, therefore [or, half of it], is how much the year definition can be off for nobody to notice. Multiplying this number by the mean length of the sidereal year for epoch 2000.0 given above, we get 0.0169100168057407 days - let's round to 0.017 days. That's about 24 minutes of time.

I don't recall EVER seeing an SSRY value that was 24 minutes greater or lesser than the mean 30:09.

Translation & Conclusion: I think you can use the contemporary example mean length of a sidereal year. (It's not that hard to work out the actual length, which only has to be done for the current year, but it probably isn't necessary.


NOTE disagreeing with myself a little: Another case where even greater precision might be needed is for Kinetic Lunar Returns. If we get ambitious and want KLRs calculated so transiting Moon truly conjoins progressed Moon to the second of arc, how close does it have to be? Progressed Moon will always be move less than 15°/year, meaning that it will move 0°00'01" in no longer period than 1/54,000 of a year (3600 x 15), which is almost 10m of time. Transiting Moon moves (typically) 5' in that time. In extreme cases, I've seen the SSRY vary by 10 minutes. One could argue that this means KLRs require more assurance of the sidereal year length (but not much, and probably not usually).

[mikestar13]

I'm thinking of listing aspects on the days when they come into orb, when they become exact (with best time estimate SE can calculate), and when they leave orb (with multiple occurrences with triple transits). Also the date range from the first time a transit enters orb to the last time it leaves.

Examples: TSu co NMa exact 2:15 PM (02/04/2021 - 02/06/21)
TPl sq NVe enters 1:47 AM (mm/dd/yyyy - mm/dd/yyyy)
TSa oc NMa leaves 10:21 PM (mm/dd/yyyy - mm/dd/yyyy)

maybe abbreviate to (E)nters, e(X)act, (L)eaves.

[mikestar13]

Calculating a KLR will be an iterative process:

1. Start with a crude guess-- the 15th of the month your are interested in, at midnight, for example.
2. Calculate the Q2 Moon for that moment.
3. Determine the date/time transiting Moon is exactly conjuct Q2 Moon (itself an iterative process).
4. Recalculate the Q2 Moon for that date/time and see how close transiting moon is to exact conjunction to Q2 Moon
5. Repeat as needed using the date/time in step 3 as the new estimate.

A monumental PITA to do it that by way by hand, not that hard in software.

[Jim Eshelman]

Yes, got it. I was calculating how much uncertainty a fixed (representative or average) Sidereal year length would impact it.

[mikestar13]

Typically, imprecision in the birth/event time will overwhelm the imprecision caused by minute change in the length of the sidereal year. If I can find the formula, I will use the mean sidereal year for epoch of date, but the length at epoch 2000 Jan 0 Oh UT is close enough.

[Jim Eshelman]

At some point, you'll create a function (for calculating PSSRs) to determine the length between current and next SSR. This is exactly the value you need (in ET, not ST, of course) for the current years calculator. (All Completed whole years don't need further calculation because, by definition, they equalled one ET day regardless of their length.)

[Jim Eshelman]

At some point, you'll create a function (for calculating PSSRs) to determine the length between current and next SSR. This is exactly the value you need (in ET, not ST, of course) for the current years calculator. (All Completed whole years don't need further calculation because, by definition, they equaled one ET day regardless of their length.)

I think the above was clear, but (for people looking in) let me lay this out in more detail now that I'm back home.

Today, I am 24,436 days old, expressed otherwise as 66 years 329 days old.

If we define 1 year = 1 day as 1 sidereal year = 1 mean solar day, then the first part of the equation is whole orbits of Earth around Sun. In other words, each start of a new 24-hour period (day) after my birth necessarily runs from SSR to SSR. (I don't think I've ever seen it written this way before, but it's necessarily true.)

Therefore, when my SSR last occurred on October 10, 2020, 1:20:55 AM PDT, the equivalent secondary progression was for exactly 66 days after my birth, down to the second. Technically this is in Ephemeris Time. I was born October 10, 1954, 4:13 AM CST = 10:13 UT. Since Delta T was 31 seconds when I was born, my birth was 10:13:31 ET. 66 days later (my progressed chart for October 10, 2020, 1:20:55 AM PDT) was December 15, 1954, 10:13:31 ET.

This is true because "day = year" is defined to be true regardless of how long the day is or how long the year is. So, when a new sidereal year begins for me, exactly 24 hours of progressed motion has necessarily occurred.

The problem to be solved is how to move from there up to now - how to calculate this for 5:51 PM PDT on September 4, 2021 (the minute I'm typing this sentence). Do calculate this, we need two numbers: The length of the mean solar day (what we normally call "a day") and the length of the current sidereal year from my last SSR to my next one.

