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 transformation spatial origins coinciding at time : Note that the last equation expresses the assumption of a universal time independent of the relative motion of different observers. In the language of linear algebra, this transformation is considered a shear mapping, and is described with a matrix acting on a vector. With motion parallel to the "x"-axis, the transformation acts on only two components: Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods in special relativity. The Galilean symmetries can be uniquely written as the composition of a "rotation", a "translation"