Happy New Year to Everyone.

Hi Christina,

Sorry for my tardy reply but I do not have internet access at home at present. My question regarding Morin was picking up your reference to Zoltan Mason as another source you recalled for the 16' orb for a parallel of latitude. As Zoltan Mason was so influenced by the ideas of Jean-Baptiste Morin I was wondering whether he got the idea from him originally?

Charles Jayne was undoubtably a very original modern astrologer in developing the use of declination. However, I would still like to know what the traditional sources said in this area regarding orbs for a parallel of latitude.

The mathematical system for orbs you describe proposed by Jayne(?) sounds very rationalist. It reminds me of Kepler's new aspects based more on a mathematical division of 360 degrees rather than the Greek Zoidia and the ability of planets to 'see' each other underlying the Ptolemaic aspects. One issue for modern astrologers using the suggested 16 minute orb is incorporating Pluto. This means you have to adopt a planetary zodiac 34 degrees wide (17 degrees north and south of the ecliptic) rather than the 14 degrees limit using traditional planets. Maths is definitely not my area so I will leave others to ponder the implications of that.

However, I wonder if a more traditional approach to latitude would not have given more weight to observational astrology and have been more influenced by the actual planets involved rather than being based on standardised statistical averages? Observational astronomy was certainly sophisticated enough to note such differences by the time of the Arab era astrologers. Clearly, moeity orbs used by Al Biruni and others for ecliptical longitude are too wide since many planets would be in almost constant contact with each by moeity orb. The planetary orbs would need to be much smaller but also vary according to the planets involved. I confess I have no astrological sources to support this idea so its only a tentative speculation on my part.

Putting the other side of the case early astrologers didn't have the sophisticated resources to measure latitude with the incredible accuracy as we can today and may have adopted a standardised approach to aspect by latitude for the sake of pragmatic simplicity. More speculation I concede. This subject clearly needs some detailed research as it seems quite neglected.

I completely agree that a traditional source is the preferred reference for parallel of latitude orbs. Even if none can be found to date it would still tell us something.

Hi,

I thought I would just provide a little update on this subject.
I have recently been studying Ben Dykes translation of Guido Bonatti's 'Book of Astronomy'.

Bonatti makes it clear that he considers a parallel of latitude (or conjunction by latitude) when two planets are within the same degree of the ecliptic. He interprets this in a similar way to a conjunction although he considers this a less powerful consideration than a conjunction by longitude. In fact, he doesn't consider latitude a very important factor at all compared to the ptolemaic aspects. Nevertheless, its interesting that Bonatti seems to allow a 1 degree orb similar to modern practice.

Bonatti interprets two planets in contrasting but equal degrees north or south of the ecliptic as similar in interpretative terms to a conventional parallel. This contrasts to modern astrology which describes this as a contra-parallel and interprets it like an opposition rather than a conjunction. Bonatti is generally regarded as one of the most important astrologers of the medieval period so I assume his views on this issue are fairly representative of astrological thinking in that period as a whole.

Mark,

Thanks for the latest contribution. It?s still a topic of interest to me. One degree seems like a lot compared to the total latitude span involved, but it is Bonatti and he did say that it was a weakish effect. The north/south equal, opposite degree information was a surprise.

I hope this topic is has not run its course, because I have a number of questions.

I've always been relatively strong in math. That has been a great advantage for me in astrology.

I can't locate a single star in the sky. I'm a moron in astronomy. This has been my downfall. Here is my first question:

1) When we look at figures for latitude, quite obviously this indicates the degrees above or belowe the ecliptic, the Sun's. Right?

However, the inclination of the earth itself is about 7 and a 1/4 degrees maximum, above or below the solar ecliptic. When we read about the latitudes of planets, is that relative to the Sun's ecliptic only or relative to the plane of earth's orbit? In other words, although the Sun is defined as 0 degrees latitude, since it is always in the center of our orbit, when I read (today) that Mars is -2:27 (south), does that mean at the moment that Mars is inclined that amount to the ecliptic of the Sun? Or to the plane of our orbit?

It appears to me that it's to the second. Does anyone know the answer?

Man, do I feel stupid.

Gaer

My understanding is that 0 degrees celestial latitude means that a point is on the plane of the ecliptic (the earth/moon barycentric orbital plane around the sun). Latitude values are degrees of deviation from that plane in the direction of the north or south celestial pole.

I'm confused by your distinguishing the earth's orbital plane and the ecliptic.

