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# Newton3 - Newton's Shell Theorem Gravitating Spheres While...

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Newton's Shell Theorem Gravitating Spheres While exploring Netwon's gravitational discoveries, we calculated g using the fact that the distance between the mass m and the earth was the radius of the earth. In other words, we assumed that all the mass of the earth is concentrated at its center. This supposition may seem reasonable when we are far away from the earth (that is we are at such a distance that the radius of the earth is negligible in comparison), but it doesn't seem so good at all when we are at the earth's surface. However, we will see that this assumption does hold exactly for any body outside the surface of a gravitating sphere (to which the earth is a good approximation). This is a profound result. It is a consequence of superposition, the inverse square law, and the symmetry of a sphere. The following theorem was proved by Newton in the Principia : A spherical mass can be thought of as built up of many infinitely thin spherical shells, each one nested inside the other.

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Newton3 - Newton's Shell Theorem Gravitating Spheres While...

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