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the correct orbit for such a force law was. Newton did not reply.

The problem did serve to revive Newton's interest in dynamics, though, and he took up the challenge of determining the force law that would cause a body to revolve around a point of attraction in an elliptical orbit. With Hooke's ideas about the dynamics of circular motion, Newton quickly mastered his own dynamical principles, and took a huge step forward when he managed to show that any body moving subject to a central force would satisfy Kepler's law of areas. Elliptical motion was clearly non-inertial, and so a body moving in such an orbit must be continually subject to a force, but it is not obvious at all what the direction and magnitude of such a force should be. Newton may well have believed that the force varied inversely as the square of the distance from the Sun and was directed toward the Sun, but he wanted to provide a mathematical demonstration of the fact. These demonstrations were written up in a short tract usually referred to as De motu (On Motion) that Newton sent to Edmond Halley

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