Ed F wrote:My understanding is that 0 degrees celestial latitude means that a point is on the plane of the ecliptic (the earth/moon barycentric orbital plane around the sun). Latitude values are degrees of deviation from that plane in the direction of the north or south celestial pole.

I'm confused by your distinguishing the earth's orbital plane and the ecliptic.

My understanding is the same. I have always thought that (celestial) latitude is nothing more than exactly what you just said.

I was mixing up the ecliptic with the invariable ecliptic plane. Wikipedia gives this definition:

"The invariable plane is within 0.5? of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital planes."

I was simply on the wrong track. I went wrong here, information again from Wiki:

Pluto
Inclination 17.14175?
11.88? to Sun's equator

If the inclination of Pluto, for instance, is a maximum of + or - 17.14175? or about 17?09', I could not understand why the readout from Astrolog shows a peak north position in the spring of 1979 and 1980 as +17:43, but a drop to 16:36 in the fall of 1979.

I notice that the average of 17:43 and 16:36 is so close to 17:09 that the rounding of the figures would account for the very, very small error.

I now think that this variation is due to the postion of the earth at it's southern and northern peak (celestial latitude) in its own orbit OR is linked to it's greatest distance from Pluto and nearest distance to Pluto, which goes roughly through a yearly cycle (roughly because Pluto is also moving a bit each year, but very slowly).

In other words, somehow the angle at which we view Pluto, relative to the ecliptic or our own orbital plane changes in a yearly cycle as we orbit the sun.

I may be completely wrong, so I hoped an astronomer, or someone who is very knowledgeable in astronomy, could either confirm that I'm on the right path, or correct me if I'm totally on the wrong track.

Gaer

Hi Astrojin,

It is my belief that the ancients consider declination for sun and celestial latitude for other wandering stars i.e. planets. With all of the explanations above (amongst others), we can conclude that the path of the sun is very much referenced to the celestial equator.

I'd second that ... and also like to keep in mind that there was also a shift in astronomy away from the the zodiac coordinate system (which is approx. 5000 years old) which designated the ecliptic as the equatorial plane, ie. the ecliptic was once regarded as the ?celestial equator?.

Not to confuse the zodiac's equatorial plane with the Earth's equator which is so named the ?celestial equator? because it serves as the equatorial plane for our terrestrial coordinate system.

Modern astronomers have used equatorial coordinate systems since Early Modern times (1500-1800) and of course this shift also affected astrology.

This shift in the framework, imo, is significant especially when it comes to interpreting what the ancients intended via their writings.

Also put the stars into motion as the frame of reference became more firmly fixed to a projection of middle earth.

The zodiac system uses the ecliptic rather than the terrestrial equator for its equatorial plane and is not susceptible to the drifting of stars across the celestial equator as in the commonly used equatorial coordinate system (right ascension, declination).

In the Almagest Ptolemy criticizes Hipparchus? use of an equatorial plane in some of Hipparchus? variously specified coordinate systems for this very reason.

We don't want moon to be in Pisces (WHY?????????????)

January Full Moon (wolf moon) follows a high path across the sky (northern hemisphere pov) from which point it then descends to it?s lowest point during summer solstice and then the ?dog days?.

In ?Pisces? it?s on the path down, descent. Voluminous tides. From electional pov perhaps may result in a ?wash out?. Something may get swamped, or need to be sacrificed ?

Steven,

Perhaps it would have been clearer if I?d written ?modern western? astronomers instead.

From early modern times, modern (western) astronomers began to mark the stars according to tropical co-ordinate systems such as the equatorial co-ordinate system, tropical zodiac etc instead of the zodiacal co-ordinate system ?ie. the shift to this ?solar-earth? framework time-wise was also commensurate with Gregorian calendrical reform, colonialization, empire building.
In other words, and in another context, in keeping with a more materialistic (earth) conquest (sun) driven cultural paradigm.

And there?s ?tropical? [modern: the tropical year defined as the interval during which the Sun's mean longitude, referred to the mean equinox of the date, increases by 360 degrees] and then there?s ?tropical? [traditional: "vernal-equinox year"].

Ref: http://aramis.obspm.fr/~heydari/divers/ir-cal-eng.html

Declination co-ordinates relate directly to the terrestrial framework, ie. terrestrial (earth) co-ordinate systems for which the celestial equator ? a projection of earth?s equator ? is key.

