Lilith

On the subject of Lilith, viewed from an astrological perspective, it is easy to be confused. Consider the following description taken from https://darkstarastrology.com/three-liliths/: 

There are three Liliths in astrology that you can place in your chart. We have Black Moon Lilith, Asteroid Lilith and the lesser known Dark Moon Lilith. I used to see them together as the Triple Moon Goddess and thought it made sense to use them in that way. I then found out that Demetra George had come up with a similar concept about Lilith, so I thought we might be onto something. Comparing the three Liliths to the bible story she says:

“The Asteroid Lilith describes the first stage in the mythical journey where she is suppressed, humiliated and flees in a fiery rage to the desolate wilderness. The Dark Moon Lilith depicts the pain of her exile where she plots and executes revenge. The Black Moon Lilith shows how she transmutes her distorted image back into its natural healthy expression

Not to be outdone, this site includes a fourth, Osculating Lilith:

• Black Moon Lilith is also known as Mean Lilith. This Lilith uses the average orbit of the theoretical Black Moon. This is why she is called mean Lilith. Mean refers to the average, not her temperament. 

• Asteroid Lilith is the only Lilith that is an actual, verifiable physical body. 

• Osculating Lilith is also called True Lilith. Her orbit oscillates wildly this is why she is called true Lilith. This Lilith uses the real orbit of the Black Moon. Her orbit is the real orbit of the Black Moon rather than an average. This is another theoretical point. Some people, like Juan Antonio Revilla, believe that she is the most important Lilith and most accurately portrays Lilith’s uncontrollable nature. 

• Dark Moon Lilith is also called the Waltemath Black Moon, or Waldemath Black Moon. Some people have claimed to have seen this Moon, but those claims cannot be substantiated.

To find your Liliths, go to Astro.com, free horoscopes, extended chart selection and scroll to the bottom of the page. Copy and paste these numbers into the empty box on the bottom left side of the screen: 1181, H13, H21, H58
Press “Click here to show the chart.”

• Asteroid Lilith: 1181
• Osculating Lilith/ True Lilith: h13
• Black Moon Lilith/ Mean Lilith: h21
• Dark Moon Lilith/ Waldemath Black Moon: h58

The fixed star Algol (associated with Lilith) is at a fairly steady 26˚ Taurus. Algol is a star in the head of Medusa in the constellation Perseus.

I tried it and it works fine. However, an astrological chart is already cluttered enough. We have the luminaries (Sun and Moon) and the planets (Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune) as well as the recently demoted, dwarf planet Pluto. It's quite common to include Chiron, one of the Centaurs, and perhaps Ceres, the largest of the asteroids orbiting between Mars and Jupiter. These astronomical bodies are located within the circle of the zodiac and the circle of houses, all mutually interacting by casting various aspects to one another. To introduce one Lilith, let alone three or four, will complicate things even more, so there needs to be a good reason for doing this. Let's see if the inclusion of one, two, three or even four Liliths can really be justified.

Let's start with asteroid Lilith because it's the most straightforward to deal with. Here are some astronomical facts about the asteroid taken from Wikipedia:

1181 Lilith, provisional designation 1927 CQ, is a metallic asteroid from the middle region of the asteroid belt, approximately 23 kilometres in diameter. It was discovered on 11 February 1927, by Russian–French astronomer Benjamin Jekhowsky at Algiers Observatory in Algeria, Northern Africa, and named after French composer Lili Boulanger. The asteroid orbits the Sun in the middle main-belt at a distance of 2.1–3.2 AU once every 4 years and 4 months (1,587 days). Its orbit has an eccentricity of 0.20 and an inclination of 6° with respect to the ecliptic.

In terms of asteroid size, Lilith is rather puny. Ceres, the largest asteroid in the belt has a diameter of about 945 kilometres and can be spotted with a pair of binoculars. Other large asteroids include Pallas Athena, Juno and Vesta, all measuring in the hundreds of kilometres. It doesn't seem logical to assign too much importance to this little asteroid. I personally wouldn't include it in a chart analysis. The Dark Moon Lilith, also known as the Waltemath or Waldemath Black Moon, I would also dismiss because it's not really been proven to exist.

