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Solar Returns and Leap Year corrections
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Andrew Bevan



Joined: 20 Dec 2005
Posts: 4674
Location: Oslo, Norway

Posted: Fri Dec 12, 2014 11:36 am    Post subject: Solar Returns and Leap Year corrections Reply with quote

Solar Returns and Leap Year correction

Everybody who has worked with Solar Returns will have noticed that they jump a bit backwards and forward with a day according to the birth year and where the solar return occurs according to the leap year cycle. I could make fun of this during a consultation session, suggesting to the client it was a good opportunity to celebrate oneself on both days. In the case of myself, I am born on August 6. but my Solar Return could occur on the August 5. So I could be Merry on both, or when people come by on August 6., I could try and shy the occasion off and say: "Naw... it was Yesterday." Confused

Today's client was born 4 a.m. on January 17. I am going through several Solar Return charts and in 2015 her Solar Return will be on January 16. In 2014 it was on January 16., but in 2013 she rounded the Sun at 20.00 hrs CET on January 15!!! How the heck could that be possible?? Shocked

My reasoning is that this could not have been possible if she were born during the Summer. But in January the Earth is at perigee and closest to the Sun, picking up a daily and apparent motion of 101'. This is much swifter than the sluggish 057' that accompanies the Summer, but which does cause the Summer season in the Northern hemisphere to be considerably longer than the Summer. However, I never before realized that this difference could toss a Solar Return two days, and this came to me as new learning! Idea Exclamation
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AquarianEssence



Joined: 10 Nov 2006
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Location: Michigan, USA

Posted: Mon Dec 15, 2014 5:45 pm    Post subject: Reply with quote

Hi Andrew. I decided to try this myself, looking at 3 charts dated January 13, 28 and feb 9 but couldn't get it to repeat your findings. I even cast a chart for your location for Jan. 17, 4 am, year before, during and after a leap year but none of 5 solar returns checked for any given natal year were further away than the day before. What am I missing?

I always thought it interesting that I have a brother born the day before me and he managed to be born with the same exact Sun degree, to the minute, as me. He accomplished that by coming in 6 years later during a leap year, 10 hours 56 minutes later in the day than me. I was born half way between leap years.
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Andrew Bevan



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Posted: Tue Dec 16, 2014 9:14 pm    Post subject: Reply with quote

Hi AquarianEssence,
The explaination appears to be that I am partially wrong, because there is another factor I forgot to take into account - the precession of the equinoxes. The deviation from the moment of birth, i.e. relationship to that same time of the day appears to increase with age. Could this be the counting factor? It's still interesting. Thanks! Surprised
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AquarianEssence



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Posted: Tue Dec 16, 2014 10:18 pm    Post subject: Reply with quote

Ok. I don't precess. Thanks. I thought at first maybe I just didn't have a birth time early enough in the day so created one to test and that one didn't work either. I was surprised to seem my dad's date didn't change during the 5 years I looked. His birthday is January 28, 1937. I use sunrise because his birth certificate doesn't have a time recorded.
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Andrew Bevan



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Posted: Wed Dec 17, 2014 8:59 am    Post subject: Reply with quote

AquarianEssence,
I don't precess, either, but now this has got me all confused. Check this chart out, the client is born on Jan 17. 1940, Hamburg, Germany, at 03.52 CET. The Solar return for 2015 is due at 07.55 UTC on Jan 16. In 2014 it occurred at 01.58 UTC on Jan 15. Then in 2013 it is to have occurred at 20.01 UTC on January 15.

What is going on?? Confused
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AquarianEssence



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Posted: Wed Dec 17, 2014 12:46 pm    Post subject: Reply with quote

Wow!, You're right. It is the years following the leap year.

2009 SR 9:49:26 pm Jan. 15 1 day 6 hours before birth anniversary
2010 SR 3:38:17 am Jan. 16 just under 1 day shy of birth time of 3:52 am
2011 SR 9:25:35 am Jan. 16 6 hour jump
2012 SR 3:19:59 pm Jan. 16 6 hour jump with leap day coming
2013 SR 9:01:02 pm Jan. 15 6 hour jump, back 1 day
2014 SR 2:58:11 am Jan. 16 6 hour jump, near birth time

I wonder if it is due to the distance it is from the leap day, combined with being less than 6 hours after midnight. She was born during a leap year, but before the day was added. But, perhaps just as relevant is the speed on that day. It is the same rate as at the solstice, when Sun reached 0Cap 07'38", that is 101'06"/day. At the exact solstice point, the rate is 101'05" but it gains 5" of speed as it moves through the first 1912' of Capricorn, then starts to decelerate from there. So, she was born when Sun had reached 1 second faster than the solstice point, but on the decelerating side. Sun was only at this speed Jan. 16 and 17th but most of the 17th was 1 second slower, the same as when Sun entered Capricorn. Also interesting is the fact that Sun reaches this solstice rate of speed on Dec. 19 with Longitude 26 Sagittarius 33', at the galactic center and just under 30 before her Sun degree. It holds that rate until late on the 22nd. I wonder what her mother experienced at that time. I also wonder if her vibrational frequency is aligned with the GC.
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Andrew Bevan



