Aspects, Midpoints, & Circles of Position

[Jim Eshelman]

I think I've finally figured out why I can't tell the difference between a planet square a midpoint and the conjunction-opposition contact usually called a direct midpoint. To me, they seem the same in effect - and I just realized that there is a mathematical reason that they are identical.

But first, I have to explain what a circle of position is and how this determines the nature of an aspect.

Positions vs. Circles of Position
Very casually (but routinely) we describe aspects as certain angular relationships between planets. That's not exactly right, though.

Most planets are not exactly on the ecliptic. Planets' latitude measures how far they are north or south of the ecliptic. When we say that a planet is at a particular longitude (or "location on the ecliptic") we mean that, if you drop a great circle through the planet at right angles to the ecliptic, it crosses the ecliptic at a particular place. A great circle is a circle on the surface of a sphere that has the same center as the sphere. (All circles of geographic longitude are great circles. So is the equator. These all have the center of the Earth as their center. But, aside from the equator, circles of latitude are not great circles - they're small circles - because their center is not the same as the center of the Earth. If this isn't immediately obvious, it will be if you think about it a few minutes or look at a globe.)

So, geographic longitude is measured around the circle of Earth's equator. Neither Chicago nor London is on the equator, but they both have longitudes: London is 0°10' West and Chicago is 87°39' West. This is because when we drop a great circle of longitude (a circle containing the North Pole and the South Pole) through the city intersects the Equator at these positions. London at 0W10 and Chicago 87W39 are 87°29' of geographic longitude apart - we might call them "square" (with a 2°31' orb) on the globe, about one-fourth of the way around the globe measured along the equator. However, if you were to take a piece of string on a globe and mark measure the distance between London and Chicago, you'll see that in no way is it one-fourth of the way around the globe. The 87°29' difference in longitude is true along the equator but not by a direct measurement between the cities.

The same is true of planets. My Venus is 1°53' Scorpio. My Pluto is 2°06' Leo. Measured along the ecliptic they are 89°47' apart. But neither is on the ecliptic. My Venus is 5°48' south of the ecliptic; my Pluto is 9°55' north of the ecliptic. That is, in latitude, they're 15°43' apart. They aren't really 90° apart when you measure directly around the sphere from Venus to Pluto. They are only in partile square when you measure their longitudes, i.e., their positions projected onto the ecliptic.

Solar Fire, by the way, has a way for you to compare these two ways of calculating aspects. They called "3D Aspects" or "True Body Aspects." These don't measure along the ecliptic but, rather measure directly between the two planet on the sphere. In this case, the difference isn't much, but the Venus-Pluto orb is a little different measured 3D. (One weird example: By 3D aspects, I have a partile Moon-Pluto quincunx. By longitude they are 5° from that aspect.)

If this seems complicated, it's easier than you think. It's just like London and Chicago. Their longitudes are one-fourth of the way around the globe from each other. A string directly connecting the two cities shows they are much closer than 87° in "3D."

I looked at 3D aspects a few years ago, looking mostly at Pluto aspects (which would be the most extreme case usually). It was quickly evident that they are not operative - that the aspects operate ecliptically, not "3D," so-called.

Circles of Position
The great circle that defines a planet in terms of the ecliptic (or another measuring circle) is called a circle of position. Fleshing out what was mentioned above, it is a great circle on the celestial sphere, containing the north and south ecliptic poles, passing through the position of a planet at right angle to the ecliptic.

Please notice, though - and this is the single most important point in this post! - that this is a circle. Not a semi-circle. It's not just on one side of the globe. It wraps 360° around the globe.

That is, the great circle passing through my Venus crosses the ecliptic at 1°53' Scorpio wraps all the way around the celestial sphere and also crosses the ecliptic at 1°53' Taurus. This is exactly the same geometry of the horizon (which is a great circle) crossing the ecliptic at two opposite points (Ascendant and Descendant - same circle).

Aspects are Between Circles of Position
If aspects are not formed by an arc between the two planets themselves (and I am sure they are not), then they are formed between the circles of position of the two planets. In my case, for instance, one great circle (passing through my Pluto) wraps around the sphere at 2°06' Leo AND 2°06' Aquarius, another (passing through my Venus) wraps around the sphere at 1°53' Scorpio AND 1°53' Taurus, and these two great circles are square each other.

This has some fascinating implications. One of them (which matches my experience) is that there is that there is no difference between a conjunction and an opposition - they are the same aspect. When two planets are exactly conjunct OR are exactly opposite, the effect is the same: Their circles of position converge. (There is no mathematical difference.)

We can pursue these fascinating implications below in this thread or elsewhere - I don't want to dwell on it much or take up too much space at the moment - but I need to establish the basic concept. One difference I'll address: Many astrologers think that there is more of a sense of polarity or separation in an opposition that isn't present in a conjunction, and this (as a mild effect) matches my experience. However, this may not be a difference in the aspect but in the sign positions of the planets which, by themselves, create a sense of polarity.

What Does This Have To Do With Midpoints?
Here's what I realized today, i.e., here's where it gets really cool.

Just as aspects are formed between two circles of position, so are midpoints formed between two circles of position. This understanding produces at least one fascinating phenomenon. I can show it best by an example.

My Uranus is 3°20' Cancer. My Pluto is 2°06' Leo. They are 28°46' apart. Their midpoint is easy to calculate: The point half-way from Uranus to Pluto is 17°43' Cancer; or, if you circle the zodiac the other way, the point half-way from Pluto to Uranus is 17°43' Capricorn. Any planet conjunct either end of this is said to form a direct midpoint planetary picture.

My Mercury is 17°20' Libra. It squares this 17°43' Cancer-Capricorn axis. Normally it isn't considered
a direct midpoint, even though, in practice, I can't tell the difference.

Ah, but wait: We've missed half of it!

The great circle defining my Uranus' position isn't just 3°20' Cancer, it's 3°20' Cancer-Capricorn, as my Pluto's circle of position is 2°06' Leo-Aquarius. If (as I strongly believe) midpoints are formed between two circles of position, then there are four positions involved. There are four direct midpoints, those between 3°20' Can and 2°06' Leo, between 2°06' Leo and 3°20' Cap, between 3°20' Cap and 2°06' Aqu, and between 2°06' Aqu and 3°20' Can. In other words, there are four direct midpoints: 17°43' Cancer, 17°43' Libra, 17°43' Capricorn, and 17°43' Aries.

These are all direct. My Mercury is indeed within 0°23' of the midpoint between Pluto's circle of position at 2°06' Leo and Uranus' circle of position at 3°20' Capricorn.

[SteveS]

Most interesting Jim.

[Danica]

Jim, thank you, excellent formulation.

From all I have seen so far in experience, the Midpoints, measured in this way - along the circle of 360* with which we represent the ecliptic/zodiac - provide fascinating insight, especially in Synastry!

My Uranus is 3°20' Cancer. My Pluto is 2°06' Leo. They are 28°46' apart. Their midpoint is easy to calculate: The point half-way from Uranus to Pluto is 17°43' Cancer; or, if you circle the zodiac the other way, the point half-way from Pluto to Uranus is 17°43' Capricorn.

I would have missed this one.
There's no emoticon for: Beautiful-Wonderful-Perfection! so, just