What name is given to Galileo's coordinate change between inertial reference frames?

Galileo's coordinate change between inertial reference frames is called the Galilean transformation.

In Newtonian mechanics, it relates measurements made by observers moving at constant velocity relative to one another. For motion along the x-axis, the standard equations are x' = x − vt, while y' and z' remain unchanged and t' = t. The shared time reflects the classical assumption that time is universal.

The transformation expresses ordinary velocity addition: if one frame moves at speed v, an object's measured velocity changes by v, but its acceleration remains the same. That is why Newton's laws retain the same form in all Galilean inertial frames.

A common mix-up is the Lorentz transformation. It replaces the Galilean transformation in special relativity, where measurements must remain consistent with the invariant speed of light. The Galilean version is an excellent approximation at everyday speeds, but it fails as relative speeds approach light speed. Although named for Galileo, the formal mathematical framework belongs chiefly to Newtonian mechanics.