The Core is the name given to the planets and moons inside the Asteroid Belt.
The Core was the seat of The Society's power and prides itself as being more civilized than The Rim. The Core was established upon defeat of Earth in The Conquering. The Core also defeated The Rim in the two Moon Lord Rebellions. These rebellions were spurred on by a lack of Rim representation on Luna and trade sanctions remaining from the First Moon Lord Rebellion as well as the nuclear annihilation of Saturn's moon Rhea.
The Core includes all of the inner planets and moons before the asteroid belt. This includes Mercury, Venus, Earth, Mars, and their moons, Luna, Phobos, and Deimos. All planets and moons in The Core are inhabited by large populations.