[time-nuts] Timing Distribution in Mountainous Terrain

jimlux jimlux at earthlink.net
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.

http://www.physics.ucsd.edu/~tmurphy/apollo/apollo.html talks about "few 

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 

In other parts of that site, they say that getting cm scale precision 
requires about 10 photons..

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