The mature inflorescence of sunflowers (Helianthus annuus) orients eastward after its anthesis (the flowering period, especially the maturing of the stamens), from which point it no longer tracks the Sun. Although several hypothetical explanations have been proposed for the ecological functions of this east facing, none have been tested. Here we propose an atmospheric-optical explanation. Using (i) astronomical data of the celestial motion of the Sun, (ii) meteorological data of diurnal cloudiness for Boone County located in the region from which domesticated sunflowers originate, (iii) time-dependent elevation angle of mature sunflower heads, and (iv) absorption spectra of the inflorescence and the back of heads, we computed the light energy absorbed separately by the inflorescence and the back between anthesis and senescence. We found that the inflorescences facing east absorb the maximum radiation, being advantageous for seed production and maturation, furthermore west facing would be more advantageous than south facing. The reason for these is that afternoons are cloudier than mornings in the cultivation areas of sunflowers. Since the photosynthesizing green back of mature heads absorbs maximal energy when the inflorescence faces west, maximizing the energy absorbed by the back cannot explain the east facing of inflorescences. The same results were obtained for central Italy and Hungary, where mornings are also less cloudy than afternoons. In contrast, in south Sweden, where mornings are cloudier than afternoons, west-facing mature inflorescences would absorb the maximum light energy. We suggest that the domesticated Helianthus annuus developed an easterly final orientation of its mature inflorescence, because it evolved in a region with cloudier afternoons.