≈5 arcseconds typical for the previous McDonald Lunar Ranging Station (MLRS). The better seeing helps two ways—it both increases the laser beam intensity on the Moon and reduces the lunar background, since a smaller receiver field-of-view may be used, gathering light from a smaller spot on the Moon. Both effects scale as the inverse square of the seeing, so that the signal-to-noise ratio of the lunar return is inversely proportional to the fourth power of the seeing. APOLLO should therefore gain about 20 (from the bigger telescope) × 25 (for better seeing) = 500 × in return signal strength over MLRS, and additional factor of 25 in signal-to-noise (from fewer stray photons interfering with the desired ones). Likewise APOLLO should get a signal about 50 times stronger than the OCA LLR facility, which has a 1.5 m telescope and seeing of about 3 arcsec. The increased optical gain brings some problems due to the possibility of getting more than one returned photon per pulse. The most novel component of the APOLLO system is the integrated array of Single-Photon Avalanche Diodes (SPADs) used in the detector. This technology is needed to deal with multiple photon returns within each pulse. Most single photon detectors suffer from "dead time": they cannot detect a photon if it arrives soon after another. This means that if more than one photon comes back in a single pulse, a conventional single-photon detector would only record the arrival time of the first photon. However, the important quantity is the centroid of the time of all returned photons (assuming the pulse and reflectors are symmetrical), so any system that can return multiple photons per pulse must record the arrival times of each photon. In APOLLO, the incoming photons are spread over an array of independent detectors, which reduces the chance that two or more photons hit any one of the detectors. Modeling station locations Any laser ranging station, APOLLO included, measures the transit time, and hence the distance, from the telescope to the reflector(s). But for lunar ranging science, what is really wanted is the distance between the center of mass of the Earth and the center of mass of the Moon. To do this, the positions of the telescope, and the reflectors, must be known to comparable precision (a few mm). Since both the telescope and the reflectors are stationary structures, it might seem they could be precisely