Wonderful illustrations Ren?. If I only could handle computers and programs, it would save me a lot of writing.

Another interesting definition of the MC is the one of Morin's house system.
The ecliptical projection of the point on the meridian crossing the equator.

The 'usual' MC can also be defined by the method how it is calculated. To calculate the MC (on the ecliptic) the point on the crossing of the equator with the eastern horizon (thus exactly in the east) and then projected on the ecliptic. The result is MC+90? so only that 90? have to be subtracted.

LIkewise the point 90? before the Ascendant can be found via the zenith point projected on the ecliptic.

Thes points can easily be found using the formulae to convert from equatorial to ecliptical coordinates. http://en.wikipedia.org/wiki/Ecliptic_c ... oordinates

Personally I find that this makes it less troublesome that a planet on the ecliptic MC doesn't necessarily coincide with the meridian (and likewise with Ascendant and horizon). In these cases one can consider these points as a sort of nodes.

After all most people use the positions (aspects of planets) to lunar nodes, 0?Aries/Libra in the reference plane of the ecliptic and not on the real orbit of the Moon and the equator respectively. A similar thing is done with Pars Fortunae, here too the ecliptical ascendant and not the horizon serves as a base for this point.

Although I personally prefer the ecliptic (tropical) reference frame considering it the most perfect one for the purposes in astrology, I don't condemn the alternative uses of other frames but in that case I think everything should then be done consistently.

johannes susato wrote

Drop a perpendicular from Alphard to the ecliptic . . . and you get the connection between Alphard and MC now!

Right you are! But it's a rather twisted way.

Deb wrote

I also want to thank you 3D (such an appropriate user-name) - your diagrams show the 3D effect beautifully.

Thank you Deb, too!

Margherita wrote

But which software it is? How it is called? It looks so beautiful...

Yes it does. It?s called STARLIGHT and comes from Zyntara (better known under Bernadette Brady).
http://www.zyntara.com/starlight.html
It?s nice to switch from Skyview to Horoscope view with the click of a button! And I like the delineation of the stars and their parans with the traditional planets.

Eddy wrote

Personally I find that this makes it less troublesome that a planet on the ecliptic MC doesn't necessarily coincide with the meridian (and likewise with Ascendant and horizon). In these cases one can consider these points as a sort of nodes.

Agree with you Eddy because you call the Meridian-Ecliptic intersection a point. But the Meridian itself is a great circle.

Although I personally prefer the ecliptic (tropical) reference frame considering it the most perfect one for the purposes in astrology, I don't condemn the alternative uses of other frames but in that case I think everything should then be done consistently.

Yes I think too that the Ecliptic is a great reference frame. The planetary energies play here, with the Sun at the centre. But I still think that the Meridian and the Horizon belong to another frame, that of the observer on earth. This frame represents the gravity playing a role on earth.
Our horoscopes use the ecliptic projections to represent the heavenly situation. So I think we should be aware of that when we put in MC and AC as points on the Ecliptic. Especially when we use terms like ?conjunction? etc.

I enjoy this discussion!

Ren?

I agree that we need to be aware that we are dealing with ecliptic projections (or even ?affiliations?). It has to be that way doesn?t it? Otherwise everyone would expect to have the degree of Polaris on either their MC or IC at all times.

3D wrote:But I still think that the Meridian and the Horizon belong to another frame, that of the observer on earth. This frame represents the gravity playing a role on earth.
Our horoscopes use the ecliptic projections to represent the heavenly situation. So I think we should be aware of that when we put in MC and AC as points on the Ecliptic. Especially when we use terms like ?conjunction? etc.

I enjoy this discussion!

Ren?

It sure is enjoying, I also like the mathematical theories around astrology.

At least the 'real' horizon and meridian play a very significant role in several life aspects on earth like climate and tides from Sun and Moon. Some astrologers relate the 'mundane' factors of Sun Moon and planets to more 'concrete' events in astrology rather than those in an 'emotions/feelings' sense that often seems to be related to the ecliptic.

3D wrote:

johannes susato wrote

Drop a perpendicular from Alphard to the ecliptic . . . and you get the connection between Alphard and MC now!

Right you are! But it's a rather twisted way.

Perhaps it sounds a bit queer because of my deficits in English. But isn't it technically correct, to start from the known point, here Alphard, and then to go the correct way to the frame of reference, here the ecliptic, to give the point a measure in that reference? And the correct way is that in square to the ecliptic.

I would like you to correct me, that means the technically way or my description because the terms must be clear.

Johannes

PS: Me too, I like this discussion a lot, especially with your graphics now. And as Deb already wrote last week, it is very necessary.

Johannes
I didn't understand what you were saying before, but I do now. Perpendicular is a correct term, but it would be better to say "Drop a perpendicular line from the ecliptic to Alphard" since the ecliptic is above Alphard in the picture.
And yes, you are treating the MC as the pole of the ecliptic (as I speculated before), but I notice that Ptolemy does that too when he says that there is a configuration "whenever the fixed stars and the planet's are on one and the same great circle drawn through the ecliptic's poles". Differences in translations makes me unsure whether this applies to stars within the latitudes of the planets, or whether that is just the preferred situation. (In fact I am struggling with how that should be applied exactly, and wonder if it is this that Ptolemy says - at the end of chapter VIII - would be too difficult to observe and apply in practice).

But this is only one of the ways that Ptolemy recognised a valid configuration, because he said that they could be configured with respect to the planets or Sun and Moon or ecliptic / or with respect to the earth / or through a combination of those. The main emphasis of his text then falls upon defining the phases, by which the longitude position becomes the 'true rising' position (because here the Sun conjoins the star) so this degree keeps a special affinity with the star at all times.