Where latitude is concerned, there's geodetic or geographic (common) latitude that relates to positioning on earth, then there's astronomical latitude (eg. angle between horizon & pole star) not to be confused with declination - and there's ecliptic latitude, which is what I believe's being talked about here.

Something can be located above earth?s projected equator (positive declination) yet be below the ecliptic (negative latitude). There?s ?above?, and then there?s ?above?, where a positive can be a negative, depending how one looks at it.

The tropical (?vernal equinox year?] was also regarded as a wandering calendar within the zodiacal co-ordinate system, so therefore when reaching back in time to ascertain why/how certain degrees etc were allocated their meanings, or use of parallels etc I?d have thought it reasonably important to have an idea of which co-ordinate system (zodiacal or equatorial) was being referenced.

The 360 degree dial we use in astrology today has roots back to the 360 day calendar of ancient times (ancient Mayans also had a tradition of a 360 day year).

Eg. http://webexhibits.org/calendars/calendar-ancient.html & http://www.12x30.net/artifact.html


Since the zodiac coordinate system (which is some 5000 years old) is celestially centered it is insulated against the many eccentricities of earth?s motion that equatorial co-ordinate systems, such as the tropical co-ordinate system, are subject to.

The zodiac co-ordinate system uses the ecliptic instead of a projection of earth?s equator as it?s equatorial plane and therefore it?s not subject to stars drifting across its celestial equator as occurs in the commonly used equatorial co-ordinate systems, eg. Tropical.

I thought it was made reasonably evident that our ancient counterparts also used equatorial (earth) co-ordinates through mentioning:

?In the Almagest Ptolemy criticized Hipparchus? use of an equatorial plane in some of Hipparchus? variously specified coordinate systems for this very reason" ? because of stars drifting across it.


The point I guess being that when travelling back in time in an effort to understand how astronomer-astrologers arrived at certain conclusions, it?s important to understand what frame of reference (co-ordinate system) they were using and for what purpose.

Otherwise displacement along with separation occurs.

It was the Arabs who invented spatial geometry. In fact it was they who first started using the equatorial system of co-ordinates.

Here we do differ as from my pov, no, they didn?t ? they inherited a vast amount of knowledge from Greek, Indian etc predecessors and further developed this knowledge, making highly significant contributions as well as propelling it further afield.

But it appears you?ve grasped hold of the wrong end of the stick ? no-one here has denied Arabic contributions to the field of astronomy-astrology. Referencing changes that occurred in early modern era ? a particular period in time - does not obviate the work of generations previous.

The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago. The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian's base sixty system of numeration. The Sulba Sutras written in India, between 800 BC and 500 BC, correctly computes the sine of (=45?) as in a procedure for "circling the square" (i.e., constructing the inscribed circle).

Indian mathematicians were pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha (circa 1350-1200 BC) is the first person thought to have used geometry and trigonometry for astronomy, in his Vedanga Jyotisha.


And no, they weren?t the first to use an equatorial system of co-ordinates (for example ref. Hipparchus above).

?It was this math that gave Christopher Columbus the faith to sail out in spite of the ignorant European belief that the world was flat!?

Columbus was refused permission because his calculations were wrong, not because of some ?flat earth? theory that captured popular imagination following publication of Washington Irving's 1828 biography of Columbus.

From ancient times, maritime navigation relied on the stars and the curvature of the spherical Earth.

Ref: http://en.wikipedia.org/wiki/Christopher_Columbus and http://www.columbusnavigation.com/cn.shtml

Underestimating the length of such a journey could result in sailors dying from starvation etc and the authorities & scholars of the day weren?t about to sign off their approval on what they saw to be an ill fated mission owing to calculations that were known to be incorrect.

Kind regards,
TS

Kirk,

We hear about declination these days ? some people even use it ? but in the older works latitude seems to be what they used. I don?t remember coming across discussions of declination until the 19th century.

I?ve been giving this some further thought, and what comes to mind is that our predecessors used the stars, moon & sun for navigation as much as anything else (Babylonians used sidereal).

Today I think someone would be hard pushed to navigate from a tropical chart.

Therefore, I think it might be relevant to turn to the old art of celestial navigation when considering latitude.

Our predecessors used ?astronomical latitude? (as well as ecliptic latitude) which is different to ecliptic latitude.

Astronomical latitude (which can be determined by using something like a plumb line from fixed star to horizon, kamal, measure via hands etc) is identical with the declination of the zenith direction.

