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What is Newton's Cannonball?

Newton's Cannonball, also known as Newton's thought experiment, is a conceptual illustration devised by Sir Isaac Newton to explain the fundamental principles of gravitational motion and his law of universal gravitation. The thought experiment involves considering the motion of a cannonball fired horizontally from a tall mountain with increasing velocity. Imagine placing a tall mountain on the surface of the Earth and firing a cannonball horizontally from the mountaintop with sufficient velocity. According to Newton's first law of motion (the law of inertia), the cannonball would travel in a straight line at a constant speed without any forces acting on it. However, as the cannonball moves horizontally, it is also subject to the force of gravity, causing it to fall towards the Earth. Crucially, as the cannonball moves forward and falls simultaneously, the Earth's surface also curves away beneath it due to the Earth's spherical shape. Thus, if the cannonball were fired with a sufficiently high initial velocity, it could travel a considerable horizontal distance before eventually hitting the ground. Newton's thought experiment helps demonstrate that the motion of the cannonball is a combination of its horizontal motion (governed by inertia) and vertical motion (due to gravity). This insight laid the groundwork for Newton's law of universal gravitation, which states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The cannonball thought experiment helped Newton explain why objects, such as planets and moons, move in elliptical orbits around celestial bodies like the Sun, applying the same principles of gravitational motion to the motions of celestial bodies as he did to the cannonball's motion on Earth. Newton's law of universal gravitation became a fundamental pillar of classical mechanics, revolutionizing the understanding of motion, gravity, and the mathematical description of physical phenomena.