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 ρ=5.5×103 kg/m3\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 m/s2g=9.8~\text{m}/\text{s}^2. Determine the thickness hh in kilometers of the disk. You may assume that hRh\ll R, where RR is the radius of the disk.

Details and assumptions

The universal gravitational constant is G=6.67×1011 m3kg1s2 G=6.67\times 10^{-11}~\text{m}^{3}\text{kg}^{-1} \text{s}^{-2}

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