  We have constructed an analytical model to simulate the behavior of an
adaptive optics system coupled with a sodium laser guide star. The code is
applied to a 3.6-m and 8m class telescopes. The results are given in terms of
Strehl ratio and full width at half maximum of the point spread function. Two
atmospheric models are used, one representing good atmospheric conditions (20
per cent of the time), the other median conditions. Sky coverage is computed
for natural guide star and laser guide star systems, with two different
methods. The first one is a statistical approach, using stellar densities, to
compute the probability to find a nearby reference. The second is a
cross-correlation of a science object catalogue and the USNO catalogue. Results
are given in terms of percentage of the sky that can be accessed with given
performances, and in terms of number of science object that can be observed,
with Strehls greater than 0.2 and 0.1 in K and J bands.
