I heard one explanation of this passage in Sefer Yehoshua, that the "stopping" of the sun had to do with the ceasing of its light. Yehoshua arrives at Giv'on at night, and thus Yehoshua prays for the extension of the night, rather than the extension of the day, which was covered by the hail prior to his prayer. Makes sense. At the same time, according to Aztec lore in Mexico, the sun failed to rise for a whole day in the "City of the Gods", Teotihuacan (north of Mexico City). Likewise, it failed to rise for 20 hours in the Andes, according to Inca legends. Since an "endless day" and an "endless night" are the same phenomenon in opposite sides of the world, this would seem to confirm the biblical account of the sun standing still at Giv'on.
Wouldn't the calendar be affected if the sun stood on the sky for 24 hours?