The Coriolis force (more precisely the Coriolis effect) is an apparent force that acts on any object moving within a rotating reference frame. 

The Earth rotates about its axis, completing one full rotation every 24 hours. Because the Earth is spherical, different latitudes have different tangential velocities: points at the equator travel faster than points at higher latitudes. When a parcel of air moves from one latitude to another, it retains its original tangential velocity but finds itself over terrain moving at a different velocity. This mismatch causes the air parcel to appear deflected relative to the Earth’s surface below it. 

The deflection is to the right in the northern hemisphere and to the left in the southern hemisphere, and its magnitude is proportional to wind speed and latitude (zero at the equator, maximum at the poles). The Coriolis effect is the sole cause of the characteristic rotation directions of cyclones and anticyclones. 

The rotation of the Earth → CORRECT. The Coriolis force is entirely a consequence of the Earth’s rotation. As air moves across the rotating spherical Earth, its path appears curved to an observer on the Earth’s surface due to the rotation of the reference frame beneath it. Without Earth’s rotation, there would be no Coriolis effect and atmospheric circulation patterns would be fundamentally different.

The pressure gradient between high- and low-pressure cells → INCORRECT. The pressure gradient force is a separate and distinct atmospheric force that drives air from high to low pressure. It is the initiating force that gets air moving. The Coriolis force then deflects that moving air. The two forces are independent in origin: pressure gradient causes motion, Coriolis deflects motion.

The friction of air moving over the Earth’s surface → INCORRECT. Surface friction is a separate force that acts in the atmospheric boundary layer (below approximately 2000 ft). Friction reduces wind speed and deflects wind toward lower pressure by reducing the Coriolis deflection. Friction does not create the Coriolis effect; it acts in opposition to the geostrophic wind balance.

The gravitational pull of the moon on the atmosphere → INCORRECT. Lunar gravity does exert a small tidal effect on the atmosphere, producing atmospheric tides. However these are extremely small compared to the dominant driving forces of atmospheric circulation and have no meaningful connection to the Coriolis effect. The Coriolis force is purely a consequence of Earth’s rotation, not lunar gravity.