We analyzed in detail the theoretical problem of ground tracking for auxiliary telescopes in the REM95 technique. We have given a limiting magnitude for the system, we have defined the error due to non perpendicular configuration of the two reference stars and we have shown the geometry of the problem with some track path examples.
We performed several calculations in a particular case study showing the tolerance angle dependence of the mean distance of the perpendicular companion of the closest star and the Poissonian distribution of these two around the observed astronomical target.
It is to be pointed out that we performed such a simulation run assuming the worst case both for the star density and the for requirements to be imposed on the goodness of the correction. Moreover the calculation is made assuming that the objects have to be LGS tilt corrected at any time.
Given a certain ground occupation around the main observatory it can be easily figured out that most objects can be tracked at some particular instant.
Finally we did not make any attempt to exploit the non-vanishing length of the Sodium beacon as seen from the auxiliary telescopes. Assuming a ratio between the thickness of the Sodium layer with respect to its altitude of the order of ten, at a distance of 500 m from the main
observatory this will translates into a tolerance band of 50m width. Non straight paths, with deviations smaller than this size, can be substituted by a straight track.