Adventure of Superman #473: From Earth, Superman threw an alien space craft clear of Earth’s gravity and into outer space. This craft was larger than an aircraft carrier and over a mile long (a typical aircraft carrier is about a 1/4 of a mile long and weighs about 100,000 tons, so this ship was about 4x that size)
Several events show Superman as a moon-mover. In JLA # 7, as Electro-Superman, he halted the fall of the Moon towards Earth (caused by Neron’s magical machinations), then moved the Moon back its proper position in orbit. He later commented that he’s more powerful as "regular" Superman. Writer Grant Morrison and artist Howard Porter had originally intended the moon-moving event in JLA #7 be done by "regular" Superman , but DC forced them to use Electro-Supes. This event is butressed by several more. In JLA: The Century War, ancient "alchemical engines" were causing the moon to fall towards the Earth. Superman and Green Lantern took turns holding the moon back against the "geometrically increasing force" that was causing it to fall. Superman got the last "moon-bracing" shift. In Superman Man of Steel #30, Superman grabbed, easily broke the forward movement of, and easily threw in the opposite direction, a space ship the size of a small moon. In JLA # 58, Superman , Wonder Woman and Green Lantern collaborated to tow Earth’s moon a distance of 238,900 miles in mere seconds, indicating a fantastic acceleration, and then pulled the moon out of Earth’s gravity (which increases its weight tremendously). As he is universally regarded as the JLA’s most powerful member, I’m inclined to give Superman more than one-third, and - conservatively - about one-half, the work effort. In the Lex 2000 special, with a single strike, Superman split one of Saturn’s moons in half. Saturn’s moons are small moons.