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Durations of solar phases

 
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Martin Gansten
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Posted: Sun Feb 21, 2016 8:07 pm    Post subject: Durations of solar phases Reply with quote

I'd be grateful for any tips on where I might find traditional figures for the durations of the different phases in the solar cycles of the planets -- for instance, from the heliacal setting of Mars up to its rising, X days; from rising up to retrogression, Y days; etc. It's the sort of thing I'd expect ancient/medieval authors to mention, but so far I haven't found anything.
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RegulusAstrology



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Posted: Mon Feb 22, 2016 5:11 pm    Post subject: Reply with quote

for superior planets at opposition there are two solar phase conditions:

"Acronycal rising" when a planet is seen to rise for the last time after sunset.

"Cosmical setting" first time a planet is seen to set betor sunrise.

Babylonian observations recorded only acronycal rising and not cosmical setting. For acronycal rising, Neil Swerdlow has estimated these degree ranges:

Saturn - 3 degrees
Jupiter - between 2 and 6 degrees
Mars - between 6 and 7.5 degrees

which John Steele metions in his paper here:

http://www.academia.edu/2360685/Acronycal_Risings_in_Babylonian_Astronomy

Claim no expertise on the Babylonian literature, though trying to work through it, but so far Steele's paper appears the best we have for superior planets at acronycal rising.

Hope this helps.
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Martin Gansten
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Posted: Mon Feb 22, 2016 7:45 pm    Post subject: Reply with quote

Thank you. What I'm really looking for, though, is periods of time (in days or months). I basically want them for the purpose of comparison: an Indian text that I'm working on has turned up some figures that don't seem right to me, but I might just be reading them the wrong way...
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RegulusAstrology



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Posted: Mon Feb 22, 2016 9:38 pm    Post subject: Reply with quote

I think several of the System A Babylonian models have measures of synodic time between certain solar phases which might help you. Will check on these in next day or two.
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RegulusAstrology



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Posted: Tue Feb 23, 2016 6:18 pm    Post subject: Reply with quote

Martin,

Here are the times for subdivisions of the synodic cycle for Saturn, Jupiter, and Mercury based on the most up-to-date research by Mathieu Ossendrijver. Babylonian Mathematical Astronomy: Procedure Texts, Springer, 2012.

This data obviously predates the Hellenistic astrological tradition, so if you find any kind of match with your Indian sources, it would suggest the Babylonian astronomy as the root of both traditions. That's something I am not going to get into.

Definitions

Superior Planets
FA - first appearance (after superior conjunction as a morning star)
S1 - first station (stationary retrograde)
AR - acronychal rising (immediately before opposition)
S2 - second station (stationary direct)
LA - last appearance (prior to superior conjunction)

For Jupiter and Saturn, the following periods were identified. Measurements are in mean tithis. To convert to days, multiply by 0.984353.

Jupiter A.s1
LA to FA 30.0
FA to S1 120.0
S1 to AR 60.0
AR to S2 60.0
S2 to LA 132.0
LA to LA 402.0

Jupiter A.s2
LA to FA 30
FA to S1 120
S1 to AR 60
AR to S2 64
S2 to LA 128
LA to LA 402

Saturn
LA to FA 40
FA to S1 120
S1 to AR 52.5
AR to S2 60
S2 to LA 120
LA to LA 392.5

There are two Jupiter systems which vary in the last two categories. For Saturn, Ossendrijver has a question mark by LA to FA = 40 as a value of 32 would be more consistent with reality.

Ref: Jupiter Table 3.38a, p. 93
Ref: Saturn Table 3.581, p. 108

Mars I was unable to work out. This material is quite formidable on a first glance given the vocabulary, sexagesimal computation system, and the impact of greater orbital eccentricity for Mars and Mercury. Ossendrijver reports that no subdivisions for Venus have been found.

For Mars, see Table 3.29, p. 86. I can tell you that only three subdivisions are reported: LA to FA, FA to S1, and S1 to LA.

For Mercury now it gets complicated.

Definitions for inferior planets,
EF - evening first
ES - evening station
EL - evening last
MF - morning first
MS - morning station
ML - morning last

System A(1), see Table 3.8, p. 70.

This system computes two subdivisions of the solar phase:
MF to ML and
EF to EL

The duration of solar phase between these two pairs of dates varies based on for which sign the starting point begins. This is the complication because of greater orbital eccentricity.

MF to ML starting in Aries is only 14 tithis; but 46 starting in Sagittarius
EF to EL starting in Gemini is 45 tithis; but 14 starting in Libra and Scorpio
Every sign has a different number of tithis/days - what I have just written shows the range of values.

System A(2), see Table 3.11, p. 72

This system computes different subdivisions, skipping the stations like A1.
ML to EF and
EL to MF

ML to EF starting in Virgo is 52;15 but only 22;15 from Gemini
EL to MF starting in Aries is 38 but only 10 from Capricorn.

----------------------------------------------

I am sure you had something different in mind when posting your original query, from somewhat later Hellenistic/Medieval sources. But this material is foundational for what came later.

Additional discoveries continue to be made with the latest from Ossendrijver reported on Jan 28 2016 on the use of trapezoid geometrical equations for computing subdivisions of Jupiter's synodic period, something which didn't happen in the west until 1500 years later.

http://science.sciencemag.org/content/351/6272/482.full?ijkey=qgiw36Ak9gSes&keytype=ref&siteid=sci

http://amor.cms.hu-berlin.de/~ossendrm/cuneiform.html
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Martin Gansten
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Posted: Tue Feb 23, 2016 7:53 pm    Post subject: Reply with quote

Thank you very much for this. I shall have to go over it more carefully in a few days' time. As you say, it wasn't what I had expected, and I'm still interested in later sources as well, but the Babylonian material looks quite promising. Thanks again.
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skyrack



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Posted: Wed Feb 24, 2016 11:19 am    Post subject: Reply with quote

https://www.google.co.th/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&ved=0ahUKEwjixLGTm5DLAhVKco4KHblMC2EQFgg5MAU&url=http%3A%2F%2Fastropolis.pl%2Findex.php%3Fapp%3Dcore%26module%3Dattach%26section%3Dattach%26attach_id%3D118149&usg=AFQjCNFxg86lli2CcA91n8NXo8Dogx58Zw&sig2=wypau0PgzStxyde-bEGCRA&bvm=bv.114733917,d.c2E&cad=rja

That link will download a PDF : THE ARCUS VISIONES OF THE PLANETS
which doesn't answer your question regarding planetary heliacal cycles in terms of time but in terms of space.
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Martin Gansten
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Posted: Wed Feb 24, 2016 7:08 pm    Post subject: Reply with quote

Thanks. For the purpose of comparison, though, it's the time units I need.
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