# The ascendant

For many astrologers, the ascendant is one of the most import positions in the horoscope.
The name ‘horoscope’ actually has been derived from he ascendant, in Hellenistic times astrologers used the term ‘Horoskopos’ to identify the ascendant.
Most house systems use the ascendant as starting point for the houses.

Astronomically, the ascendant is the intersection of the ecliptic and the horizon. This intersection will be roughly – but not exactly – pointing to the east. The east point itself is the intersection of the equator with the horizon. The ascendant will be positioned somewhat to the north or to the south of the east point. The declination of the ascendant determines if it is north or south. In signs with northern declination (Aries up to and including Virgo) the ascendant will be to the north of the east point. In signs with southern declination (Libra up to and including Pisces) it will be to the south.

## Formula

To calculate the position of the ascendant you will need the following three values:

• Sidereal time, which we convert to the RAMC (Right ascension of the MC), see Medium Coeli
• GL: Geographic latitude
• E: Obliquity, the angle between equator and ecliptic, see Oblique angle of the ecliptic

You will use these three values in this formula:

`tan (Longitude asc) = cos RAMC / -(sin E . tan GL + cos E . sin RAMC)`

If you also want to know the declination you will need a separate formula (see Declinations), keep in mind that the ascendant is exactly positioned on the ecliptic and therefore has zero latitude.

## Example calculation

For the location we use Enschede in the Netherlands (52º 13′ north en 6º 54′ east). Date and time: November 2, 2016 (Gregorian calendar) 21:17:30 UT. This results in a sidereal time of 0:35:23.6, decimal 0.5899018653 (see Medium Coeli) and an obliquity E of 23° 26′ 13.56586091”, decimal 23.437101628 (see Oblique angle of the ecliptic).

Calculate the RAMC by multiplying the sidereal time with 15:

`RAMC = 15 . 0.5899018653 = 8.8485279795`

The geographic latitude GL in decimal degrees is 52 + 13/60 = 52.2166666666667

Use these values in the formula:

`tan (Longitude asc) = cos RAMC / -(sin E . tan GL + cos E . sin RAMC)`

This results in:

`tan (Longitude asc) = cos 8.8485279795 / -(sin 23.437101628 . tan 52.2166666666667 + cos 23.437101628 . sin 8.8485279795)`

Calculate the goniometric functions:

`tan (Longitude asc) = 0.9880984521266581 / -(0.3977420952671163 . 1.28996687154847450 + 0.9174972619318949 . 0.1538227840890365)`

Simplify:

`tan (Longitude asc) = 0.9880984521266581 / -(0.5130741263148573 + 0.1411319832244320)`

And simplify a bit more:

`tan (Longitude asc) = 0.9880984521266581 / -0.654206109539289`

This results in:

`tan (Longitude asc) = -1.5103779034141179`

The longitude of the ascendant becomes:

`arctan(-1.5103779034141179) = -56.4920166543327382`

Finally, we need to correct for the correct hemisphere, the ascendant should be somewhere in the 180 degrees following the MC in zodiacal direction. The MC is 9°38′ Aries. If the calculated ascendant is not in the expected position we will need to add 180 degrees until it fits.
In this example we only need to do it once:

correction for hemisphere:

`-56.4920166543327382 + 180 = 123.5079833456672618 = 3°30'28.7" Leo.`

## References

• Dean, Geoffrey and Arthur MatherRecent Advances in Natal Astrology: A critical review 1900-1976. The Astrological Association, Bromley, 1977. p. 187.
• Kampherbeek, JanHet huizensysteem van Alcabitius. In Spica vol. 3 no. 4, January 1980, p. 14. An alternative formula for the calculation of the ascendant. In dutch.