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 combination (formula_14) of groups is required. Here, we only look at the Lie algebra of the Galilean group; it is then easy to extend the results to the Lie group. The relevant Lie algebra is spanned by and (an antisymmetric tensor), subject to commutation relations, where This Lie Algebra is seen to be a special classical limit of the algebra of the Poincaré group, in the limit . Technically, the Galilean group is a celebrated group contraction of the Poincaré group (which, in turn, is a group contraction of the de Sitter group "SO"(1,4)). Renaming the generators of the latter