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The Orbits of 150 Visual Binary Stars, by Dibon Smith (Accessed 2/26/06)
Astronomical coordinate systems Angle Observational astronomy
In astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
, position angle (usually abbreviated PA) is the convention for measuring angles on the sky. The International Astronomical Union
The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...
defines it as the angle measured relative to the north celestial pole
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...
(NCP), turning positive into the direction of the 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 ...
. In the standard (non-flipped) images, this is a counterclockwise
Two-dimensional rotation can occur in two possible directions or senses of rotation. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands relative to the observer: from the top to the right, then down and then to ...
measure relative to the axis into the direction of positive declination
In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or ...
.
In the case of observed visual binary stars, it is defined as the angular offset of the secondary star from the primary relative to the north celestial pole
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at ...
.
As the example illustrates, if one were observing a hypothetical binary star with a PA of 30°, that means an imaginary line in the eyepiece drawn from the north celestial pole to the primary (P) would be offset from the secondary (S) such that the angle would be 30°.
When graphing visual binaries, the NCP is, as in the illustration, normally drawn from the center point (origin) that is the Primary downward–that is, with north at bottom–and PA is measured counterclockwise. Also, the direction of the proper motion
Proper motion is the astrometric measure of changes in the apparent places of stars or other celestial objects as they move relative to the center of mass of the Solar System. It is measured relative to the distant stars or a stable referenc ...
can, for example, be given by its position angle.
The definition of position angle is also applied to extended objects like galaxies, where it refers to the angle made by the major axis of the object with the NCP line.
Nautics
The concept of the position angle is inherited from nautical navigation on the oceans, where the optimumcompass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with No ...
course is the course from a known position to a target position with minimum effort. Setting aside the influence of winds and ocean currents, the optimum course is the course of smallest distance between the two positions on the ocean surface. Computing the compass course is known as the ''inverse geodetic problem
Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...
''.
This article considers only the abstraction of minimizing the distance between and traveling on the surface of a sphere with some radius : In which direction angle relative to North should the ship steer to reach the target position?
See also
* Parallactic angle *Angular distance
Angular distance or angular separation is the measure of the angle between the orientation (geometry), orientation of two straight lines, ray (geometry), rays, or vector (geometry), vectors in three-dimensional space, or the central angle subtende ...
Further reading
*References
{{ReflistExternal links
The Orbits of 150 Visual Binary Stars, by Dibon Smith (Accessed 2/26/06)
Astronomical coordinate systems Angle Observational astronomy