For example, if the Northern Pole Star (Polaris) is measured via span of hand (width of fist with thumb tucked in, or your palm, equals approx 10 degrees and your arm needs to be fully stretched out in front of you), or a kamal etc to be at 40 degrees up from horizon (astronomical latitude), then your latitude here on earth is +40 degrees and zenith is + 40 degrees declination (ie. you?re at 40 degrees latitude from the equator, which is 0 degrees).

For latitude on Earth equator is key ? 0 degrees.
For declination the celestial equator, projection of earth?s equator, is key -0 degrees.

This gives us our north-south position on Earth as well as in the heavens and is an important co-ordinate.

If sailing for example, and you knew your hometown was also at 40 degrees latitude then you?d beat a direction east or west (longitude) to get there.
If you weren't at correct latitude you?d adjust your position via measure of the stars.

Knowing at what astronomical latitude a star culminated, and if you knew it culminated at the same degree of a particular island or port you wanted to visit, then you?d know you were on the right track if you were travelling at the same latitude on earth as the culminating degree of this star.

This leaves the other co-ordinate, longitude (motion east to west, ecliptic & use of stars near/on ecliptic), which also gives us time.
Much more difficult.
For this, Moon was key.

For example, in celestial navigation, lunar distance is the angle between the Moon and another celestial body, eg. a star.
A navigator can use a lunar distance and a nautical almanac to calculate Greenwich time. The navigator can then determine longitude without a chronometer.

Of importance to longitude is the Meridian (Prime Meridian) of which they?ve been many.

Going back, Hipparchus specified location using latitude and longitude as co-ordinates. He proposed a zero meridian passing through Rhodes.
He further suggested that absolute time be determined by observing lunar eclipses, measuring the time when a lunar eclipse started and finished, and finding the difference between this absolute time and local time.

The use of lunar distance in western history was relatively recent, ie. Within last few centuries, however our Arabic, Indian, Babylonian etc predecessors focused a great deal of attention on the Moon - they also used it to measure the stars.

Converting this to an estimate of distance to be travelled involved other calculations.

But getting back to initial question, astronomical latitude is identical with declination of zenith, therefore declination has been in use for ages.

I have much more trouble working with astronomy and the celestial sphere than with astrology itself. Picturing it in my mind and placing it in the sky is a slow affair.

A suggestion that hopefully might help.

Find a chart you're familiar with that has a fixed star on the angle, eg. on the Ascendant (east) and change this chart to sidereal (eg. Use Hindu/Lahiri).

Then visit:

http://www.fourmilab.ch/cgi-bin/Yourhorizon

and insert same data as chart (be easier if you know universal time equivalent) & press ?update?. This will bring up a horizon view for you of this data or any number of skymaps of your choosing.

Then compare this skymap to your sidereal chart (& tropical). This can help orient what you know astrologically to the celestial sphere.

Simply switching to sidereal doesn?t mean someone also needs to take up Vedic astrology etc. I feel it can simply help when trying to make sense of certain aspects of the tradition. And, imo, you can still use many of the techniques you already know from traditional studies for interpretation ? switching to sidereal simply brings forward a previously hidden dimension.

The ?tropical zodiac? was used by our predecessors largely for civil time (agriculture, taxes, etc).
I personally view it more as the terrestrial zodiac, ie. Solar seasons on earth ? as a timing device (eg. longitude) helping to tell us where Earth?s at time-wise when compared back to the celestial construct.
Whereas sidereal provides us with our celestial zodiac, an easier to follow picture of our position on earth, and earth?s position, with respect to the stars.

Wikipedia mentions astronomers (western) started mapping stars using equatorial co-ordinate systems (eg. Tropical) from early modern times (something that I?m also looking into ? I?d like to know why the change, I?m thinking it?s due to the rise in popularity of the heliocentric view which grew to dominate, cultural shift. ) As such, this change also naturally carried through to modern western astrology and the emphasis on use of tropical.

What this also suggests (at least to me) is that if we?re considering sources prior to early modern times, then we should also be considering them from a sidereal pov, ie. Zodiacal co-ordinate system.

Kind regards,
TS

A belated thank you for the reply. The celestial equator, the ecliptic and its obliquity, right ascension ? the whole mess ? has always been my weakest area. Right now my anxiety-ridden mind will probably cave in and finally crumble if I try to figure out these invisible markings in the sky. And then all those goings-on in the polar regions ...