effective lighting for moon (for a day night cycle)

Hello,

I am playing around with lighting and textures. I created a sun (directional light with nice coloring), and it rotates properly. I tried another direction light but it did not work. Therefore I am using the same directional light as the sun, but as soon as it goes down it rotates forward and comes up with a different color (for the moon). However I cant get the settings right. The color, the intensity, I dont know what it is. What settings on a directional light would be best for a moon.

what are some other options for creating a sun and moon to make a scene look nice? and as an extra, if it is possible could you point me to an example?