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The Coriolis force is what seems like a force on a moving object when it is viewed from a rotating frame of reference. The object's motion appears to curve as if there exists a sideways force. For example, if you are at the axis of an enclosed room that is rotating once every ten seconds, and you throw a ball toward some spot on the room's wall, then the ball will appear to you to veer away from that direction even though it is moving straight. Some of this same effect occurs no matter where in the room you throw it from, and the same phenomenon affects wind and water currents here on Earth: over a large scale, as the Earth rotates, moving air appears to veer as compared to the Earth's surface. This phenomenon is a large factor in weather and weather prediction, assuring that air induced to move can result in the rotating air of storms.
This "force" is a factor within rotating fluids, e.g., atmospheres, stars, circumstellar disks, clouds in galaxies, etc. The apparent force is to the left if the rotation is clockwise, and to the right if it is counterclockwise. The apparent deflection of the object is called the Coriolis effect.
A beta plane is a planar approximation of a surface affected by the Coriolis force. It is used to model phenomena without all the complications of a spherical surface, and is presumably most useful for phenomena with a span much smaller than the size of the spherical surface