In the context of a computer simulation of satellites that orbit earth, I am looking for a (accurate) method for converting Keplerian orbital elements directly to Equatorial coordinate system.
The simulation describe the orbit of a satellite by a set of Keplerian orbital elements in order to determine an orbit and move the satellite along it.
However, in order to show the satellite position graphically, the orbital elements are converted into an equatorial coordinate system. This allow a very simple projection of the satellite location on a 2D map.
Currently the orbital elements are converted to equatorial coordinates by (1) converting the orbital elements into Cartesian coordinates (x,y,z) as described in the following link in the Computing Position from Orbital Elements section and than (2) converting the Cartesian coordinates into Equatorial coordinate system. However, the double conversion cause lost of precision.
It "feels" as might be a direct way to convert orbital elements to equatorial coordinate, since both use angles it might be possible to transfer the orbital elements representation into equatorial one, but I am yet to find it.
is it possible to convert this:
directly to this: