His earliest astronomical activities include observations of a comet in 1596 and of Kepler's supernova in 1604. In 1608 he learned of telescopes and started to acquire the skills of producing one (like Galileo). Apparently, he independently discovered Jupiter's Moons (despite Galileo's claim of a plagiary, which had some evidence because it seems that he had already helped Capra in Padua to plagiate Galileo's note describing the use of compass), and proposed the names they have since. His credibility is also not enhanced by the fact that he improved his funds from astrology.
Moreover, Marius found (independently rediscovered) the "Nebula in the Girdle of Andromeda", actually the Andromeda Galaxy (M31), on December 15, 1612, and was the first to observe it with a (very moderate) telescope; he described it as looking like a "flame seen through horn." He was not aware that this object had been seen previously by medieval Persian astronomers, and described by Al Sufi as early as 964 AD.
Simon Marius was lately honored by the astronomical community by naming a Lunar crater after him in 1935; Moon crater Marius is at 11.9 N, 50.8 W and 41 km in diameter. Also, in 1979, a region on Jupiter's moon Ganymed was named Marius Regio (12.1 N, 199.3 W, 3572 km diameter).