Tides above, and tides below

Classical Mechanics Level pending

Suppose \(g_\downarrow(h)\) is the acceleration due to gravity at a depth \(h\) below Earth's surface, while \(g_\uparrow(h)\) is the acceleration due to gravity a height \(h\) above Earth's surface. Form the function \[f(h) = \frac{g_\downarrow(h)}{g_\uparrow(h)}.\]

How does \(f(h)\) vary as we move from \(h=0\) to \(h=R\)?

Details

  • Assume Earth to be a uniform sphere of radius \(R\).

This problem is originally part of set Mechanics problems by Abhishek Sharma. Try more problems here.

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