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Physics: Gravity field at points interior to a uniform spherical shell of mass

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Show that the gravity field of a spherical shell of matter is zero at all points within it.

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The gravity field of a mass M at a distance r from its center, is:
(1) g= G M / r^2.
SEE ATTACHMENT #1
STEP 1. It is obvious that at the center of the spherical shell, the gravity field of any surface mass element is exactly canceled by an equal mass element diametrically opposite so all elements of the field are canceled.
For a point not at the center, attachment #1 shows two opposite surface elements of mass ...

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