Galilean moons century when other inner moons were discovered, and Marius' names became widely used. Galileo was able to develop a method of determining longitude based on the timing of the orbits of the Galilean moons. The times of the eclipses of the moons could be precisely calculated in advance, and compared with local observations on land or on ship to determine the local time and hence longitude. The main problem with the technique was that it was difficult to observe the Galilean moons through a telescope on a moving ship; a problem that Galileo tried to solve with the invention of
Galilean invariance a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called "Newtonian relativity". Among the axioms from Newton's theory are: Galilean relativity can be shown as follows. Consider two inertial frames "S" and "S' ". A physical event in "S" will have position coordinates "r" = ("x", "y", "z") and time "t" in "S", and "r' " = ("x' ", "y' ", "z' ") and time "t' " in "S' ". By the second axiom above,