Space communications with variable elevation angle faded by rain: Radio links to the Sun-Earth first Lagrangian point L_1

摘要

How rain attenuation affects space links with variable elevation angles is not yet fully researched. The aim of this paper is to investigate this topic by simulating rain attenuation at K_a Band, in slant paths with variable elevation angles, with the Synthetic Storm Technique (SST), in links connected with spacecrafts at the Sun-Earth first Lagrangian point L_1 viewed from Spino d'Adda (Italy), Tampa (Florida), White Sands (New Mexico). The input to the SST is a large database of time series of 1-min rain rate recorded on site, 10 years in Spino d'Adda, 4 years at Tampa and White Sands. After recalling known results on the elevation angle of the Sun (i.e. L_1),θ_s(°), seen from latitude λ (°), I report what seems to be a new result: the mode of the probability density function of θ_s in a year, in the range 0 ≤ λ ≤ 90° - ε (Earth axis tilt angle ε=23.44°), coincides with the peak angle found at the day of the Winter solstice at the site, a result valid also for other planets, once their tilt angle is used. Compared to the complementary probability distribution function (pdf) of rain attenuation calculated for a geostationary (GEO) link (fixed elevation angle), the pdf to L_1 depends on the rain-rate pdf during the contact time with L_1; according to the local climate. I show that, to obtain a good and easier estimate of the rain attenuation pdf in L_1 links, we can consider a GEO link with elevation angle equal to the mean angle and rain rate pdf, both during the contact time, and that the mode angle gives an upper bound to the rain attenuation pdf in the sites considered.