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Perigee and Apogee

 
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Andrew Bevan



Joined: 20 Dec 2005
Posts: 4676
Location: Oslo, Norway

Posted: Thu Jan 14, 2010 8:31 am    Post subject: Perigee and Apogee Reply with quote

Has anyone read anything about whether the points of the Moon's perigee and apogee have any significance in astrological terms? The perigee and apogee are those shifting points where the Moon in its orbit is closest to and furthest away from the Earth.



The distance from the Moon to the Earth varies from 363 104 km at perigee to 405 696 km at apogee. That's a variation of roughly 10% and causes its apparent diameter to vary from 29.3' to 34.1' of arc. This is an all-important factor when it comes to deciding whether an eclipse of the Sun may be annular or total. During the annular eclipse the Moon is so remotely placed in relation to the Earth that its apparant size becomes too small to completely cover up the apparent disc of the Sun. Opposite, when the Moon is close to us it appears large and passing in a straight line between the Earth and the Sun, it will cause a total solar eclipse. (This should not be confused with the optical illusion that occurs when the luminaries appear large to their placement close to the horizon). The size of the Solar disc varies from 31.6' - 32.7' of arc, which is a 3% variation that reflects the Earth's orbit and variation in our distance to the Sun (perihelion and apohelion).

The line that joins the perigee and the apogee is called the line of the apsides and moves gradually in the direction of the zodiac, completing one revolution in 8,85 years. That should work out to an average motion of 323' a month.



Another way in which the perigee and apogee points are important is that they determine whether the apparent movement of the Moon in the Sky is slow or swift, and whether her motion is increasing in speed, as when moving from apogee to perigee, or whether her motion is decreasing as when moving from perigee to apogee. A planet moving swift and increasing in motion is taken to be a more potent sign of vitality, in contrast to a planet that is slow and decreasing in apparent speed.

A calculator for when the Moon is in perigee and apogee may be found here: fourmilab.ch

Whether the Moon is close to or far away from the Earth is also important when measuring fluctations in the tides, although these are mainly caused first by the Moon itself, but secondly by the Sun and the relationship between the Sun and the Moon and whether the combined gravity influences from both these bodies are pulling in the same direction.
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Eddy



Joined: 04 Feb 2009
Posts: 922
Location: Netherlands

Posted: Thu Jan 14, 2010 12:39 pm    Post subject: Re: Perigee and Apogee Reply with quote

Andrew Bevan wrote:
Has anyone read anything about whether the points of the Moon's perigee and apogee have any significance in astrological terms? The perigee and apogee are those shifting points where the Moon in its orbit is closest to and furthest away from the Earth.

The apogee is what (modern) astrologers call 'Lilith' or 'Black Moon'. If you have a look in the astrodienst ephemeris http://www.astro.com/swisseph/ae/2000/ae_2010.pdf the Black Moon (at the end of the list after the Mean Node symbol) is now close to the place where the next solar eclipse take place. Moon is thus close to apogee and hence the annular eclipse.

Here a technical Astrodienst article I liked: http://www.astro.com/swisseph/swisseph.htm#_Toc226863925 This part on the Nodes and Apsides discusses the difficulty/impossibility of defining a 'true' Node or Apogee. The position of these points are in fact only true when the Moon is actually in perigee/apogee or at 0 latitude or exactly on the ecliptic (in case of the Nodes).
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Andrew Bevan



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Location: Oslo, Norway

Posted: Thu Jan 14, 2010 6:23 pm    Post subject: Reply with quote

Here is a link to to Astrodienst's article on Lilith and the Dark Moon:
http://www.astro.com/astrology/in_lilith_e.htm

I have to give this a think. The second focal point in the elliptic relationship between the Earth and the Moon is not a 'dark moon' but a function of the an orbital direction. The Moon has 1/84 of the Earth's mass, so the two bodies revolve around a common centre of gravity that is remoted 1/84 of distance between the Earth/Moon when measured from the Earth's centre. On average this point, called the barycentre, is approximately 4650 km from the Earth centre, but this means that the common point of gravety in the Earth/Moon system is located 180 km beneith the Earth's surface. In comparison the Moon's distance to Earth from perigee to apogee varies with about 10-11%, or about 42 600 km. 11% of this figure is 4685 km, which is the distance of the Earth's centre from the common point of gravity.

