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 and a "uniform motion" of spacetime. Let represent a point in three-dimensional space, and a point in one-dimensional time. A general point in spacetime is given by an ordered pair . A uniform motion, with velocity , is given by where . A translation is given by where and . A rotation is given by where is an orthogonal transformation. As a Lie group, the Galilean transformations span 10 dimensions, i.e., comprise 10 generators. Two Galilean transformations compose to form a third Galilean transformation, . The set of all Galilean transformations on space forms a group with composition as the