Sources of Centripetal Force
For a satellite in orbit around a planet, the centripetal force is supplied by gravity. Some sources, including Newton, refer to the entire force as a centripetal force, even for eccentric orbits, for which gravity is not aligned with the direction to the center of curvature.
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. For an object swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope. For a spinning object, internal tensile stress provides the centripetal forces that make the parts of the object trace out circular motions.
The rope example is an example involving a 'pull' force. The centripetal force can also be supplied as a 'push' force such as in the case where the normal reaction of a wall supplies the centripetal force for a wall of death rider.
Another example of centripetal force arises in the helix which is traced out when a charged particle moves in a uniform magnetic field in the absence of other external forces. In this case, the magnetic force is the centripetal force which acts towards the helix axis.
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