Position angle
Position angle, usually abbreviated PA, is the convention for measuring angles on the sky in astronomy. The International Astronomical Union defines it as the angle measured counterclockwise relative to the north celestial pole.
In the case of observed visual binary stars, it is defined as the angular offset of the secondary star from the primary, measured counterclockwise, relative to the north celestial pole.
As the example illustrates, if one were observing a hypothetical binary star with a PA of 135 degrees, that means an imaginary line in the eyepiece drawn from the north celestial pole (NCP) to the primary (P) would be offset from the secondary (S) such that the NCP-P-S angle would be 135 degrees.
When graphing visual binary orbits, the NCP line is traditionally drawn downward—that is, with north at bottom—and PA is measured counterclockwise.
Also the proper motion angle (see proper motion) is sometimes called the position angle.
The definition of position angle is also extended to apply to extended objects like galaxies, where it refers to the angle made by the major axis of the object with the NCP line.
The concept of the position angle is inherited from nautical navigation on the oceans, where the optimum compass course is the course from a known position s to a target position t 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 problem of geodetics.
This article considers only the abstraction of minimizing the distance between s and t traveling on the surface of a sphere with some radius R. In which direction angle p relative to North should the ship steer to reach the target position?
Detailed evaluation of the optimum direction is possible if the sea surface is approximated by a sphere surface. The standard computation places the ship at a geodetic latitude φs and geodetic longitude λs, where φ is considered positive if north of the equator, and where λ is considered positive if east of Greenwich. In the global coordinate system centered at the center of the sphere, the Cartesian components are
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