Academic authority derives from constituted educational institutions investing their instructors with the mantle of "professor". Generally this is in recognition of their great knowledge or contribution to a field of study.
The non-academic public tends to recognize professors as knowing more than ordinary people, and their pronouncements are given extra weight.
When professors assert things which a majority of the public disagrees with, academic controversies may arise.
The history of science is rife with examples of academic authority being unrelated to reality. Aristotle, for one thousand years considered the pre-eminent expert on physics, was incorrect about the laws of motion. For example, he asserted vaguely that heavy things fall faster than light things. This is true only for great differences of density (such as a feather and a sword). Galileo proved that a 2-pound cannonball and a 10-pound cannonball fall at the same rate. Moreover, Aristotle neglected acceleration due to gravity. Galileo's cannonballs both fell with greater and greater speed, the longer they were in motion.
The Roman Catholic Church exalted the academic authority of professors who taught that all celestial objects revolve around the earth. They were, as we know now, only correct about the Moon. Actually, the Earth and its moon (like the other planets) revolve around the Sun (see solar system).