Student Question

Calculate the kinetic energy of Earth due to its spinning about its axis, and compare your answer with the kinetic energy of the orbital motion of Earth’s center of mass about the Sun. Assume Earth to be a homogeneous sphere of mass 6.0 × 10^24 kg and radius 6.4 × 10^6 m. The radius of Earth’s orbit is 1.5 × 10^11 m.

Expert Answers

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Use the definition of rotational kinetic energy. First, to find Earths rotational KE use it when I is its moment of inertia with respect to Earth's axis of rotation. Next to find the orbital know that the center of mass of the Earth-Sun system is so close to the center of the Sun and the Earth-Sun distance so large that we can use the Earth-Sun distance as the separation of their centers of mass and assume each to be a point mass. Then the moment of inertia can be found by treating the Earth as a point mass rotating about the sun. Lastly, compare the ratio of rotational kinetic energies.

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