How does the motion of the Moon relative to the Earth affect measurements of the distance between the Earth and the Moon using Lunar Laser Ranging (LLR)?
Here's how I have imagined the problem: A laser beam is fired from the surface of the Earth, and a clock is started in the Earth's frame of reference. When the beam reaches the Moon, it is instantly reflected back to the Earth by a mirror (I understand that the actual reflectors are more complex). The beam returns to Earth, and the arrival of the beam stops the clock on Earth.
It seems to me that since I am measuring the departure and return of the beam relative to the Earth's reference frame, and the beam is reflected directly, I can simply calculate the range to the Moon in the Earth's reference frame using
$R_{ange}= c*\frac{t_{total}}{2}$
I appreciate your patience as I work to develop a basic sense for special relativity.
Edit: Looks like what I've described is the radar metric, as referred to in this answer.
