[math-fun] liquid mirrors
As I (vaguely) recall, you got one of those wide shallow cookie tins, put a plastic bag inside, put plastic resin inside mixed with some kind of colorant, got it spinning on the phono turntable, added hardener catalyst. (And all with a lid on to avoid wind from passing air.) Or for nonpermanent, use water mixed with ink. The earth is not flat, causing parabola, not really to be. This is not problem since earth large, but would be a problem for an asteroid. Also, ripples in the liquid, surface tension, nonuniform g-field, etc, all would be a serious problem in a very weak g-field of some asteroid. In an inverse square law g-field, y=altitude, r=distance from spin axis, neglecting surface tension and self-gravitation, the equipotential surface is C=sqrt(r^2+y^2)*(B+A*r^2) where A,B,C constants, which is y^2 = (-A^2*r^6 - 2*A*B*r^4 - B^2*r^2 + C^2) / (A^2*r^4 + 2*A*B*r^2 + B^2) which as you can see is not at all a parabolic curve, it is degree=6... but whatever it is, is locally parabolic. In practice when this method is used to cast giant glass mirrors in rotating furnace, I suspect the biggest problem is thermal stresses. They need very slow cooling to try to avoid this problem -- months. They cast them with a custom mold below intended to create honeycombed beam structure of the glass on the other side of the mirror, so it is stiff and strong. It occurs to me that a perhaps better idea would be to place the liquid glass on top of liquid tin within the rotating furnace. Then perhaps it would be possible to cool it much more quickly. The resulting mirror then would be smooth on both sides and look a bit like an eggshell. The beams would be absent, but could be replaced by external beams I suppose.
participants (1)
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Warren D Smith