Caelum is a small mod that aims to improve the way celestial objects work in Minecraft. As of now, it changes the Moon's movement so it actually moves across the sky - relative to the sun, making lunar phases actually possible. Furthermore, it allows you to change how long the lunar month is, affecting how long the lunar phases last (which should affect Slime spawning in swamps).
After installing the mod you can just start the game and play. You can also change the length of the lunar cycle and the likelihood of lunar eclipses in the server config file (caelum-server.toml - located in the save folder).
Q: Is it compatible with X?
A: It should be compatible with pretty much all mods that don't change the sky rendering. (That, unfortunately, means that mods like Optifine are out of the question - the game runs fine with them, but the Moon is not in the correct position make the whole mod pointless)
Q: Will you add solar eclipses?
A: I sure would like to add them (and possibly some other things) in the future!
Q: Will you port the mod to Fabric?
A: I might do it at some point, but definitely not anytime soon.