The coordinate system that is used to specify the location of the point of firing and the location of the target is the system of latitudes and longitudes, which is in fact a rotating coordinate system, since the Earth is constantly rotating. For small arms, this rotation is generally insignificant, but for ballistic projectiles with long flight times, such as extreme long-range rifle projectiles, artillery and intercontinental ballistic missiles, it is a significant factor in calculating the trajectory. During its flight, the projectile moves “basiclly” in a straight line (not counting gravitation and air resistance for now). Since the target is co-rotating with the Earth, it is in fact a moving target, relative to the projectile, so in order to hit it the gun must be aimed to the point where the projectile and the target will arrive simultaneously.
When the straight path of the projectile is plotted in the rotating coordinate system that is used, then this path appears as curvilinear. The fact that the coordinate system is rotating must be taken into account, and this is achieved by adding terms for a “centrifugal force” and a “Coriolis effect” to the equations of motion. When the appropriate Coriolis term is added to the equation of motion the predicted path with respect to the rotating coordinate system is curvilinear, corresponding to the actual straight line motion of the projectile.
For an observer with his frame of reference in the northern hemisphere Coriolis makes the projectile appear to curve over to the right. Actually it is not the projectile swinging to the right but the earth (frame of reference) swinging to the left which produces this result. The opposite will seem to happen in the southern hemisphere. The Coriolis effect is latitude dependent and is at its maximum at the poles and negligible at the equator of the Earth. The reason for this is that the Coriolis effect depends on the vector of the angular velocity of the earth ´s rotation with respect to xyz – coordinate system (frame of reference).