Lunar Prediction Software
For every shot we send to the moon, we want to know precisely when the return should appear so that we may turn on the APD for approximately 100 ns at the right time. Given that we would like to land in the same part of the gate each time, we would like to have the prediction good to a few nanoseconds. Each nanosecond of round-trip delay corresponds to 15 cm of radial displacement of the moon. So we are looking for sub-meter predictive ability.
The way I envision this working is rather than re-computing the lunar position for each laser shot (20 times a second), we will generate a suitable polynomial at the beginning of the observation with enough terms to hold us for a few hours. Then it becomes a simple computation per event.
But the polynomial must be based on a very precise calculation. The primary avenue for this is the JPL lunar ephemeris, which claims few-cm precision based on—you guessed it—lunar laser ranging. For an input time (in ephemeris time, presumably), the JPL ephemeris will spit out the XYZ positions of the moon and earth, as well as their first time derivatives (velocities). The ephemeris also presents nutation and libration information. Combined with information on earth orientation (UT1, polar motion), we should be able to convert the center-to-center separation to a site-to-site separation.
But we may not need to re-invent the wheel entirely. Randy Ricklefs at the University of Texas has nailed the lunar prediction for McDonald, and is extending prediction software for arbitrary stations. We will likely be able to sweep up this product and use it out of the box. Priority on this front should be to contact Randy and see where he is on this.
Nonetheless, it would be useful to develop a more rudimentary version based on the JPL ephemeris in order to understand the process and have something against which to compare Randy's prediction.