I feel so lonely and unloved. Nobody thinks to ask me this stuff. *sniff*
On a bright night, ie. the moon is big and it's relatively clear. You can see something like this.
It's the reflection of the moon off of the earth, and reflected back to you in the airplane. It appears to move fast because you are moving fast, and even though your perception is changing because you are moving there is still plenty of moonlight to reflect back up to you. Moonlight is everywhere, not just where you perceive it to be at that particular moment.
It is especially noticeable over water, for example, during the flooding in Tennessee recently, you can really see how much water was down there by seeing the light reflected back to you from the moon.
I hope this is what you were looking for, I have experienced what you have described before.