Reference frames Reference frames and coordinate systems To be useful, the coordinates given by the theories must be transformed and expressed in different coordinate systems. We'll see how to deal with that.

# Reference frames and coordinate systems

In [BDL98], they make the difference between a reference system (the theoretical concept) and reference frame (the materialization of this concept). Here, we apparently only manipulate reference frames.
The notion of coordinate system can also be found in litterature. I couldn't find a precise definition. I considered that "coordinate system" and "reference frame" refer to the same notion, and used the term frame in the API.

A frame can be charcterized by :
• the reference system it materializes,
• its center,
• its refence plane,
• its reference axis (the two other are deduced because we use direct orthogonal frames) ;

• For display purposes, we need an other characteristic : the names of the spherical coordinates when they are expressed in this frame.
• ## Coordinates

The coordinates are coordinates of position and velocity vectors. For positions, the coordinates of the body (a "point") are equal to the coordinates of the vector.

Let's see a point and its coordinates in a reference frame :

As shown in the figure, there are two ways to express the coordinates : cartesian (X, Y, Z) and spherical (r, q, j). A third way (cylindric coordinates) is not used in astronomy, so I didn't keep it for JEphem.
Cartesian coordinates are sometimes called rectangular.
Transformation between cartesian and spherical coordinates (specially for velocities) are detailed in a page of the library : "Cartesian and spherical coordinates".