Should ballistic be a castle age tech?

Ballistics, the science of projectile motion, was founded in 1531 by Italian mathematician Niccolò Tartaglia, who first studied the trajectories of cannonballs. It was later put on a solid scientific basis by Galileo in 1638 (parabolic trajectory) and Isaac Newton in 1687 (laws of motion and gravity). Do you think it's historically accurate to get the tech in castle age? Can we shift the tech to imperial age with only strong archer civs have access to it?