As far as I understand it, the second focal point in the Moon's orbit is a derivation of the lunar fluctation of 42 600 km and global wobble of 4 650 km around the common point of gravity, the barycentre. The difference between these two figures is 37 950 km, which is the distance the 2nd focal point is remoted from the Earth's centre.

It's been a few years since I did these sort of calculations last, so someone might want to check me out.

I am not sure whether I want to call this point a 'Dark Moon' or 'Lilith'. I will stick with the astronomy for the time being but I am intrigued. Wink
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Eddy



Joined: 04 Feb 2009
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Posted: Thu Jan 14, 2010 8:06 pm    Post subject: Reply with quote

Hi Andrew, I assume you meant ca. 1800 and not 180, but for the remaining part I think you are correct.

Here's an orbit simulator. http://ww2.unime.it/weblab/mirror/ExplrSci/dswmedia/orbit.htm
You can change issues like gravity to make things more apparent. 'Trails on' show the trace of the orbit. The Earth's distance to the Sun thus varies, close and far. (more other types of animations: http://www.educypedia.be/education/spacejava.htm )

This is not the only thing that happens. Viewed from the side the Earth also goes 'up and down' because the Moon's orbit is tilted 5, she is sometimes above or below the mean plane of the orbit, likewise with the Earth. The definition of the ecliptic as used in astronomy is based upon this barycenter and of the barycenter of the Sun (caused mainly by the gravity of the giant gaseous planets Jupiter and Saturn) ( http://www.springerlink.com/content/q1871220887u8x7u/fulltext.pdf?page=1 ). Hence in exact calculations the Sun will have a latitude as you can see here: http://www.ephemeris.com/ephemeris.php
The change is small, + and - 00'1.2" and can safely be neglected.

For astrology I personally would prefer a definition of the ecliptic based upon the center of the Earth, but not related to Earth's orbit around the Sun (a solar zodiac) because this makes the view more heliocentric. I'd rather choose for a definition of the astrological ecliptic as the circle that is produced by precession (a precessional zodiac). However these are theoretical views only and can safely be omitted in practice for the differences are very small.
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Andrew Bevan



Joined: 20 Dec 2005
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Posted: Thu Jan 14, 2010 11:03 pm    Post subject: Reply with quote

1800 it is. In metric 180 miles converts to 1800 km. A zero got lost on the way! My apologies and I am glad it wasn't worse! Smile Thumbs up

It would seem that this focal point, or c-vector, is the derivate of a Bi-Planetary Centre, which is interesting for those reasons, but should/ could be separated from the phenomena of perigee/apogee, which have attribues of their own. However, it would appear they are closey related, although I am unsure why the apogee should be more important than the perigee. This is like saying that Pluto, or a comet, is more important when it is farthest distant from the Sun instead of closest.

I still have concerns about calling this point for Lilith or the Dark Moon. Are these traditions strong? They seem like an astrological ariefacture. Goldstein-Jacobsen took us for a ride in her book on Lilith, which she ironically dedicates it to her colleague astrologers, - us. Some of Goldstein-Jacobsen's stuff is great, dont get me wrong on that! But then there is the asteroid Lilith. It seems as if this concept has been used, abused, misused and already used up. Is there any room to revise or definitions and consepts?
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Andrew Bevan



Joined: 20 Dec 2005
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Location: Oslo, Norway

Posted: Thu Jan 14, 2010 11:12 pm    Post subject: Reply with quote

A Great illustration. Follow the link!



This is very much Kepler! Note the the eccentricity of the Lunar orbit is greatly exaggerated in the figure.

Source: http://www.astro.com/astrology/in_lilith_e.htm
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Andrew Bevan



Joined: 20 Dec 2005
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Posted: Sun Jan 17, 2010 2:05 pm    Post subject: Reply with quote

Possible keywords assosiated with the perigee and apogee -

Perigee: 'Swift', 'assertive', 'direct', 'amplified', 'loud' and 'obvious'
Apogee: 'Thorough', 'delayed', 'compact', 'deep' and 'seeking'.

Are there any traditions along these lines?
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