Variations in summer insolation at high northern latitudes on a timescale of 100 ka are very small. Thus a common belief is that the pronounced ∼100 ka glacial cycles are not directly linked to the very weak 100 ka insolation periodicity. Here we show, analytically and numerically, that the annual maximum (and minimum) of daily equatorial insolation has pronounced eccentricity periodicities, with timescales of ∼400 ka and ∼100 ka, as well as a pronounced half-precession periodicity with timescale of ∼11 ka. The timing of the maximum (and minimum) annual equatorial insolation may change around the equinoxes (solstices), alternating between the vernal and autumnal equinoxes (summer and winter solstices) where the time of the maximum (minimum) equatorial insolation may occur up to more than 1 month from the equinoxes (solstices). We also show that when considering the mean insolation of periods larger than 1 d, the ∼11 ka periodicity becomes less dominant, and it vanishes when the averaging period is half a year; for the later case the maximum (minimum) may occur for any day in the annual cycle. The maximum equatorial insolation may alter the timing and amplitude of the maximum surface temperature of the summer hemisphere and in this way may drastically affect the Hadley circulation. Changes in Hadley circulation affect the heat and moisture transport from low to high latitudes, affecting the buildup of the high-latitude Northern Hemisphere ice sheets.