BTW, I also want to say that I appreciate the efforts made by those who are stretching to write in English.

Hi Johannes, you said:

Perhaps it sounds a bit queer because of my deficits in English. But isn't it technically correct, to start from the known point, here Alphard, and then to go the correct way to the frame of reference, here the ecliptic, to give the point a measure in that reference? And the correct way is that in square to the ecliptic.

I would like you to correct me, that means the technically way or my description because the terms must be clear.

I think I understood perfectly what you were saying and your English is perfect for me. And I completely agree with you. Sorry for my perhaps misleading remark about the ?twisted way? ? I just wanted to point out that the two reference frames (ecliptic and topocentric) are being mixed.

Whether you draw the perpendicular line from Alphard to the Ecliptic or vice versa doesn?t matter to me. I think what one does is to connect Alphard, the north and the south ecliptic pole with a great circle and then see where it falls on the Ecliptic.

Ren?

Hi Deb,

I notice that Ptolemy does that too when he says that there is a configuration "whenever the fixed stars and the planet's are on one and the same great circle drawn through the ecliptic's poles". Differences in translations makes me unsure whether this applies to stars within the latitudes of the planets,

Interesting what Ptolem?us says here. He only refers to planets and stars, so he doesn?t mix two reference systems. Relating bodily objects like planets and fixed stars within ecliptic longitude and latitude is ? IMHO ? legitimate, even for stars further away from the Ecliptic. I have problems, however, when he starts to mix the two reference frames - or I don't quite understand this...:

But this is only one of the ways that Ptolemy recognised a valid configuration, because he said that they could be configured with respect to the planets or Sun and Moon or ecliptic / or with respect to the earth / or through a combination of those. The main emphasis of his text then falls upon defining the phases, by which the longitude position becomes the 'true rising' position (because here the Sun conjoins the star) so this degree keeps a special affinity with the star at all times.

Regarding the last sentence, I recognise that many famous and respected ancient and medieval mathematicians only regarded the projection points on the ecliptic as relevant. E.g., Primary in mundo Directions without Latitude.
My suspicion is that it was just too labour-intensive to include latitude . In my early Astrology days, when there was no Astrology Software like today, I calculated the Ascendant by Spherical Trigonometry. I had a pocket calculator with Trigonometry functions, but it still took 10-15 minutes to calculate just the Ascendant. The ancients didn?t even have pocket calculators so I can imagine how tedious it must have been with self-made logarithmic tables!! I have great respect for what people like Placidus, Kepler and Johannes M?ller from K?nigsberg (Regiomontanus) achieved with limited means.

Ren?

This is somewhat off topic, but:

3D wrote:I recognise that many famous and respected ancient and medieval mathematicians only regarded the projection points on the ecliptic as relevant. E.g., Primary in mundo Directions without Latitude.

What would 'in mundo without latitude' mean? The usual definition of primary directions in mundo is that they include latitude, i.e., use the actual positions of the planets.

3D wrote:Regarding the last sentence, I recognise that many famous and respected ancient and medieval mathematicians only regarded the projection points on the ecliptic as relevant. E.g., Primary in mundo Directions without Latitude.
My suspicion is that it was just too labour-intensive to include latitude . In my early Astrology days, when there was no Astrology Software like today, I calculated the Ascendant by Spherical Trigonometry. I had a pocket calculator with Trigonometry functions, but it still took 10-15 minutes to calculate just the Ascendant. The ancients didn?t even have pocket calculators so I can imagine how tedious it must have been with self-made logarithmic tables!! I have great respect for what people like Placidus, Kepler and Johannes M?ller from K?nigsberg (Regiomontanus) achieved with limited means.

Ren?

Absolutely, they must have spent nights calculating. The calculating of planetary positions is even much more difficult than of ascendant and houses. Just imagine that every year we all had to make our own ephemeris. It makes me think that one of the most obvious reasons of the use and popularity of primary directions in the past is simply because it requires only the natal chart and a couple of calculations of houses. (and perhaps a bit more for secondary motion). Secondary progressions require already more effort, then the solar returns but calculating the ephemerides required for transits is the most time consuming of all.

I found an online star catalogue. http://www.alcyone.de/
http://www.alcyone.de/SIT/bsc/
Note that the positions are in Right Ascension and declination and for the equinox 2000. So they need some converting. However in a quick glance one can see if a star is close to the meridian (for all clarity I don't mean the MC and ecliptic). The location of stars are expressed in RA hours and minutes and are similar to the sidereal time which on its turn is used to find MC and Asc. People who use the Meridian house system can use the positions also to find stars on the cusps of any other house instead of only IV and X.

This suddenly make me think about the definition of the meridian. In the Meridian system the meridian X starts at the north celestial pole and goes through the south to the south celestial pole. Regiomontanus and Campanus however use the points in the north and south as the 'poles' of their system. A few days ago I suddenly realised that Placidus can be defined in two ways. From the north pole or from the point in the north. The result will usually be the same but I believe if one uses the method of Michael Wackford for circumpolar objects then the first definition would be the only one that counts. The second definition, resembles Haly Abenragel's system of the parallel circle of the ascendant also used by some 1930's Dutch astrologers.

Another rough but very quick and easy mean is to buy a planisphere http://commons.wikimedia.org/wiki/File:Planisphere.jpg
for the required location. This is in fact almost the same as the ancient astrolabium in a modern plastic jacket.

Martin,

What would 'in mundo without latitude' mean? The usual definition of primary directions in mundo is that they include latitude, i.e., use the actual positions of the planets.

You are right of course, just leave out the ?in mundo?. Mea culpa

Ren?

3D wrote:You are right of course, just leave out the ?in mundo?. Mea culpa

Phew! I won't have to rewrite that book, then.