In astronomy, coordinate systems are used for specifying positions of celestial objects (satellites, planets, stars, galaxies, etc.)

These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle.

Rectangular coordinates, in appropriate units, have the same fundamental (x, y) plane and primary (x-axis) direction, such as an axis of rotation.

The following table lists the common coordinate systems in use by the astronomical community.

The horizontal, or altitude-azimuth, system is based on the position of the observer on Earth, which revolves around its own axis once per sidereal day (23 hours, 56 minutes and 4.091 seconds) in relation to the star background.

It is based on the position of stars relative to an observer's ideal horizon.

The coordinates are based on the location of stars relative to Earth's equator if it were projected out to an infinite distance.

Popular choices of pole and equator are the older B1950 and the modern J2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as when a measurement of the position of a planet or spacecraft is made.

The supergalactic coordinate system corresponds to a fundamental plane that contains a higher than average number of local galaxies in the sky as seen from Earth.

Again, in solving the tan(h) equation for h, use of the two-argument arctangent that accounts for the quadrant is recommended.