Mathematics
Orbital ones
In this page and the following ones I will proceed to the specific development of the radial coordinates for some of the measurement and constructions that can be carried out using these coordinates.
As first application point we can consider that it is measurement and creation of orbital ones around the central point C.
In this case, and as we can see in the drawing, the formula consists on to apply or to substitute the index of R for an oscillation function of H on the coordinate O, with a maximum and a minimum that will be the limits of ascent of the H coordinate.
The formula, taking as starting point the value 0 in H and O coordinates, it would be:
Nš sen.Oa
R
O + wo.t
The value Nš is the maximum angle of H. And the other data are already well-known.
In this case when the H coordinate is below the coordinate O the values will be negative.
As we can see, once synchronized the initial values of the formula with the real situation of the orbital one, we can know the situation of this orbital so much in a certain moment of the future as the situation that had in any moment of the past, that is to say, we have a formula that allows us to follow the movement of the orbital one around the point C in a constant way. Alone we need to introduce in the formula the time for which we want to know the situation of the orbital one.
------In the following pages we will see some of the many figures and space bodies that can be built with the radial coordinates.