Important Definitions¶

For reference, below, we define some key terms as they are used in coordinates, due to some ambiguities that exist in the colloquial use of these terms. Chief among these terms is the concept of a “coordinate system.” To some members of the community, “coordinate system” means the representation of a point in space (e.g., “Cartesian coordinate system” is different from “Spherical polar coordinate system”). Another use of “coordinate system” is to mean a unique reference frame with a particular set of reference points (e.g., “the ICRS coordinate system” or the “J2000 coordinate system”). This second meaning is further complicated by the fact that such systems use quite different ways of defining a frame.

Because of the likelihood of confusion between these meanings of “coordinate system,” coordinates avoids this term wherever possible, and instead adopts the following terms (loosely inspired by the IAU2000 resolutions on celestial coordinate systems):

• A “Coordinate Representation” is a particular way of describing a unique point in a vector space. (Here, this means three-dimensional space, but future extensions might have different dimensionality, particularly if relativistic effects are desired.) Examples include Cartesian coordinates, cylindrical polar, or latitude/longitude spherical polar coordinates. Note that this term applies to the positions, not their velocities or other derivatives (which are represented as “differential” classes).
• A “Reference System” is a scheme for orienting points in a space and describing how they transforms to other systems. Examples include the ICRS, equatorial coordinates with mean equinox, or the WGS84 geoid for latitude/longitude on the Earth.
• A “Coordinate Frame,” “Reference Frame,” or just “Frame” is a specific realization of a reference system (e.g., the ICRF, or J2000 equatorial coordinates). For some systems, there may be only one meaningful frame, while others may have many different frames (differentiated by something like a different equinox, or a different set of reference points).
• A “Coordinate” is a combination of all of the above that specifies a unique point.