If the Earth were a perfectly smooth sphere, with no mountains, valleys, or any irregularities on its surface, it would still be in motion due to several factors:
Rotation: The Earth rotates around its axis, completing one rotation approximately every 24 hours. This rotational motion causes day and night cycles. Even if the Earth's surface were perfectly smooth, the rotation would still continue.
Orbit: The Earth orbits around the Sun in an elliptical path, completing one orbit in about 365.25 days. This orbital motion is responsible for the changing seasons. The smoothness of the Earth's surface would not affect this orbital motion.
Tides: The gravitational pull of the Moon and the Sun causes tides on Earth. The tidal forces arise due to the difference in gravitational attraction between the near and far sides of the planet. These tidal forces would still be present even if the Earth's surface were smooth.
Precession and Nutation: The Earth's axis experiences a slow, cyclical wobble known as precession. This wobble has a period of about 26,000 years and is caused by the gravitational interactions between the Earth, Moon, and Sun. Nutation refers to smaller irregularities in the precession motion. These motions would still occur even if the Earth's surface were perfectly smooth.
In summary, even if the Earth's surface were perfectly smooth, the planet would still exhibit motion due to its rotation, orbit around the Sun, tidal effects, and axial precession and nutation. These motions are fundamental to the dynamics of our planet and are not dependent on the surface's smoothness.