By means of a simple mathematical model recently developed by the authors (2010 Phys. Educ. 45 641), the passage of the seasons on the Earth is simulated for arbitrary latitudes, taking into account sunlight attenuation in the atmosphere. The method developed can be used to predict a realistic value of the solar energy input (insolation) that can be absorbed by horizontal ground at sea level on any cloudless day of year. Some ideas for estimating daily insolation on to horizontal ground using the duration of daylight and the length of a shadow at the solar noon are discussed.