In short, the dust that covers the moon’s surface is a fairly good reflector of light.
So the light you’re seeing is not necessarily “the color of the moon”, rather it’s the “color of light after being bounced off the moon”.
Think about this, if you had an (insanely strong) blue flashlight, and shone it at the moon, would you expect the moon to look the color of the moon (dark grey) or would you expect it to look somewhat blue?
What’s the difference between white and gray?
Gray is darker, of course. Otherwise they appear the same.
So what if you see an object on its own, with nothing around it. It’s the brightest thing around, by far. It’s either white or gray. How do you know which?
You don’t, plain and simple. The moon looks white because it’s the brightest thing around. It’s being lit by the sun but nothing else is and it’s surrounded by much darker space.
Gray isn’t really a color it’s a mix of white (all colors) and black (no color/light). Gray is just dark white. The only light that is reflecting back to us is white light. the biggest reason the moon looks white is because the sky looks black. Think of the “which gray square is lighter” optical illusions.
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