So that leaves us with the Black Moon Lilith (also known an Mean Lilith) and Osculating Lilith (also known as True Lilith). Let's try to differentiate between the two of these. A diagram will help:

The eccentricity of the Moon's orbit is highly exaggerated in the diagram above but it illustrates the idea behind the Black Moon. An ellipse has two foci: the Earth occupies one focus and other focus is empty. The line of sight from the centre of the Earth to this empty focus points to a position on the ecliptic and this should mark the position of the Black Moon Lilith. This empty focus is about 36,000 kilometres from Earth so it's not far away and, because of its proximity, there is a not inconsiderable difference between its geocentric and topocentric position in the zodiac.

What complicates the matter even more is that the Moon doesn't simply move around the Earth in a simple ellipse. What happens is that The Earth and the Moon both orbit around the centre of mass of the Earth and Moon. This is called the Earth-Moon Barycentre or EMB. It is about 4,671 km from the centre of the Earth or about 1,700 km below the Earth's surface. It is described further at the same site from where the diagram was taken:

The Moon travels along an elliptical path around the Earth. An ellipse has two focal points, and the other focal point, not occupied by the Earth has been called the Dark Moon, the Black Moon or Lilith. This is a slightly simplified definition, since, actually, the Moon and the Earth both move around their common centre of gravity, and the path of the Moon is not a neat ellipse, but a rather wobbly affair. One must distinguish between the mean orbit of the Moon, which is a slowly elongating ellipse, and the actual orbit, which vaccillates around the mean path, due to interference of various kinds. Just as there a "mean" and a "true" Lunar Node, so there is a "mean" and a "true" ellipse and a "mean" and a "true" Lilith. I write "true" in inverted commas, because the Moon's Node is only "true" about twice per month, when the Moon is actually on it, for the rest of the time, it is as "untrue" as the mean Node. In fact, when working with a point so close to the Earth, one should also take the great parallax into consideration, i.e. consider, from which point on the Earth one is actually looking at a point in the heavens. Astrology observes the planets geocentrically, as if from the Earth's centre, and not topocentrically, from the actual place of the observer.

This is getting complicated. Clearly the True Lilith is to be preferred over the Mean Lilith but is the inclusion of this difficult to calculate point in a chart really justified? I really don't think so. My feeling is that there's been a push to promote Lilith by one means or another because in the Hebrew tradition she is such a powerful figure (taken from Wikipedia):

Lilith is a figure in Jewish mythology, developed earliest in the Babylonian Talmud (3rd to 5th centuries). Lilith is often envisioned as a dangerous demon of the night, who is sexually wanton, and who steals babies in the darkness. The character is generally thought to derive in part from a historically far earlier class of female demons in ancient Mesopotamian religion, found in cuneiform texts of Sumer, the Akkadian Empire, Assyria, and Babylonia. 

In Jewish folklore, from the satirical book Alphabet of Sirach (c. 700–1000) onwards, Lilith appears as Adam's first wife, who was created at the same time (Rosh Hashanah) and from the same dirt as Adam – compare Genesis 1:27. (This contrasts with Eve, who was created from one of Adam's ribs: Genesis 2:22.) The legend developed extensively during the Middle Ages, in the tradition of Aggadah, the Zohar, and Jewish mysticism. For example, in the 13th-century writings of Isaac ben Jacob ha-Cohen, Lilith left Adam after she refused to become subservient to him and then would not return to the Garden of Eden after she had coupled with the archangel Samael.

With the exception of Venus, all of the planets are male: Mercury, Mars, Jupiter, Saturn and Neptune. Pluto is male as well of course. While the asteroid Ceres and the dwarf planet Eris are female, there is certainly a shortage of objects named after strong females in the traditional astrological chart. I've recently taken to including Ceres in my chart analysis but I won't personally include Lilith in any of her variants at the moment.