Amazing but true. Suppose the earth was hollow. There’s be gravity on the surface, but everywhere inside you’d be weightless. Not just in the very center, but everywhere inside.
That’s amazing, but apparently true.
assume hollow earth is a spherical shell of uniform thickness and density, we see (via equations suppressed here but viewable by the curious at the Straight Dope website) that for any two masses on opposite sides of you, the smaller but closer mass A and the larger but more distant mass B pull on you with precisely equal force. Ergo, all such forces cancel out, and you're weightless anywhere inside hollow earth.
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