If gravity exists, why doesn’t the Moon fall to Earth?

Sir Isaac Newton has answered this question of yours through a thought experiment in his book A Treatise of the System of the World. According to him, if a body gets enough velocity, it can reach free space from the effect of gravity.
For his hypothesis, he took a cannonball and freed it from the highest mountain on Earth (Agni). If the velocity of this cannon ball will be less (0 to 6000 m / s), then it will come back to the earth after going some distance. see drawing-
If the velocity of the cannonball is equal to the orbital velocity (7300 m/s), it will orbit the Earth in a fixed circular orbit.
If the cannonball attains this velocity (less than the escape velocity), it will continue to orbit the Earth in an elliptical orbit.

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