Who first observed the moons of Jupiter in 1610?

Galileo, and the observation destroyed a cosmology. Four objects visibly orbiting something other than the Earth demonstrated that not everything goes round us, which the Ptolemaic system required. He published within weeks in a short book, Sidereus Nuncius, that also reported mountains on the Moon and that the Milky Way is made of stars.

He named them the Medicean Stars, after the family he wanted a job from, and got one. The names in use - Io, Europa, Ganymede, Callisto - come from Simon Marius, a German astronomer who claimed independent discovery at the same time and whom Galileo accused of plagiarism with characteristic force. Marius's names won.

The moons then did practical work for two centuries. Their eclipses happen on a predictable schedule visible from anywhere, which made them a clock in the sky for determining longitude on land - and in 1676 Ole Rømer noticed the eclipses ran late when Earth was further from Jupiter, correctly concluded that light takes time to travel, and produced the first measurement of its speed. An observation made to please the Medici ended up measuring the speed of light.