= Ice Radiation Shielding =
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Light atomic nuclei scatter high energy particles better than heavy nuclei, so the best shielding material is hydrogen dense.  Pure solid hydrogen masses only 0.0763 g/cm3 below 14K under pressure.  This is not practical in the inner solar system.  Other forms of hydrogen-containing solids are:

|| Material      || Melting || Hydrogen ||<-2> Density g/cm3||
||               || Kelvin  || Fraction || All    || H Only ||
|| H2            ||  14     || 1.000    || 0.076  || 0.076  ||
|| H2O (Ice)     || 273     || 0.111    || 0.916  || 0.102  ||
|| CH4           ||  91     || 0.250    || [[ https://pubchem.ncbi.nlm.nih.gov/compound/methane#section=Solubility | 0.415 ]] || 0.104 ||
|| CH4 Clathrate || 273     || 0.138    || 0.9    || 0.124  ||
|| LiH           || 962     || 0.126    || 0.78   || 0.098  ||
|| Polyethylene  || 400     || 0.14     || 0.9    || 0.126  ||

Of the materials above, the best are [[ PolyethyleneShield | polyethylene]] or clathrate ice (launched from Earth), or water ice (from the poles of the Moon).  Launch loops can launch polyethylene for less than $10/kg, but an expensive apogee kick motor is required to add angular momentum at apogee, and raise perigee above crowded LEO.

Another way to add angular momentum at perigee is to launch water pellets from the Moon into a "catcher" at apogee. Water is biologically useful, so it may be desirable for crew missions to Mars and beyond. Water in nutrient-lined polyethylene tanks may provide both radiation shielding and algae feedstock for food synthesis.

How can we extract and launch ice from the Moon?

Although ice has been detected on the Moon, it is unlikely to be pure.  Probably the first step is to use sunlight focused on moon-glass boilers to distill water out of a sand slurry, perhaps multiple distillation cycles to extract toxic impurities.