Earth has no orthodox exoteric rulership -- it is not read as a placement in traditional astrology, but esoterically it becomes visible as the sphere of lived human experience itself, always standing opposite the Sun in a geocentric chart.
Esoterically Earth represents the field of intelligent activity -- the established personality living through the experiences that gradually shift awareness from the separate self toward the soul, forming a bridge between inner and outer.
Hierarchically Earth points toward the complementary sign and its planets and rays -- the 'other' that must be integrated, resolving what begins as opposition into eventual partnership between the Sun-self and its Earth-shadow.