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Posted: Wed Dec 17, 2014 3:49 pm    Post subject: Reply with quote

Thank you for the detail and easy to read feedback! Smile

Her first SR on Jan 15. appears to occur in 1993 when she was 53 years old. But here can I see that my astrology program isn't including the zone time (-1 for CET). Europe is 1 hour ahead of UTC or GMT, so for this woman the first Solar return on Jan. 15 in local terms occurs on Jan 15. 1997.
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AquarianEssence



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Posted: Wed Dec 17, 2014 4:11 pm    Post subject: Reply with quote

Do you think that adding leap seconds would make this happen, assuming the software is taking them into account? Between 1972 and 1979 they added 9 leap seconds. They are added simultaneously worldwide, without waiting for the time zones. For example, there was a leap second added December 31, 2005 23:59:60 UTC. It was December 31, 2005 18:59:60 EST where I live but was January 1, 2006 in +1 time zone and further east.

ETA: They began adding leap seconds in 1972 and have added 25 so far, 15 on Dec. 31 and 10 on June 30. Also, Kepler is using CET, 1 hour east of UT for all returns.

Connie
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Martin Gansten
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Posted: Sat Mar 07, 2015 9:47 pm    Post subject: Reply with quote

I'm resurrecting this thread rather than starting a new one on basically the same theme... Did someone figure this out in the meantime? It's to be expected, of course, that the time of a solar revolution increases by about 6 hours, or a quarter of a day, every year (the year is about 365.25 days long), and jumps back a day in relation to our calendar every time there's a leap year. But there is clearly more to it than that, whether one uses the sidereal/precessed or tropical/non-precessed year.

Earlier authors both east and west calculated revolutions by adding a fixed number of days, with fractions, to the original birth time, suggesting that the length of year is fixed (and at least one Indian author I've read, Balabhadra, explicitly says that this is a true value, not a mean one). But modern software disagrees, as anyone can see for themselves by running a few consecutive solar returns on their application of choice: the time between two returns of the Sun to the same longitude can vary quite considerably. Here are some values I got for my own revolutions (sidereal/precessed, but the situation is the same in either case, as I said):

365, 06:11:11
365, 05:54:31
365, 06:14:56
365, 06:12:30
365, 05:59:30
365, 06:14:13

Perhaps the programmers among us can shed some light on the variables that go into these algorithms?
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jventura



Joined: 04 Jan 2011
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Posted: Sat Mar 07, 2015 11:25 pm    Post subject: Reply with quote

Hi Martin,

I am curious as well in what conditions the solar return is more than 24h apart from the birth time. Unfortunately, I had a problem with my computer recently, lost some of my source code files and I can't test it now. I hope to be able to try something and contribute back something of value in a few days or weeks.

Regarding the last question, I don't know how others do it but this is my approach: nowadays it is computationally "cheap" to compute the planetary positions (specially with computer libraries such as the Swiss Ephemeris). Therefore, in my case, I use something similar to the Newton's Method to iteratively find the date until the distance between the intended sun's longitude and "real" sun's longitude is smaller than a certain threshold.

Algorithmically, and with an example, it is something like this:

0 - Imagine we want the next date when the sun will be at 120.52 and today the sun is at 0. In other words, we want the next solar return date starting from "today's" date.
1 - We add 120.52 days to our "search date" and recompute the sun's position.
2 - Since the sun's motion is not constant, we may get some other value for the sun's longitude, for instance "120.4"
3 - We add 0.12 (120.52 - 120.4) to the "search date", recompute the sun's position, and get a closer value.
4 - We iterate over (3) until the error is small enough. The final "search date" is the date of that solar return. The smaller the error, the better the date.

To be more correct, instead of dates I use a number called Julian Date (which represents a date), and instead of adding for instance 120.52 to the julian date, I add 120.52 * mean-motion-of-sun. This algorithm iterates about 3 or 4 times, to an error smaller than one second (of time).

I hope my explanation is understandable enough.
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jventura



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Posted: Tue Mar 10, 2015 6:08 pm    Post subject: Reply with quote

Hello again,

I think I have figured this out. It seems to me that has nothing to do with precessions, but allow me to explain (beware, this is quite a dense post).

As Martin said previously, the year has an average of 365.25 days. And because of that, the time of a solar revolution is expected to increase 6 hours each year. As an example, if someone was born in 1980, the time of solar revolutions on the subsequent years would be as:

1980 - Birth time
1981 - Birth time + 6h
1982 - ............... + 12h
1983 - ............... + 18h
1984 - ............... + 24h
1985 - ............... + 30h
1986 - ............... + 36h

However, in a few years our calendar would be ahead of the astronomical reality by many days. Thus, to compensate, every 4 years (leap year) we must include an extra day in our annual calendar. The expected effect for the 1980 birth would be something like:

1980 - Birth time
1981 - Birth time + 6h
1982 - ............... + 12h
1983 - ............... + 18h
1984 - ............... + 0h (Leap year)
1985 - ............... + 6h
1986 - ............... + 12h

The leap year has an effect of "reseting" somewhat the calendar, by setting the time distance back to zero.