My next SSR is October 10, 2021, 7:24:27 AM PDT. My last one was October 10, 2020, 1:20:55 AM PDT. Therefore, the time between them (the length of a sidereal year so far as it applies to me at the moment) is 365 days 6:03:32, or 365.2524537037037 days. The time from my last SSR to right now (9/4/21 5:51 PM PDT) is 329 days 16:30, or 329.6875 days. Divide this last number by the one right before it to learn that 0.9026291176333771 of a year has elapsed since the moment of my last birthday. That means that the same percentage (0.9026291176333771) of a day has elapsed in my progressions, i.e., 21:39:47. Add that to my progressed chart's date/time at the moment of my last SSR (December 15, 1954, 10:13:31 ET) to learn that the moment for which to calculate my secondary progression for right now is December 16, 1954, 7:53:18 ET (if I did the math in my head correctly).

How does this compare to traditional calculations (particularly Solar Fire which, like probably all astrology software on the market, uses a tropical year and probably a mean value)? If I use Solar Fire to calculate my secondary progressions for my home (34N03'46" 118W18'47") for September 4, 2021, 5:51 PM PDT, I get:

MC 1°33'13" Gemini
Asc 1°54'27" Virgo
Moon 20°53'58" Leo

If I calculate using what I calculated above (December 16, 1954, 7:53:18 ET), I get:

MC 0°39'19" Gemini
Asc 1°05'01" Virgo
Moon 20°51'54" Leo

Almost a degree different? Yes. As I wrote earlier today, the difference of the tropical to sidereal year is about 20 minutes a year (an hour in three years). In 66 years, that amounts to 22 hours or nearly one day. Therefore (maybe not a big deal to most people) that means that, at my age, my progressions will be about 22 hours off (about a day off). Not too bad for progressions... except for the quotidian angles! The 1° displacement is the whole orb of the angle! So, all this time, my SNQ quotidians (in recent years) have been about 1° earlier than my software has calculated.



One more thing to check: While the above is no big deal when calculated in software, using the routines Mike will be writing, maybe all those extra steps are unnecessary. How close do we get if we use a mean? Here is how that math goes:

The mean length of the sidereal year for 2000 (i.e., its length at epoch J2000.0) is 365.256363004. For the time today for which I performed the above calculations, I was 24,436 days 14:38 old, or 24,436.60972222222 days. Divide this number by the mean sidereal year figure of 365.256363004 to find that my progressed chart would be 66.90262565516103 days after birth.

October 10, 1954, 10:13 UT + 66.90262565516103 days is December 16, 1954, 7:52:47 UT (7:53:18 ET). THIS AGREES TO WITHIN ONE SECOND OF TIME WITH THE MOMENT I CALCULATED ABOVE BY THE LONGER ROUTE. Therefore, at least in this example, the longer route to the answer is unnecessary. All you need is age at the moment desired divided by the J2000.0 epoch length of the sidereal year.

So, there you have the exacting method and the "surely good enough" method, both of which significantly outstrip Solar Fire's method. Perhaps, also, this will serve as a worthwhile clarification of the theory of exactly what a secondary progression is.

[mikestar13]

I am convinced that I will use the "good enough method" and get much greater accuracy for sidereal progressions than Solar Fire has. (Imagine using the tropical year to calculate sidereal anything: it is idiocy, to be frank). The above calculation is so simple that I may well go ahead and use it to program quotadian progressions in this release--maybe doing the PSSR in the returns module in version 0.3.

[Jim Eshelman]

I effectively introduced the idea to Mark Pottenger 40 years ago but nobody has mentioned it to the authors of Solar Fire or Janus, I think. (Hey, it's a year, right? We know what a year is <g>.)

Anyway, I was surprised it would be that simple (while retaining accuracy). I knew it was true in principle, I just thought it might lose a bit in translation. My chart right now is a good test because I have a shorter SSRY than average (about 6 minutes shorter) and I'm barely a month before my birthday - so small errors would have accumulated by now if they were going to, I think.

If I'm wrong, I hope somebody points it out eventually so that a different approach can be used in the future

[mikestar13]

Well I changed direction and didn't finish this for version 0.2, but now I'm about ready to begin for version 0.4. I'm thinking a a calendar options page where we have two sets of options what bodies/angles to track transits/progressions/direction to and what bodies/angles to track transits/progressions/directions by. For bodies, the contact may be by conjunction, opposition, square or octile within a 1° orb (by default).
I assume that contacts to/by angles will be by conjunction only but will consider consider all angles including minor angles. A a few questions:

1. Are my assumptions reasonable?
2. Are angle to angle contacts valid? Example Q2 As on Natal MC.
3. For Eastpoint, also calculate in (precessed) RA? In my case to the point RA 47°18', adjusted for precession.
4. Another Eastpoint question. For example, my Eastpoint has a longitude of 25Ar36, should I be tracking crossings of this point, or of the point 20Ar41 (the exact ecliptic square to the MC)?
5. Should I attempt to track contacts to vertex and antivertex in azimuth (this would be optional, of course, if I try it at all--it might be overcomplicated).
6. The whole issue of transits/contacts in mundo...

