astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...

, 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 the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

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 Earth's orbit, Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making. Fr ...

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. Discussion Any arc of a great circle is a geodesic of the sphere, so that great circles in spher ...

containing the ecliptic poles 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 edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...

allow for the

conversion Conversion or convert may refer to: Arts, entertainment, and media * ''The Convert'', a 2023 film produced by Jump Film & Television and Brouhaha Entertainment * "Conversion" (''Doctor Who'' audio), an episode of the audio drama ''Cyberman'' * ...

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

latitude In geography, latitude is a geographic coordinate system, geographic 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 t ...

(=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 equinox (celestial coordinates), March equinox to the (hour circle of the) point in questio ...

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

hour angle In astronomy and celestial navigation, the hour angle is the dihedral angle between the '' meridian plane'' (containing Earth's axis and the zenith) and the '' hour circle'' (containing Earth's axis and a given point of interest). It may be ...

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

\tan\lambda_ =

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 orbital ...

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

Ascendant The ascendant (Asc, Asc or As) or rising sign is the astrological sign on the eastern horizon when the person was born. It signifies a person's physical appearance, and awakening consciousness. Because the ascendant is specific to a particula ...

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. It is defined such that one radian is the angle subtended at ...

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 ''antitrigonometric'', ''cyclometric'', or ''arcus'' functions) are the inverse functions of the trigonometric functions, under suitably restricted Domain of a functi ...

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