Alternative analytic method for computing mean observation time in space-telescopes with spin-precession attitude motion

Space -telescopes placed in the Sun -Earth second Lagrange point (L2) observe the sky following a scan strategy that is usually based on a spin -precession motion. Knowing which regions of the sky will be more observed by the instrument is important for the science operations and the instrument calibration. Computing sky observation parameters numerically (discretizing time and the sky) can consume large amounts of time and computational resources, especially when high resolution is required. This problem becomes more critical if quantities are evaluated at detector level instead of considering the instrument entire Field of View (FoV). In previous studies, the authors have derived analytic solutions for quantities that characterize the observation of each point in the sky in terms of observation time according to the scan strategy parameters and the instrument FoV. Analytic solutions allow to obtain results faster than using numerical methods as well as capture detailed characteristics which can be overseen due to discretization limitations. The original approach is based on the analytic expression of the instrument trace over the sky. Such equations are implicit and thus requires the use of numeric solvers to compute the quantities. In this work, a new and simpler approach for computing one of such quantities (mean observation time) is presented. The quantity is first computed for pure spin motion and then the effect of the spin axis precession is incorporated under the assumption that the precession motion is slow compared to the spin motion. In this sense, this new approach further simplifies the analytic approach, sparing the use of numeric solvers, which reduces the complexity of the implementation and the computing time.