Quote Originally Posted by banana
Your eyes are detecting photons that are coming from the moon.
Sure, but some of those photons hit you and deflect back to the moon. Some photons that didn't originate from the moon and wouldn't have gone there if you hadn't looked at it are now deflected in that direction. By looking at the moon, you're changing the initial conditions that existed before you looked at the moon. Just changing your posture changes your gravitational relationship with the moon. In fact standing perfectly still won't help, even if you could, because the moon is moving, so is the earth, so your gravitational relationship with the moon is constantly changing.

Observation is interaction, and interaction changes the initial conditions.