Who are the most famous astronomers? What are their major discoveries?

The most famous astronomers are Hipparchus (in ancient times), Galileo (in medieval times) and Hubble (of modern times).

Hipparchus is believed to be the founding father of astronomy in ancient times. He compiled the first known star catalog to organize astronomical objects. He came up with a scale to define the brightnesses of stars, a system still in use today.. He measured the distance from to the Moon to be 29.5 Earth diameters (close to the real value is 30 Earth diameters). Perhaps his greatest discovery was precession of the Earth's axis, which is caused by the gravitational pull of and Moon.

Galileo Galilei is considered to be the father of observational astronomy. With the help of his own refracting telescope, he saw the craters, mountains, and valleys of the Moon, discovered four moons orbiting Jupiter, saw the Rings of Saturn, kept precise records of sunspot activity and the phases of Venus, and noticed the huge number of stars making up the Milky Way. He's most well known for his staunch defense of the idea of a heliocentric solar system, providing hard evidence for the fact.

Edwin Hubble made an incredible contribution to astronomy when he magnified the Universe from the domain of the Milky Way Galaxy of about a hundred thousand light years across, to an indefinite realm of intergalactic space, billions of light years across. He discovered that faraway galaxies are moving away from us. Known as Hubble's Law, the theory states that galaxies recede from each other at a rate proportional to their distance from each other. This concept is a cornerstone of model of the universe.