Friends, I am putting here a simplification (or static form) of the orbital coordinates, which in this case would simply be the orbital or spherical situation of a point (Ps) in relation to a point (C) or central point of reference.
As we can see, the Cartesian coordinates are not used here, a circumstance that in principle helps us to simplify the problem since it is not necessary to know the values of the coordinates (x, y, z) to later calculate the resultant R with trigonometry.
Here we just need to measure R, and point out the direction in which that distance R is located.
*(As can be seen on the orbital coordinates page, this simplification is similar to that of polar coordinates and spherical coordinates, but to be able to extend them to orbital coordinates, the procedure of putting a primary angle alpha, on which, the secondary angle beta is measured, all this in order to be able to apply movement of each of the coordinates and achieve that particles can orbiting around the center C.
Cartesian coordinates are also not used.)
This way, it is pointed out that by giving movement to each of these coordinates (radius, with linear speed; and direction angles with angular speed) and using a common time (t) for all of them, we will obtain an orbital movement for the particle or satellite that we are measuring.

For tracking and computing:

Among other things, it is a method or computational formula.
First of all, this is a system for the construction of geometric figures, as well as an orbit tracking method.
In the construction of geometric figures, this system recreates each figure as if the point Ps were the tip of the pencil with which we are going to draw.
With it you can create multiple figures: circles, spirals, spheres, cones, stars, cylinders, etc.
Referring to the monitoring and construction of orbits with this system or method, a software can be built that draws any type of orbit around a central point C, as well as the construction of all kinds of geometric figures.
For example in orbital tracking:
If we apply this formula system to the tracking of the planets of the solar system (because it is a more or less stable orbital system), we can first adjust the radius and angular velocity parameters of each planet, and once inserted in the formula, with a application of a common measurement time, we can adjust in which position each one of the planets will be for any future time that we wish to know.