An early major objection to the idea that the Earth is spinning on its axis was that Earth would turn so fast at the equator that people would be thrown off into space. Show the error in this logic by solving the following problems for a 97.0 kg person standing on the equator where the Earth’s radius is 6378 km. Such a person moves in a circular path due to the Earth’s rotation about its own axis. (a) Determine the centripetal force necessary to keep this person moving in such a fashion. (b) Determine the pull of gravity acting on the person. (c) Determine the normal force acting on the person. (Note: the person is not “at rest” unless the Earth’s surface is the frame of reference. For this problem, let the Earth’s axis be the frame of reference. The person is in motion around the axis even though he is not moving relative to the surface of the Earth.)