Centripetal force

Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The term centripetal force comes from the Latin words centrum ("center") and petere ("tend towards", "aim at"), signifying that the force is directed inward toward the center of curvature of the path. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center." The magnitude of the centripetal force on an object of mass m moving at a speed v along a path with radius of curvature r is:

F = mv² / r

The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle, the circle that best fits the local path of the object, if the path is not circular. This force is also sometimes written in terms of the angular velocity w of the object about the center of the circle:

F = mrw²

For a satellite in orbit around a planet, the centripetal pseudo-force is an artifact of classical Newtonian model of gravitational attraction between the satellite and the planet. The gravitational force acts on each object toward the other, which is toward the center of mass of the two objects; for circular orbits, this center of gravity is the center of the circular orbits. For non-circular orbits or trajectories, only the component of gravitational force directed orthogonal to the path (toward the center of the osculating circle) is termed centripetal; the remaining component acts to speed up or slow down the satellite in its orbit. Alternatively, some sources, including Newton, refer to the entire gravitational force as centripetal, though it is not strictly centripetally directed when the orbit is not circular.