# [time-nuts] Timing Distribution in Mountainous Terrain

Hal Murray hmurray at megapathdsl.net
Sat Sep 11 08:38:22 UTC 2010

```jimlux at earthlink.net said:
> I seem to recall that the returned beam divergence was no narrower than  the
> incident beam divergence, so if you want a X km footprint on Earth,  you
> need a X km footprint on the Moon.

Please let me know if you find that again.

I poked around on the web and can't find anything that confirms my impression
that they picked the size of the corner cubes to make sure the beam was large
enough to cover the telescope motion due to the Earth's rotation.  They are
made out of fused silica.  Thermal distortions are important.

There are arrays from Apollo 11, 14, and 15.  11 and 14 are 100 cubes in a
10x10 array.  15 is 3x bigger.  There is also an array of larger French cubes
on Lunokhod, a Russian rover.  There are brighter than Apollo 11 adn 14, even
though the total reflecting area is smaller.
http://www.physics.ucsd.edu/~tmurphy/apollo/lrrr.html
(That's at night.  During day, thermal distortion costs a factor of 30.)

This page says the beam is 7 km dia on the moon due to atmosphere and 20 km
back on the Earth due to diffraction.
http://www.lpi.usra.edu/lunar/missions/apollo/apollo_11/experiments/lrr/

Dickey et al, 1994 is a good review article.
http://www.physics.ucsd.edu/~tmurphy/apollo/doc/Dickey.pdf
http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/32452/1/94-0193.pdf
(The second looks like an early version of the paper.)

It confirms the beam diameters above.

My calculation for the motion due to the Earth's rotation while the beam is
in flight is 1or 2 km so 20 km easily covers that problem.  There is a
comment about correcting for something like the telescope not being in the
center of the beam.

Overall optical efficiency is about 1E-21.
At 10 pulses per second with 1E19 photons each pulse, that's 1 photon every
10 seconds.
A run is several hours.  (The numbers get better over time.)

In 1994, the RMS error was about 3 cm.

A French station is getting a lot of good data.

They have to consider solid tides and a zillion other details that I don't
understand.
(So add that one to the tides in solid rock list.)

The Earth-moon distance is increasing by about 3.8 cm per year.

I remember another story from long ago that one of the variables they had to
add to their model was the location of the telescope on the surface of the
Earth.  The data fit better with the telescope a mile down the road from
their coordinates from the USGS maps.  I don't know if they ever tracked that
down.

----------

There is a new Lunar Laser Ranging program called APOLLO.
Apache Point Observatory Lunar Laser-ranging Operation
http://www.physics.ucsd.edu/~tmurphy/apollo/apollo.html
They are aiming for mm precision.
They have a 3.5 meter telescope.

Good geek data (graphs) here:
http://www.physics.ucsd.edu/~tmurphy/apollo/first_range.html
(Other stuff is good too, AKA time sink warning.)

--
These are my opinions, not necessarily my employer's.  I hate spam.

```