[Jim Eshelman]

Are angle to angle contacts valid? Example Q2 As on Natal MC.

I have never tracked them and don't know how I would interpret them.

In a world where each angle has a distinctive house-like meaning, we could eek out a meaning for these. I consider that speculative at best (admittedly because I've never tracked them).

For Eastpoint, also calculate in (precessed) RA? In my case to the point RA 47°18', adjusted for precession.

Didn't check your math, but that's the idea. Except... having not calculated it both ways, I don't know that they give the same answer... my approach has always been "take the planet to the angle," not "take the angle to the planet." The correct way to do this, I think, is to precess the transiting planet back to the birth (or other) epoch. (I could dwell on the subtleties, but I think you have a grasp of this or can visualize where it could do wrong doing it the other way - I've just never tested to see how far off it could be in a normal human lifetime.)

Another Eastpoint question. For example, my Eastpoint has a longitude of 25Ar36, should I be tracking crossings of this point, or of the point 20Ar41 (the exact ecliptic square to the MC)?

Ecliptical contacts to EP are to the square of MC. The point written as EP (i.e., ecliptical longitude which is also 90° from MC in RA) has no ecliptical value.

Should I attempt to track contacts to vertex and antivertex in azimuth (this would be optional, of course, if I try it at all--it might be overcomplicated).

I read this as, "Should I take contacts to Vertex/Antivertex mundanely?" Since you aren't tracking contacts to other angles mundanely, the answer would be no.

I do think that, eventually, there should be an option to do all of these transits to angles, quotidian crossings, etc. mundanely just so we can finally determine what's what. (I don't think they're valid, but I could be wrong.) This is a more complicated problem that I think you probably want to do at a later stage (but I could be wrong about that, too ).

The whole issue of transits/contacts in mundo...

I think you mean what I just answered

[mikestar13]

Thanks Jim. Precessing transits back to the time of the nativity is the exact opposite of what I've been doing in solunars -- I've been precessing natal positions forward to the time of the return. IIRC, that's what Rob Hand advocates in Planets in Transit and Horoscope Symbols, and its how I've always done it. In theory, either method should yield identical results, but I need to test this (definitely true in longitude, may well not be true in RA).

I'm wondering why we even plot the Eastpoint longitude in the wheel at all, since it is not relevant to either contacts by longitude or contacts by RA. I know that some programs call it the Equatorial Ascendant, and I'm convinced it has no significance other than when it happens to coincide with the actual ascendant.

[Jim Eshelman]

Precessing transits back to the time of the nativity is the exact opposite of what I've been doing in solunars -- I've been precessing natal positions forward to the time of the return.

Right: "Take the planet to the angle" is consistent with both of those. With the SLR you "take the natal planet to the SLR angle." With transits to natal angles the ideal is "take the transiting planet to the natal angle." The question is: What (in a given problem) is the epoch of the angle?

If it makes a big difference to be able to precess the natal position, here is the trick: Don't do it to the EP. Instead, precess the MC then add 90°. Doing it the other way will create small discrepancies (RA-to-long ratios are slightly different in different parts of the zodiac).

I'm wondering why we even plot the Eastpoint longitude in the wheel at all, since it is not relevant to either contacts by longitude or contacts by RA.

It's not as necessary when all the math is being done in the background, as you're doing in TMSA. Its essential, though, if someone isn't calculating the angularities for you - otherwise, the astrologer has to calculate the EP-planet RA difference for every chart rather than see the (likely) angularity off the face of the chart. (Most of the time it is close enough if treated in longitude - just like usually you can tell angularity to horizon or meridian from the longitudes - but for better outcome one should calculate all of these mundanely.)

[mikestar13]

So for NQ-angles the planets of the nativity are precessed to the time of the quotadian, But what about contact by quotadian planets to natal planets? To natal angles? The can be safely ignored in SQ's and PSSR's as we are looking at most at the accrued precession in 30+ hours, but in the NQ case accrued precession in up to about a quarter of a year, and longer in the case of national charts (imagine examining NQ's to England's 1066 chart).

[mikestar13]

On the other point it is clear to me: don't precess other angles directly (I think this also applies to ascendant, and to the vertex if used), but precess the midheaven and derive the other angles from the precessed RAMC.