I recently encountered the Hollow Earth theory, and I realize that This kind of theories can be used to give a really interesting discussion of a physical law.

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For example, If we take the hypothesis that the earth is hollow and if we ignore the border effects of the pole holes and approximate it as a hollow sphere, we know that the gravitational field inside a hollow sphere is:

$$\Psi_{earth}=\begin{cases} 0 &\mbox{if } R < r_{earth} \\ \frac{mG}{R^2} & \mbox{if } R > r_{earth} \end{cases} $$

Using this we can conclude that the people living inside wouldn't feel any kind of gravitational attraction from the earth, so they would be floating.

We also can conclude that if we put a sun inside the earth the things inside would get attracted to it and there is just no way of nothing being there to start with.

Now that I've said this:

Do you know any other theories that can be used with this approach ?


closed as off-topic by ACuriousMind, Kyle Kanos, Kyle Oman, David Hammen, John Rennie May 3 '15 at 19:33

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    $\begingroup$ Or you could teach them in the same amount of time how the old Greek already measured Earth's real diameter... with an actual experiment. Nonsense vs. reality.... hmmm.. I know what I would do. $\endgroup$ – CuriousOne May 3 '15 at 1:09
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    $\begingroup$ you can teach physics by asking hypothetical questions. Like: how behavior of hollow earth/people living there differs from what we observe? As I understand, OP uses mainstream physics, but model system is fancy. $\endgroup$ – aaaaaa May 3 '15 at 1:22
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    $\begingroup$ This is just an example of how can we apply a physical law in an exciting and funny way. Just to have fun, just to show that doing physics is not some kind of mysterious thing. This is to show that you can enjoy it just like a game $\endgroup$ – Keith May 3 '15 at 1:23
  • $\begingroup$ Consider a thick, disc-shaped Earth? Walking towards the outer edge would cause your weight vector to align with the plane of the disc. You'd feel like you're marching uphill! On the edge, you can rest easily. $\endgroup$ – zahbaz May 3 '15 at 2:14

Due to the rotation of the Earth, "inner-Earth-dwellers" would feel a fictitious centrifugal force pointing away from the axis of rotation. Ask your students how strong that force would appear to be.

Once they realize it's a very weak force indeed, ask them to determine how fast the Earth would be spinning to give inner-Earth-dwellers the appearance of normal Earth gravity.


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