The aim of the paper is to investigate the influence of the solar cycle variations of the radiation pressure and time- and heliolatitude-dependent ionization rate on the spatial distribution and temporal evolution of the interplanetary hydrogen Lyman α glow, observed from 1 AU. We identify the variables affecting the distribution and evolution of the glow intensity and derive a parametric formula that links quite accurately the evolution of the intensities from arbitrary lines of sight with the variations of solar radiation pressure and net ionization rate. We illustrate that the radiation pressure ¿, ecliptic ionization rate ¿ecl, and ionization rate anisotropy qion can be derived with a reasonable accuracy from time series of ratios Q of the glow intensities from selected pairs of lines of sight because ¿, ¿ecl, qion, and Q are approximately related to each other by simple linear formulae. Further, we show the range of the north-south anisotropy in the glow that can be expected despite the north-south symmetry of the ionization rate. Finally, we qualitatively discuss the sensitivity of our results to other phenomena possibly affecting the distribution and evolution of the solar Lyman α backscatter glow, including the influence of the heliospheric interface and of the radiative transport correction.