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# Gravity field of a hollow planet

A uniform, spherical planet has a spherical space at its center.
The radius of the surface of the planet is Rp= 8.9E7 m (8.9 x 10^7 m).
The radius of the central hollow space is Rh = 6.2E5 m.
The total mass of the planet is M= 7.5E28 kg.
The distance from the center to three designated points are:
Point a is distance Ra= 9.2E8 m from center, outside of the planet.
Point b is distance Rb= 5.8E4 m from center, within the hollow center.
Point c is distance Rc= 7.1E6 m from center. between inner and outer surface.
SEE ATTACHMENT FOR A DIAGRAM
Find the gravitational field of the planet at each of the three points.

#### Solution Preview

Physics notes:
Note 1.
One important fact relative to gravity fields of masses, is:
(1) The gravity field, g, within a hollow shell of matter is zero. (At each interior point, the gravity field of any one element exactly cancels that of the element diametrically opposite).
Note 2.
(2) At points exterior to a hollow shell of matter, its gravity field, g, is the same as if the entire mass of the shell were a point mass at its center. (Note that a point on the surface is included by this rule.)
Note 3.
From Newton's gravitation law, the ...

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