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Absolute maximum declination of each planet
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Deb
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Posted: Thu Apr 01, 2010 4:38 pm    Post subject: Reply with quote

Its even better now Martin, but I think I would have labelled Venus at 9° for her max according to the geocentric perspective, since the traditional authors talk about her reaching this extreme (hence sometimes able to stay visible even when combust). The visibility, I believe, only remains at her inferior conjunction and not her superior conjunction, when her light is weaker because of the extended distance.

Anyway, since there doesn't seem to be an easily accessed source of information elsewhere, I thought I would draw up a table (which I can reuse in my CA project). This shows the furthest extensions of latitude according to Lilly's Christian Astrology, and I've added these to the OofE to get a rounded up figure for declination as explained above. I am taking most of Lilly's values on face value, although I suspect that they could all be polished up by a little by modern computer information. I am keen to correct of course, if there is anything in need of correction here.



BTW, I checked earlier, and Venus doesn't get anywhere near to extreme latitudes until 2015 at least.
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Eddy



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Posted: Thu Apr 01, 2010 6:52 pm    Post subject: Reply with quote

Several years ago I read an article about the maximum latitudes of Venus ever recorded. Unfortunately I can't find the article anymore, I never printed it Sad .

I don't understand why Lilly has different values for north and south of the ecliptic. They must be similar. The Moon's orbit's inclination for example oscillates between 5°01' and 5°17', with an average of 5°09'.
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Deb
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Posted: Thu Apr 01, 2010 7:03 pm    Post subject: Reply with quote

I just thought that is to do with the way that the orbital planes are centred around the Sun, and that there is some slight variation - but I never checked. The one to note is Mars - quite a difference there between its north and south values.
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3D



Joined: 19 Jun 2005
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Posted: Thu Apr 01, 2010 10:30 pm    Post subject: Reply with quote

Quote:
Deb wrote
Anyway, since there doesn't seem to be an easily accessed source of information elsewhere……


There is an easily accessible source. Perhaps you want to check Solar Fire’s Graphical Ephemeris. Set it for ‘Declination’, Angle 30°, Transits for about 100 years, select only one Planet or the Moon, No Radix Positions, press View and wait for a couple of Minutes and watch the picture develop. Using the cursor, you see the maximum declination North and South.

http://bildupload.sro.at/p/346249.html

http://bildupload.sro.at/p/346250.html

You can do the same with Latitude……

http://bildupload.sro.at/p/346251.html

And get this Graph for Venus.

http://bildupload.sro.at/p/346252.html

As Deb says, Latitude depends on the inclination of the orbital plane, and the position of the nodes. If the node is near summer or winter solstice point (like Jupiter’s and Saturn’s nodes), the planets Latitude is zero there and does not add to the maximum Declination of the Ecliptic. The Moon’s node moves around the Zodiac once in about 18-19 years. When it is at about 0° Aries, the full maximum Latitude of the Moon (about 5°) adds to the maximum ecliptical declination (23,5°) and we have the ‘Super Moons’.

Hope this helps
René

P.S. I don’t have any commercial ties with Solar Fire and I don’t get any commission from them. Wink
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Martin Lewicki



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Posted: Fri Apr 02, 2010 7:55 am    Post subject: Reply with quote

It's holiday time so I have a bit of time to knock these up. Here is the Mars geo lat illustration.

The differnces in north and south max geo lats is due to the large eccentricity of the Mars orbit. Other planets have less eccentricity so the differences are smaller.



Martin
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Deb
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Posted: Fri Apr 02, 2010 9:44 am    Post subject: Reply with quote

Hi Rene

Thanks for pointing that out - that seems a very useful tool - but of course it is only accesible for astrologers who have Solar Fire (not everyone does). I do like the way it shows the Super Moons.

Hi Martin

Thanks for sharing this new diagram - it's fabulous! Now I *understand* why the latitude of Mars dips further to the south.

Deb
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Eddy



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Posted: Fri Apr 02, 2010 11:38 am    Post subject: Reply with quote

As an addition to Martin's marvellously illustrated post, I'd like to say that since the nodal axis slowly moves as well as the apsides/perihelion-aphelion axis does, Mars' southern extreme could as well be in the North. This changes, just like the extreme latitudes not always coincide with the postions in Cancer or Capricorn as René points out.

I'm glad you fully understand it now Deb. Soon we can step to more advanced spherical trigonometry.


Last edited by Eddy on Fri Apr 02, 2010 1:52 pm; edited 1 time in total
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Deb
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Posted: Fri Apr 02, 2010 12:50 pm    Post subject: Reply with quote

Well, unfortunately, I no longer feel I understand the matter, now that you've said that Confused
According to Lilly's text, the most extreme limit of Mars' latitude (I always use the tem in the traditional, geocentric sense) extends to a further southern latitude than a northern latitude. This is what I thought Martin's diagram demonstrated (and so explained). But you seem to be saying this isn't so, and that its extreme latitude limit is equal, north or south. If this is the case, then there shouldn't be one figure north and one figure south; there should only be one figure which represents the maximum limit. So now I'm confused again - obviously Lilly did not invent these figures he copied them from other astronomical texts and usually his figures still stand up to scrutiny if you understand the perspective behind them. Hence I'm confused again - why are these figures saying that there is a difference and you are saying there is not ??

