I suspect the most difficult bit of the problem is defining what we mean by "the length of Antartica's shore". Crinkles below a certain size are irrelevant because water can't flow over them. So we mean the length of the shore as measured by a ruler whose length is the Capillary length of water in air, which is 2.7 mm. Of course no one has ever measured this, but perhaps we can estimate it by using coarser measurements and fitting a curve to them.
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