However, there is a slight problem: in reality, the average number of days per year is not exactly 365.25 but 365.2425. So, our 1980 birth would be in reality:

1980 - Birth time
1981 - Birth time + 05.82h
1982 - ............... + 11.64h
1983 - ............... + 17.46h
1984 - ............... - 00.72h (Leap year)
1985 - ............... + 05.01h
1986 - ............... + 10.92h

This means that we subtract 24h each leap year but never add exactly 4 * 06h. The following figure shows the hour distance from the anniversary date/time for someone born on 1980/03/21 over the course of 100 years.



Over the course of the years, the average hour distance to the birth time keeps getting behind and behind. The next figure shows the same hour distance from birth time, but for someone born on 1983/03/21.



Since 1984 was a leap year, the first solar return after 1983 sets immediately a negative distance. Over time, the distance is always larger (towards negative) that in 2016 it reaches more than 24h of distance (red horizontal line). This effect leads in some cases to solar returns up to two days before the birth day.

(This is the answer to topic, but the rest is also quite interesting.. Smile )

However, now one would expect that the longer someone lived, the greater that hourly distance increase toward negative. But watch what would happen if our 1983 native would live 400 years:



As you can see, around 2100, 2200 and 2300, the cycle would be corrected - years multiple of 100 are not considered leap years, and would not contribute to subtract the 24h from the sequence, which would allow the cycle to recover.

But now there is another problem: every 100 years, the hour distance is increasing in average towards the positive (up). It could present a problem if our 1983 native lived more than 1000 years. The following figure shows what would happen if our 1983 native would live 1000 years.



What happens is that every 400 years, that upward movement of 400 years is counterbalanced by making it a leap year and forcing the cycle to go down again. Therefore, every 400 years we must have a leap year to restore the (400-year) cycle downwards.

The leap-year article on wikipedia is also interesting and shows a picture similar to the latest one.


Sorry for the long explanation, but I couldnt come up with a simpler explanation for this. Let me end by saying that the previous pictures were done using flatlib (my traditional astrology computer library which will be open-sourced soon and which allow anyone to try these and other things) and matplotlib, a python library for plotting graphics.


Joo Ventura
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Martin Gansten
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Posted: Tue Mar 10, 2015 8:39 pm    Post subject: Reply with quote

jventura wrote:
(This is the answer to topic, but the rest is also quite interesting.. Smile )

Thanks, Joo. You're quite right, of course, and I think you probably have answered the original question. But I'm afraid there's more!

As I said previously, when you look at several continuous revolutions, you find that a year as defined by the return of the Sun to its natal longitude actually varies quite a bit in length. This is irrespective of calendar system, and it's equally true in the tropical and sidereal zodiacs. Here are some example figures from six consecutive years in my life:

(Sidereal/precessed)
365, 06:11:11
365, 05:54:31
365, 06:14:56
365, 06:12:30
365, 05:59:30
365, 06:14:13

(Tropical/non-precessed)
365, 05:47:51
365, 05:31:32
365, 05:52:25
365, 05:50:49
365, 05:38:30
365, 05:54:03

Overall, the tropical year is shorter; but the difference between two tropical years can be as great as the difference between the tropical and sidereal measures for a given year, and I haven't so far been able to work out what causes these fluctuations. Any ideas out there?
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astralwanderer



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Posted: Tue Mar 10, 2015 9:27 pm    Post subject: Perturbations Reply with quote

Hi Martin - these differences may well be due to perturbations that need to be accounted for by calculations of solar, lunar and planetary returns. Michael Erlewine's Manual of Computer Programming for Astrologers, which forms the basis of much astrological programming today, mentions the need for calculation routines to take account of perturbations in orbit.

Erlewine says of the solar and lunar return routine in his book "This program makes use of a program originally submitted to MATRIX Magazine by Robert Hand. This program includes a good number of the major solar and lunar perturbations - which is why the rather good accuracy." (p. 103-104)

The solar and lunar perturbations are due to a wide range of factors.

https://en.wikipedia.org/wiki/Perturbation_%28astronomy%29

Mitton (1991, 1993) in her Dictionary of Astronomy defines 'perturbation' as "a temporary or localised gravitational disturbance in the otherwise uniform motion of a body under a stable gravitational force." Essentially, each body in the solar system is subject to a range of gravitational forces which impact on its own motion and these need to be accounted for in the calculation of return positions.
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jventura



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Posted: Tue Mar 10, 2015 9:47 pm    Post subject: Reply with quote

Astralwanderer's answer is correct! Also, this section of the March Equinox wikipedia article is quite elucidative: the major perturbations seems to be nutation (Earth's nutation, maybe?) and other perturbations directly on the sun.

I've done the following figure which shows the solar year length compared to an average solar year of 365.2425 days (in minutes). It considers the "distance" between successive occurrences of spring equinox and shows, if I haven't commited any error, that the differences can achieve more than 25 minutes from peak to peak.



Our solar system is a quite complex clock! Smile


Joo Ventura
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Martin Gansten
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Posted: Wed Mar 11, 2015 6:32 am    Post subject: Reply with quote

Aha! That must be it. Thank you both very much!
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