One of the most relevant problem given by the use of a Laser Guide Star (LGS) to correct wavefront distortions in Adaptive Optics systems is the indetermination of the absolute tilt (Pilkington 1987; Olivier et al. 1993). This problem arises from the fact that laser beam fired from the ground passes through the atmosphere and, under its influence, generates an LGS whose relative position with respect to the scientific target changes continously. The tilt component of the turbulence detected by the science telescope is strongly degraded by the additional tilt motion of the LGS. A number of tentative solutions to the LGS tilt determination problem have been proposed (Belen'kii 1994, 1995; Foy et al. 1992, 1995; Rigaut & Gendron 1992; Ragazzoni 1996a,b; Ragazzoni & Marchetti 1996; Lukin 1996). Moreover Ragazzoni et al. (1995, REM95 hereafter) have considered a system of two small moving telescopes in the neighbourhood of the main observatory which are able to measure the undesired LGS tilt observing it from different angles of view and comparing its motion with respect to a natural star that lies in the same isokinetic patch.
It is to be recalled that other investigators considered the option to have some moving telescopes, especially for interferometric purposes (Vivekanand et al. 1988).
In this paper we further investigate the REM95 solution, especially concerning the ground area requested by the movements of the auxiliary telescopes in order to provide a full sky coverage.
The core of the paper is subdivided into three sections; i): the limiting magnitude reachable by the auxiliary telescope is derived and discussed; ii): the relationships useful to figure out the geometrical path to be followed by such small telescopes are worked out and briefly discussed; iii): simulations, especially using MonteCarlo techniques, in order to obtain the ground coverage for the auxiliary telescopes are described.