Ascendant

The Ascendant (Latin for, the Ascending ') is a term used in astrology. It is the intersection of the ecliptic with Osthorizonts and designates the at the time and geographic location on the eastern horizon rising degree of the zodiac. The opposite degrees at the western horizon is called the Descendant (Latin descendere: descend ').

Astrological definition

The Ascendant is the beginning or the tip of the first house of the twelve-part astrological houses circle. He is regarded as an important factor in the horoscope. He will show how man acts on his contemporaries, as he is seen and perceived by it. Therefore, he describes ( including other elements of interpretation ), the physiognomy. It symbolizes the influence of others on their own behavior and their own response to the environment. From the ascendant can be considered evidence of the basic motivation with the owner of the horoscope comes to life, determine.

Calculation of the ascendant

In order θ the zodiac sign of the intersection point of the horizon and the ecliptic at a given local sidereal time, latitude Φ and the obliquity of the ecliptic ε = be able to determine 23 ° 26 ' 21.45 " ( J2000.0 ), the ecliptic longitude λ must be determined. From the triangle of great circles horizon, celestial equator and the ecliptic (see graph) arising after the Kotangenssatz following relationship:

From cot (90 Φ ) = - 1/tan Φ, sin ( 90 θ ) = cos θ and cos (90 Φ ) = -sin Φ follows:

Since most implementations of the inverse tangent function possess the range of values ​​, the returned value has to be converted by λ mod 180 °. Furthermore, there are two points of intersection between the horizon and the ecliptic. To determine which point arctangent returns, considering the quadrant of θ. Applies 90 ° < θ < 270 ° returns the Deszentent, otherwise the Ascendant.

To convert between Ascendant and Deszententen adding 180 °, bringing possibly the result - for example, with ( λ 180 ° ) mod 360 - back into the range of values.

Determining the sign of the zodiac

The twelve signs of the zodiac used in astrology share the ecliptic in 30 ° increments. Using the calculated ecliptic longitude λ can be determined by the table of signs of the zodiac, the corresponding signs of the zodiac.

By Präzessionseffekt moves the base of the ecliptic coordinate system - the vernal equinox - Continue on the ecliptic. Thus, the ecliptic longitude of all the fixed stars, and thus the zodiac constellations changes. Therefore, the astronomical constellation of the Ascendant differs most from the astrological.

Declination and right ascension of the ascendant

Since β = 0 ° ( ecliptic latitude ) is the translation of the ecliptic and equatorial coordinates particularly simple: it is sin ε · sin λ = sin δ and tan λ · cos ε = tan α.

Special cases

• At the poles, the vernal equinox always intersects the horizon. The Ascendant is therefore depending on the time of day is always the ecliptic longitude 0 ° or 180 °.
• At the polar circles once on the day the horizon plane parallel to the ecliptic plane ( at θ = 90 ° and θ = 270 at the southern ° north of the Arctic circle). The two great circles then fall together and it can not be defined Ascendant.

Estimating the error

Since θ, Φ and ε are always errored sizes, the error by the total differential can be estimated. The maximum error can be calculated by maximizing the partial derivatives; However, this does not make sense because the function as the special cases mentioned at the Polar Circle is a pole and the error there would be theoretically infinite.

It makes sense is a statistical method: the error is better than 99% of all values

This means that 99% of all possible values ​​of θ, Φ and ε, the partial derivatives are smaller than the numbers shown. Since the local sidereal time is calculated by adding the longitude of sidereal time at the Greenwich meridian, can also be written.

From this it can be seen that for a determination of λ with an accuracy of 1 ° latitude of place of birth must be at least 9 ' precisely known, this corresponds to 17 km for the 50th degree of latitude. The birth time is additive in the sidereal one, which allowed error is 1 ° / 2.77, corresponding to a period of about 1.5 minutes, and the required accuracy of the birth time.

Examples

Legend: width / length: width and longitude, to the south and west negative; JD: Julian date; T: Julian centuries since J2000.0; Θ: sidereal time at the prime meridian; θ: local sidereal time; S1 and S2: intersections of the ecliptic with the horizon; Position: length difference to the Zodiac beginning