In my last entry, I mentioned the hollow-earth theory of the Koreshan religious group, who argued that we live on the inner surface of a hollow planet which has ‘outer’ space in the middle. I was picturing that and I got to wondering how gravity would work inside a hollow planet.
What strikes me as the common-sense answer is that because gravity pulls matter to matter, near the inner surface you’d be pulled ‘down’, meaning ‘against’ that surface (so that you’d walk with your feet pointing ‘out’ and your head pointed ‘in’, toward the middle of the empty space, just like all good Koreshans do (and also possibly Vyacheslav Krasheninnikov‘s dinosaurs?)) If you were to jump in a rocket ship and propel yourself ‘up’ off the inner surface, the effect of gravity would get less and less until you reached the exact centre of the sphere, at which point the equidistant gravitational forces surrounding you would all cancel each other out and leave you floating, weightless. If you moved too far one way or the other, you’d be in for a long fall and a sudden splat. That makes sense, right?
Wrong! As it turns out, if you should happen to be on the left ‘side’ of the cavity (with the shell on your left) the nearness of that part of the shell would indeed result in a stronger gravitational pull to your left- but you would, of course, have more of the shell to your right side. The gravity associated with that matter is weaker, but there’s more of it, to the extent that it completely and exactly cancels out the gravity on your left, and you’d neither crash to the inside of the shell nor drift off to attain perfect, harmonious equilibrium in the exact centre of the planet. You’d just bounce around like an idiot. The net gravitational field of every point within the cavity of a sufficiently massive (and uniform) hollow shell is exactly zero.
Pretty bizarre, eh?
(The link above does a good job of dumbing this down for regular schmucks like me, but if you have the kind of advanced intellect that can comprehend high-level mathematics, the idea is called shell theorem, and that Wikipedia article has what I’m told is called a “derivation” that proves it. This derivation, according to a few physics forums I’ve visited, is apparently so clear and transparent and idiot-proof that even the most knuckle-dragging, bungling, backwoods physicists and mathematicians can readily make sense of it.)