If the Earth were flat...

There was a time, long ago, when people thought that the Earth was flat. Let us suppose that the Earth is a flat disk with density \(\rho=5.5\times 10^{3}~\text{kg}/\text{m}^3\). The acceleration due to gravity, right at the surface of the planet, and close to center of the disk is \(g=9.8~\text{m}/\text{s}^2\). Determine the thickness \(h\) in kilometers of the disk. You may assume that \(h\ll R\), where \(R\) is the radius of the disk.

Details and assumptions

The universal gravitational constant is \[ G=6.67\times 10^{-11}~\text{m}^{3}\text{kg}^{-1} \text{s}^{-2} \]

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