[originally from October 12th, 2014]
Craziest lunar mission plan: fly a LOX/LH2 module with just enough fuel to land, and a lot of solar arrays, mine water on the moon, and use electrolysis to refuel.
Apollo ascent stage had 2,353kg of 290s fuel (http://en.wikipedia.org/wiki/Apollo_Lunar_Module#Ascent_stage). The specific impulse of LOX/LH2 is 451s (http://www.astronautix.com/props/loxlh2.htm), so they would only need 1,513kg of it – or, in ideal 2/16 mass ratio, 168kg of hydrogen, and 1344kg of oxygen.
Hydrogen in 2 kg/kmol, so it would be 84 kmol of H2. Under standard conditions of temperature and pressure (we’ll need this for estimating, not for storing it) it would take 22.414 * 84 = 1883 m3 (http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure#Molar_volume_of_a_gas). An industrial electrolyser (http://en.wikipedia.org/wiki/Electrolysis_of_water#Efficiency) consumes 10.6 MJ/m3 of H2 given 100% efficiency, and is, let’s say 65% efficient. Thus, they would need 3e10J of energy to produce that much fuel.
Very good solar arrays under ideal conditions (and lunar conditions are nearly perfect for solar arrays) can give 2.125 kW per kilogram (http://www.spacefuture.com/archive/early_commercial_demonstration_of_space_solar_power_using_ultra_lightweight_arrays.shtml).
Disregarding the mass of the electrolyser and water-mining equipment, as well as the time to find water and deploy the array (yes, that’s a very rough approximation), if instead of 2,353kg of fuel they brought 2,353kg of thin-film solar cells, THEY COULD HAVE MADE FUEL FOR THE WAY HOME IN 2 HOURS. Or they have brought just 180kg of solar cells, and made the fuel in the same 21 hours they actually spent on the Moon surface.
Even more fascinating is that all that equipment can be placed in the descent stage, which means if you wanna land on a spot nearby for the second time, you don’t even need to bring all that with you.