I'm doing an Astronomy project and need to terraform a moon. It is about the size of Mars and orbits a gas giant which is at a distance of 1.28 AU of its star. I though about putting a sunshade at the Lagrange point L1 between the planet and the star, but I don't think that would be consistently cooling the moon (by about 30K). For the purpose of this project, it's surface is mostly water, and the atmosphere is mostly water vapor. Any ideas how to tackle this problem? Any way to raise the albedo, or maybe getting a sunshade to work? Be it at a Lagrange point or in orbit around the moon? I still want to do this project by myself, I could just use an idea or two, maybe some initial help with the calculations. Thanks in advance :)
Assuming the major heat input is from the star (the gas giant may also radiate significant IR) then you could seed clouds or freeze the water in order to increase the albedo.
Alternatively, you could increase the radiative efficiency by somehow painting the side of the moon facing away from the star black. Tricky, as no doubt this hemisphere changes with time quite rapidly.
If tidal heating from the gas giant is significant then you need to get the moon into a wider orbit!
The sunshade at the L1 point idea is widely discussed. Usually it is lenses that are considered, to avoid big problems with radiation pressure. I'm sure you could calculate some appropriate numbers to block a certain percentage of light in your system.