What causes the earth-moon move through space?

The Earth and Moon move through space primarily due to the gravitational forces exerted by the Sun and other celestial bodies, as well as their mutual gravitational attraction. The Earth orbits the Sun while the Moon orbits the Earth, creating a complex motion where both bodies are influenced by the gravitational pull of the Sun. Additionally, the angular momentum from their formation and the conservation of momentum contributes to their ongoing motion through space.