In spherical astronomy, the parallactic angle is the angle between the great circle through a celestial object and the zenith, and the hour circle of the object. It is usually denoted q. In the triangle zenith—object—celestial pole, the parallactic angle will be the position angle of the zenith at the celestial object. Despite its name, this angle is unrelated with parallax. The parallactic angle is zero when the object crosses the meridian.
Uses
Depending on the type of mount of the telescope, this angle may also affect the orientation of the celestial object's disk as seen in a telescope. With an equatorial mount, 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, those directions are rotated by the amount of the parallactic angle. The cardinal points referred to here are 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; these are not the cardinal points defined by the object's axis of rotation.
The orientation of the disk of the Moon, as related to the horizon, changes throughout its diurnal motion and the parallactic angle changes equivalently. This is also the case with other celestial objects.
In an ephemeris, the position angle of the midpoint of the bright limb of the Moon or planets, and the position angles of their North poles 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.