In spherical astronomy

Spherical astronomy

Spherical astronomy or positional astronomy is the branch of astronomy that is used to determine the location of objects on the celestial sphere, as seen at a particular date, time, and location on the Earth. It relies on the mathematical methods of spherical geometry and the measurements of...

, the parallactic angle is the angle between the great circle

Great circle

A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

 through a celestial object and the zenith

Zenith

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

, and the hour circle

Hour circle

In astronomy, the hour circle of a celestial object is the great circle through the object and the celestial poles. It is perpendicular to the celestial equator....

 of the object. It is usually denoted q. In the triangle zenith—object—celestial pole, the parallactic angle will be the angle at the celestial object. Despite its name, this angle is unrelated with parallax

Parallax

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

. The parallactic angle is zero when the object crosses the meridian

Meridian (astronomy)

This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the...

.

Uses

Depending on the type of mount

Telescope mount

A telescope mount is a mechanical structure which supports a telescope. Telescope mounts are designed to support the mass of the telescope and allow for accurate pointing of the instrument...

 of the telescope

Telescope

A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

, this angle may also affect the orientation of the celestial object's disk as seen in a telescope. With an equatorial mount

Equatorial mount

An equatorial mount is a mount for instruments that follows the rotation of the sky by having one rotational axis parallel to the Earth's axis of rotation. This type of mount is used for astronomical telescopes and cameras...

, the cardinal points of the celestial object's disk are aligned with the vertical and horizontal direction of the view in the telescope. With an altazimuth mount

Altazimuth mount

An altazimuth or alt-azimuth mount is a simple two-axis mount for supporting and rotating an instrument about two mutually perpendicular axes; one vertical and the other horizontal. Rotation about the vertical axis varies the azimuth of the pointing direction of the instrument...

, those directions are rotated by the amount of the parallactic angle. The cardinal points here referred to is the points on the limb located such that a line from the center of the disk through them will point to one of the celestial poles or 90° away from them. In other words, they are not cardinal points

Cardinal Points

Cardinal Points is a student newspaper published in Plattsburgh, New York which serves the SUNY Plattsburgh community. The newspaper publishes 3,000 copies every Friday morning throughout the semester, from February until May 12...

 defined by the object's axis of rotation.

The orientation of the disk of the Moon, as related to the horizon

Horizon

The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...

, changes throughout its diurnal motion

Diurnal motion

Diurnal motion is an astronomical term referring to the apparent daily motion of stars around the Earth, or more precisely around the two celestial poles. It is caused by the Earth's rotation on its axis, so every star apparently moves on a circle, that is called the diurnal circle. The time for...

 and the parallactic angle changes equivalently. This is also the case with other celestial objects.

In an ephemeris

Ephemeris

An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...

, the position angle

Position angle

Position angle, usually abbreviated PA, is a measurement derived from observing visual binary stars. It is defined as the angular offset in degrees of the secondary star to the primary, relative to the north celestial pole....

 of the midpoint of the bright limb of the Moon or planets, and the position angles of their North pole

North Pole

The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...

s may be tabulated. If this angle is measured from the North point on the limb, it can be converted to an angle measured from the zenith point (the vertex) as seen by an observer by subtracting the parallactic angle. The position angle of the bright limb is directly related to that of the subsolar point.