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The force of the curvature of the Earth, along with gravity is known as the Coriolis effect. How this would effect any long range projectile (bullets, missiles, etc.) is that it will change the path of flight. Meaning, that gravity will slowly pull the projectile down onto the surface. While the downward pull isn't at dramatic as it is for the missile (due to its constant propulsion), the curvature of the earth is VERY important. This is because you have to take in the total distance the missile is to travel in order to his its intended target. The curvature of the Earth (if the target is far enough) will not only obstruct the line of sight (especially if the target is say in Another Country, or a few miles away), shooting straight would be out of the question. All this, due to the curvature, this, in turn, requires missiles to be shot up, and then come down onto the target in a pyramid shape... hope this helps... oh, and to actually answer your question.

The curvature of the Earth changes the time of flight on a missile because it forces us to launch the missile upwards first, then downwards. The flight path of a missile is, therefore, increased.

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