In 1614 Marius published his work Mundus Iovialis describing the planet Jupiter and its moons. Here he claimed to have discovered the planet's four major moons some days before Galileo. This led to a dispute with Galileo, who accused Marius, not only of being a liar, but also of having copied his own work so that his Mundus Iovialis was nothing but plagiarism. Today it is considered possible that Marius discovered the moons independently, but at least some days later than Galileo. Regardless of priority, it is the case that the mythological names by which these satellites are known today (Io, Europa, Ganymede and Callisto) are those given them by Marius.
Simon Marius also claimed to be the discoverer of the Andromeda Galaxy, which had in fact already been known to Arab astronomers of the Middle Ages.