![]() A uniform sphere has its center of mass at its geometric center. The center of mass of an object is the average or mean location of its mass. Since the radius of the Earth is about 6685 km and the CM between the Earth and Moon is about 4671 km from the center of the Earth, the CM between the Earth and Moon is at about 2014 km below the Earth's surface. Substitute in values to find the separation between the Earth and the CM, R M: ![]() The separation between the Earth and the Moon is R = 384,403 km, which equals 3.844*10 5 km. The mass of the Moon is m = 7.348*10 22 kg The mass of the Earth is M = 5.974*10 24 kg If one sphere is much larger than the other, the center of mass may even be within the larger object.Ĭenter of mass can be inside much larger object Earth and Moon exampleĪ good example concerns the CM between the Earth and the Moon. Start with the equation:Ĭenter of mass is at the midpoint for equal objects CM when one sphere much larger Equal sized spheresįor two objects of equal mass, the CM is the point midway between the line joining their centers. Special cases of the CM between two objects include equal-sized spheres and when one sphere much larger than the other. If you solve the equations for R m, you get: MR m = MR M can also be stated as the inverse ratio of the masses:ĬM between two uniform spheres Solve for R m and R M
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