The Medium Coeli (MC) is the intersection between meridian and ecliptic. The meridian is a large circle that runs through the northpoint and the southpoint, so the positions that are separated 90° from the intersection between equator and horizon.
The MC is not the highest point of the ecliptic. The ecliptic is a large circle that is divided by the horizon in two equal halves. So the highest point is by definition 90° separated from the horizon. The MC is the point that has the highest right ascension, so measured alongside the equator. There is a difference with the highest point on the ecliptic because of the obliquity of the angle between equator and ecliptic. (see Oblique angle of the ecliptic).
For the calculation of the MC you need to know the sidereal time (see Sidereal time) and the angle between equator and ecliptic (see Oblique angle of the ecliptic).
You do not require the geographic latitude as the MC has, for a given sidereal time, the same position at all latitudes.
Convert the sidereal time to degrees by multiplying it with 15
The formula for the longitude of the MC is:
tan L = sin ARMC / cos ARMC . cos E
L is the longitude of the MC.
ARMC is the right ascension of the MC.
E is Epsilon, the angle between equator and ecliptic.
Just like in the other examples, we use the date November, 2016 (Gregorian calendar) at 21:17:30 UT in Enschede, The Netherlands (52º 13′ North and 6º 54′ East).
The ST is 0:35:23.6, we already calculated this in (link: Sidereal time).
Convert the ST to decimal hours:
ST = 0.5899018653
E is 23° 26′ 13.56586091”, (see Oblique angle of the ecliptic).
Convert to decimal degrees: 23.437101628
Calculate ARMC by multiplying the ST with 15:
ARMC = 15 . 0.5899018653 = 8.8485279795
Enter the values for ARMC and E in the formula:
tan L = sin ARMC / cos ARMC . cos E tan L = sin 8.8485279795 / cos 8.8485279795 . cos 23.437101628
Define sine and cosine:
tan L = 0.153822784089 / 0.988098452127 . 0.917497261932
tan L = 0.153822784089 / 0.906577624337
tan L = 0.169674145878
Calculate arc tangent:
L = 9.62989868323
Converted to degrees, minutes and seconds: 9° 37′ 47.6” Aries.
You will not always get a result in the correct quadrant, if required add or subtract 180 degrees to the result. If the ST is between 0 and 12 hours, the longitude of the MC should be between 0 Aries and 0 Libra. A ST between 12 and 24 hours should result in a MC larger than 0 Libra and smaller than 0 Aries.
- Dean, Geoffrey and Arthur Mather – Recent Advances in Natal Astrology: A critical review 1900-1976. The Astrological Association, Bromley, 1977. p. 187.