Question

Using Ice sheet thickness equation (H):

If there were Ice sheets on Mars in the past, and at 10 km from the edge of the ice sheet it is 1 km thick, how thick would it be from 1 km from the edge? You may assume the Yield Strenghts and Ice densities remain constants.

Use the Ice sheet thickness equation: H = sqrt(2YL/pg),

Where: Y = Yield Stress, L = Distance to Ice margins, p = density and g = gravity.

Answer 1

$H=\sqrt{\frac{2YL}{\rho g}}$
So,
given other parameters constant, we get
   $\frac{H_1}{H_2}=\sqrt{\frac{L_1}{L_2}}$
  given H_1 = 1 km, at L_1 = 10 km, we get at L_2 = 1 km, the thickness
    ${H_2}=H_1\sqrt{\frac{L_2}{L_1}}$
   $\Rightarrow {H_2}=1\times \sqrt{\frac{1}{10}}=0.316~km$