The objective of this paper is to bring a mathematical resolution to the semi-annual anomaly of the critical frequencies foF2 which presents itself as a sinusoid.Thus, we posit two postulates about the average and monthly power of the solar radiation which would induce the semi-annualanomaly.This power result of the power caused by the angle of attack of the suns rays and that imparted to the Earth-Solar distance variable due to the fact that the orbit of the Earth is elliptical. Thus the monthly variations of the critical frequencies foF2 can be explained in these terms:If the critical frequencies foF2 are increasing from the solstices to the equinox peaks it is thus respectively because the power is increasing on the sole effect of the power with respect to from the winter solstice to the peak of the spring equinox and on the combined effects of the two powers and which are all increasing for what from the summer solstice to the peak of the autumn equinox. If the critical frequencies foF2 are decreasing from the peaks of the equinoxes to the solstices it is thus respectively because the power is decreasing on the combined effects of and which are all decreasing with respect to the spring equinox to summer solstice peak and on the sole effect of the power with respect to the fall equinox to winter solstice peak.Finally the winter anomaly, the semi-annual anomaly and the equinoctial asymmetry would be explained according to the in-phase or out-of-phase outcome of the two powers and at peaks or solstices.