earth has 9 distinct synonyms spread across 5 of its 9 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the 3rd planet from the sun; the planet we live on
“the Earth moves around the sun”
the solid part of the earth's surface
“the plane turned away from the sea and moved back over land”
the abode of mortals (as contrasted with Heaven or Hell)
“it was hell on earth”
once thought to be one of four elements composing the universe (Empedocles)
the concerns of this life as distinguished from heaven and the afterlife
“they consider the church to be independent of the world”
a connection between an electrical device and a large conducting body, such as the earth (which is taken to be at zero voltage)
connect to the earth
“earth the circuit”
Synonyms, antonyms and the broader and narrower relations for earth come from Princeton University’s WordNet. Full sources and licences.