where LOD is the length of the day in hours, and τ is the time in billions of years ago (Ga). (Prior to the beginning of the Paleozoic era, the slowing of the Earth's rotation was thought to ha...where LOD is the length of the day in hours, and τ is the time in billions of years ago (Ga). (Prior to the beginning of the Paleozoic era, the slowing of the Earth's rotation was thought to have been at a slower rate than this 4.98hr/Gyr rate.) Using this formula, the day length at the beginning of the Age of Dinosaurs (the Mesozoic era, about 250 million years ago) was only about 22 hours 45 minutes, or an hour and 15 minutes shorter than it is today.