How did newton's law of gravity explain why celestial objects stay in orbit?

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Newton's law of gravity explains why celestial objects stay in orbit through the principles of gravitational attraction and centripetal force. The law states that every mass in the universe attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

In the context of celestial objects, such as planets orbiting the Sun or satellites orbiting a planet, Newton's law of gravity explains that the gravitational attraction between these objects and the central body (e.g., the Sun or planet) creates a centripetal force that keeps them in orbit. This force acts toward the center of the central body, preventing the objects from moving away in a straight line and instead, causing them to continually curve their path around the central body.

The equation representing this relationship is F = G ((m1 * m2) / r^2), where F represents the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between their centers. This force acts as the centripetal force required to keep celestial objects in orbit. When the gravitational force is equal to the centripetal force, objects remain in a stable orbit without being pulled closer or pushed farther away.

Newton's law of gravity accurately explains the motion of celestial objects, providing a comprehensive understanding of why they stay in orbit around each other or their central bodies.
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