# [time-nuts] Timing Distribution in Mountainous Terrain

Fri Sep 10 18:42:42 UTC 2010

```Stanley Reynolds wrote:
> On the crazy side another common view object is the lunar laser ranging
> retroreflector array. Has been improvements in cost of lasers and telescopes in
> the past 41 years and it doesn't appear to be headed for shutdown anytime soon.
>

Hmm.. the SNR isn't all that huge on the echo. The target is say, 1
square meter, at a distance of 300,000 km.

The beam divergence coming back is about the same as the outbound
(that is, in order to cover 300km on earth, you need to have a spot on
the moon about 300km in diameter).. So the laser power will be spread
out by a factor of 71E9.. (about 110 dB). The power reflected back, if
intercepted by a 1 square meter aperture will have the same "loss"  for
a round trip loss of around 220dB.

Radiate 10 Watts, and you're seeing -210dBW coming back.. That's going
to be tough to detect. Just how many photons/second is that? And what's
the dark current/shot noise of your detector (a PM tube, presumably)

The first experiments with the Apollo 11 reflector were done with the
3.1m antenna at the Lick observatory.. that's a pretty big telescope.
The work at the McDonald observatory used almost as big a telescope, but
did provide ranging to 1 cm, which is 0.03 ns...

If we make the assumption that a degradation in position accuracy to 10m
requires 1/10,000 the power.. that would imply you could use a telescope
with 1/100th the area, or about 1/10th the diameter.. that's in the
reasonable range..30-45 cm aperture is an off the shelf commodity item.

picoseconds"...

they use a pulsed laser with a few watts average power 115mJ/pulse at
20Hz with a 3.5 meter telescope making a 1.8 km spot on the moon.  For
common view sync, you need to have the spot bigger, as mentioned above,
which is nice, because it means you don't need as big a telescope to
collimate the beam.
(interestingly, they use a XL-DC GPS disciplined oscillator as their
reference)

In other parts of that site, they say that getting cm scale precision