astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...

, the Equatorial Ascendant, or the East Point, is the sign and degree rising over the Eastern Horizon at the Earth's

equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

at any given time. In the

celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...

it corresponds to the intersection of the

ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic again ...

with a

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geomet ...

containing the

celestial pole The north and south celestial poles are the two points in the sky where Earth's rotation around a fixed axis, axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently dire ...

s and the East point of the horizon.

Calculation

Equations derived from

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are gr ...

allow for the

conversion Conversion or convert may refer to: Arts, entertainment, and media * "Conversion" (''Doctor Who'' audio), an episode of the audio drama ''Cyberman'' * "Conversion" (''Stargate Atlantis''), an episode of the television series * "The Conversion" ...

from equatorial coordinates to ecliptic coordinates. As points in the ecliptic have no

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

(=0º) and the East point of the horizon has a

right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the earth. When paired w ...

6^h higher than that of the meridian (or 90º more in

hour angle In astronomy and celestial navigation, the hour angle is the angle between two planes: one containing Earth's axis and the zenith (the '' meridian plane''), and the other containing Earth's axis and a given point of interest (the ''hour circle'' ...

), the equation that determines East Point's longitude can be written as: :

\tan\lambda

_EP

= \Leftrightarrow\lambda

_EP

= \arctan\left(\right)

where

\theta_

is the local sidereal time and

\varepsilon

is the

obliquity In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbit ...

of the ecliptic. The equation can also be derived from the

Ascendant The ascendant (Asc, Asc or As) is the astrological sign on the eastern horizon when the person was born. According to certain astrological theories, celestial phenomena reflect or influence human activity on the principle of "as above, so belo ...

at the

(

\phi

=0º).

* Angles in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure must be converted to decimal before calculations are performed. Whether they are converted to decimal degrees or

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...

s depends upon the particular calculating machine or program. * Angles in the hours ( ^h ), minutes ( ^m ), and seconds ( ^s ) of time measure must be converted to decimal degrees or

s before calculations are performed. (1^h = 15° 1^m = 15' 1^s = 15") * Angles greater than 360° () or less than 0° may need to be reduced to the range 0° - 360° (0 - ) depending upon the particular calculating machine or program. *When L.S.T. is 0^h 0^m 0^s (

\theta_

=0º), East Point's longitude is 90º. *

Inverse trigonometric functions In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted Domain of a fu ...

are quadrant-ambiguous, and results should be carefully evaluated by taking into account that _EP is roughly 90º more than _MC. * For the past 5 million years, Earth's obliquity has varied between 22.042500° and 24.50444°. The effect on _EP is less than 0.53°. For values referred to the standard equinox J2000.0 use 23.4392911°; for J1950.0 use 23.4457889°.

References

Technical factors of Western astrology {{Astrology-stub

Calculation

See also

References