Quote:
Soon we can step to more advanced spherical trigonometry.


We'll just wait a while, until hell freezes over. Smile
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Deb
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Posted: Fri Apr 02, 2010 12:56 pm    Post subject: Reply with quote

A new thought. Eddy these geocentric figures relate to the planetary positions north or south of the ecliptic, not the equator - are you taking that into consideration? This is what I think Martin's diagram demonstrates - that even though the poles rotate, Mars is still capable of a greater inclination south of the ecliptic than north of the ecliptic.

Correct?

Deb
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Eddy



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Posted: Fri Apr 02, 2010 1:51 pm    Post subject: Reply with quote

Both can be right. I'll have to give it a closer look but it's possible that in Lilly's days and in the centuries before and after these max/mins were of these values. I indeed did take the ecliptic into consideration. In the picture you see the purple dotted line of the planetary nodal axis (with the usual node glyph) and the red dotted/little stripes line of the planetary apsides axis. These lines too have a rotation around the Sun of less than a degree per century, hence a period of many centuries. It means that these lines also move with respect to each other. In Martin's picture we see that perihelion of Mars' orbit is in the southern part. In several hundreds of years or more, the perihelion can be close to the ascending node and hundreds of years later in the highest part between the ascending and descending node. These have to be taken into account.

So in brief the differences given by Lilly probably are right but these are correct for a certain period of several centuries. If we wait long enough the other extremes will occur on the north side of the ecliptic.

Further the extreme declinations depend on the precession. Imagine for a moment that the apsides and the nodes axes wouldn't move but only precession would occur. If in Martin's picture the Earth's position on the right would be in the (northern hemisphere) Winter, then Mars would be -23.5°-6.8° = -30.3. Half a precession period (13,000years) later the Earth's position on the right would be the Summer. Then it would be 23.5°-6.8°=16.7°. The effect is 'flattened' and much less extreme.

However the periods when these three (and even more possible) occur in the same time will happen only once (during a several centuries) in the so and so many centuries/millennia or even longer. So theoretically (with the ideal apsides and node position) Venus can be an extreme 9.7° above the ecliptic and only at inferior conjunction with the Sun and when this occurs exactly at the same time as Summer solstice (which is necessarily for the extreme declination) then it will be 23.5°+9.7°=33.2°. If we take the change of obliquity into account (like 24° some 2.5 millennia ago) then this could even be more 33.7°. But this is an extremely rare event.
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margherita



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Posted: Fri Apr 02, 2010 2:41 pm    Post subject: Reply with quote

This is a comparing table of several ancient tables taken from

Ptolemy, Bianchini, and Copernicus: Tables for Planetary Latitudes in Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 58, No. 5, p. 453 - 473 (2004)



Alf.T. is obviously the princeps edition of Alfonsine Tables, Ratdolt 1483.

In every case in the modern list given by Tuckerman I have Mars 4.38 N - 6.53 S latitude.


margherita
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Deb
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Posted: Fri Apr 02, 2010 5:55 pm    Post subject: Reply with quote

Very useful Margherita - thank you. And thankyou too Eddy, for the further post, explaining how the values change, but only over very great periods of time.
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Juan



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Posted: Sat Apr 03, 2010 12:17 am    Post subject: Reply with quote

extreme north and south declinations of planets and the Moon:

AD 1 to AD 1000 (obliquity AD 1 = 23,42')

Moon 28n59 / 28s59 (AD 1 to AD 500)
Mercury 25n39 / 25s48
Venus 27n22 / 27s38
Mars 27n49 / 29s51
Jupiter 24n16 / 24s15
Saturn 23n49 / 23s47
Uranus 24n05 / 24s04
Neptune 23n07 / 23s09
Pluto 30n20 / 30s48

AD 1001 to 2020 (obliquity AD 1000 = 23,34')

Moon 28n45 / 28s45 (1800 to 2020)
Mercury 25n39 / 25s52
Venus 27n49 / 28s05
Mars 27n32 / 29s26
Jupiter 23n52 / 23s51
Saturn 23n16 / 23s17
Uranus 23n53 / 23s53
Neptune 23n07 / 22s59
Pluto 30n20 / 29s59

Source: Riyal max/min declination output sorted with a word processor.

Juan
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Martin Lewicki



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Posted: Sat Apr 03, 2010 3:12 am    Post subject: Reply with quote

Deb wrote:

Hence I'm confused again - why are these figures saying that there is a difference and you are saying there is not ??


Eddy is correct in that the longitudes of Mars perihelion and node do precess

However the rates are slow so make a small difference over the centuries.

Peri = 1.84°/cent
Node = 0.772°/cent

Since the time of Lilly's C.A. publication (1647) perigee has advanced 6.67° and node 2.8° in longitude. The difference 3.87° in longitude is the total offset of the framework in 363 years!

This makes only minor difference to the extreme geo lats.

Current arc between peri and node is 73.49°. As this is increasing the extreme lats are also increasing whereby they will reach maximum in 16 centuries time.

Martin
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pankajdubey



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Posted: Sun Apr 04, 2010 12:44 pm    Post subject: Reply with quote

@Martin,

I have lost the Astrolab Companion files and the download link in my mail has expired .

Pankaj crying
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