In a book called On the Revolutions of the Heavenly Bodies (that was published as Copernicus lay on his deathbed), Copernicus proposed that the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system. The ordering of the planets known to Copernicus in this new system is illustrated in the following figure, which we recognize as the modern ordering of those planets.
For this reason, a heliocentric system is the Solar System with the sun in the center, so there is not an "opposite".
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The opposite of heliocentric is geocentric. Geocentric refers to a model of the universe where Earth is considered to be the center, with other celestial bodies orbiting around it.
Galileo did not propose a heliocentric theory, he agreed with Copernicus and his heliocentric theory. The Catholic church, at the time, disagreed and they held a huge amount of power and put him on trial.
Ptolemy
The heliocentric theory, proposed by Nicolaus Copernicus, states that the Earth and other planets revolve around the Sun, contrary to the previously accepted geocentric model.
He was an Italian scientist of the 17th century. He did not prove the heliocentric theory. But everyone accepts the heliocentric principle now, after it was proved right; but that happened long after Galileo's time, after new scientific discoveries in the latter half of the 1600s.
The heliocentric theory, proposed by Copernicus, states that the Sun is at the center of the solar system and that the planets, including Earth, orbit around it.