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. (Corner Stone Astrology)
The Black Moon is not a physical body or object and is not the dark phase of the Moon as many assume. Rather it is more like an energy vortex. Its position is on the Moon’s orbital path or elliptic at the point furthest from the earth ie it is the apogee of the Moon’s orbit, or that point furthest away from the earth in the Moon’s orbit. The Black Moon, or Lunar Apogee, travels along the zodiac at approximately 40 degrees per year. She spends around 9 months in each sign and has a 9 year orbit through the full zodiac. (New Dawn Astrology)