Long time ago, I was wondering which orbital element should I use to differentiate between the blue and red orientation of an otherwise same elliptical orbit on this image (all the three orbits are in an identical ecliptic plane; Sun in the center is, of course, at the foci.):
After some studies I realized Euler angles are used for these purposes in the form of inclination and longitude of ascending node. However, longitude of a. n. is useful only when inclination is non-zero so that the nodes exist. For theoretical purposes this does not pose a problem since we are free to choose any other plane so the parameters can have definite values.
In practice there could be a problem for the used methods of simulation and orbit-element communication when inclination is near- or true-zero and we are bound to use the same plane of reference. As it is stated in this question:
For a low-inclination, high-eccentricity orbit, the longitude of ascending node may be very uncertain (becoming undefined in the purely theoretical zero-inclination case) even though the orientation of the ellipse as projected to the reference plane is clear.
My questions are:
- Is there a recommended method for how to avoid non-ambiguous zero-inclination cases in computer simulation? If we solve the motion equations numerically we might like to know the present orbital parameters of an object without any possibility of errors. (You can answer this also with your own experience.)
- How is the longitude of a. n. communicated in practice through the two-line element sets in zero-inclination cases?