The Black Moon is calculated from several factors. The main factor being the lunar apogee--the spot where the Moon reaches its maximum distance from the Earth. The calculations that are formed produce an 8-year and 10-month cycle around the zodiac, or 40 per year.
The Black Moon (Lilith) in Mythology
In early Sumerian mythology, Lilith was described a handmaid to the Goddess Inanna, Queen of Heaven, in which she would gather men in from the fields for sacred rites. There are also several other versions in both Sumerian and Hebrew mythology.
In Hebrew mythology Lilith was intended to be Adam's first wife, but when he wanted to take a dominant role over her in sex, she refused to submit to the role of submissive wife, distanced herself from Adams authority and left the Garden of Eden of her own accord. God sent three angels after her however she refused to return and was forever demonised as a fallen woman who gave birth to demons and stole babies from their beds.
The Black Moon (Lilith) in Astrology
There a great deal of confusion concerning the name Lilith as used in Astrology. This is because the name is used for several bodies:
The Black Moon (an abstract, geometrical point in space)
The Dark Moon (purported to be the Earth's second Moon)
The Asteroid Lilith (Asteroid 1181, orbiting in the asteroid belt between Mars and Jupiter)
Lilith is sometimes connected with the zodiac sign of Scorpio due to her dark, sexual and intense nature and the fact that she doesn't suffer fools gladly. She represents the conscious decision to be alone and live outside polite society rather than surrender her dignity. While Lilith involves the exercise of freewill and the conscious decision to forge her own path in life the decision was forced on her to a certain extent and is thus accompanied by the anger and pain of rejection, which makes the healing process difficult.
The house and sign where Lilith is found in your chart denotes where you stand your ground with confidence and determination but also where there is an inability to let go gracefully and without bitterness. Lilith also gives us the ability to make difficult decisions and to follow them through with confidence. Some Astrologer's consider Lilith to be connected to the Tree of Life, where one can accept a deeper truth and greater wisdom. The contrasting energies of Lilith would be that of denial in which a person would rather rely on their ego-fed knowledge.
In general, Lilith may challenge individuals to connect with their instinctive passion for life, for if it is denied, this natural force can be quite troublesome or destructive. On a higher level, it may denote an embracing of your spiritual destiny - as indicated by sign, house, position, and aspect.
The Dark Moon
Dark Moon, Black Moon or Lilith, this hypothetical point in astrology is known by several names. Some argue that the Dark Moon is one thing, Black Moon another and Lilith yet another. The reality is that there is an asteroid named Lilith, but it is not the same as the Dark or Black Moon. However, when used as a point in a birthchart, all three names appear valid as they all seem to describe the same thing.
This point arises due to the Moon's path around the ecliptic forming an axis of the perigee when the moon's orbit is closest to the earth and the apogee when its orbit is furthest from the earth. It is an empty area, a void created, an empty focus. Moving at about 40 degrees a year, the perigee is from where the path of the Dark Moon is calculated. It takes a little under nine years for it to complete its course.
In astrology, the Dark Moon is representative of the darker side of our nature, the negative side. It is the hidden depths that we know exist yet we prefer not to acknowledge. It is subtle on the surface, yet profound beneath. It is the foundations of our personality and the shocking truth that we often deny and project onto others instead. The refusal to see what is really within ourselves. The subtle refusal to see what part we may have played in some unpleasant drama of our lives, how we ourselves have manifested our fears. It is the kind of thing that we intrinsically know we have to deal with, confront the darker side in order to progress unhindered, yet most often we try to ignore. It is the deeper truth that we are forever in search of within ourselves. Probably the best use we can make of the dark moon is to explore our hidden depths, realise that we all have that darker side and go within to resolve that which ultimately hinders us.
The Dark Moon is representative of the negative traits of guilt, shame, hatred, envy, and vengefulness, often brought about by personal wounds and hurts. The true dark side of things we try to hide.
There is another side of the Dark Moon astrologically. Carl G Jung, the famous psychoanalyst described something that he called the "anima". The anima is a man's image of the ideal woman and also the feminine side of his personality. For a woman it is the image of the ideal man and the masculine side of her personality. So the dark moon in a birthchart will represent these ideals too.
It is also representative of the enchantress or the seducer, one who lures another by use of sexuality or devious means. The kind who tempts another by implying that the grass is greener on the other side, that they can "rescue" someone, but it is in reality for their own selfish gain.
The Dark Moon, Lilith, also has associations with motherhood, like her counterpart the Moon. With Lilith however, the instinctive nurturing is replaced by a strong protection of her offspring to the point that she would kill if necessary any that threatened them or caused them harm. She is also reactive against the ties involved with motherhood and the emptiness that mothers sometimes feel by isolation and the perceived lack of individuality that accompanies it.
These things do not only apply to women, they apply to men as well, as the Black Moon is also their feminine side.
Keywords: danger, darkness, deceit, destruction, devious, devouring, dreams, emptiness, enchantress, envy, fears, guilt, hatred, imagination, isolation, jealousy, magic, marriage-wrecker, mystery, night, poison, secrets, seduction, shame, the "other woman" who thinks a man needs rescuing from the "chains" of his partner, vengefulness
The manner in which the Dark Moon plays out will be of the character of the sign in which it is posited and with over tones of the ruling planet of that sign. For example, if your Dark Moon is in Aries, it will act in the manner of Aries with over tones of Mars.
source = http://www.cornerstone-astrology.com/articles/black_moon_lilith.htm
source = http://www.aquamoonlight.co.uk/lilith-dark-moon.html