The equations of motion for orbiting satellites refer to the satellite center of mass; this is the point whose motion reflects the dynamics that we are trying to interpret. The retroreflector arrays are on the exterior of the satellite, sometimes decimeters and even meters away, so a correction is required to extrapolate the laser range measurements to the satellite center of mass. This correction requires very careful engineering measurements, an understanding of the size and shape of the array, properties of the corner cubes, information on satellite orientation, and properties of the ground-based systems (pulse energy, pulse width, wavelength, receiver characteristics, etc.)
Some ground-based systems, typically those powerful enough to operate at multiphoton return levels, use detectors (e.g. photomultipliers) that "see" the entire return signal shape that is then discriminated at some level on the leading edge of the detection pulse to close the range measurement. These measurements are then in effect biassed towards the front of the satellite array, and the centre of mass correction will be relatively large.
Many of the newer ranging systems exploiting low-energy lasers use Single Photon Avalanche Photon Detectors (SPAD), which are sensitive to single photons within the returning pulse. Depending upon the return signal strength, measurements with these systems may either be biased towards the front of the satellites, or, for low-energy systems, may be based upon detections of photons randomly distributed within the whole return pulse. in this latter case, the centre of mass correction will be relatively small.
Satellite center of mass corrections must be available to treat the different configurations presently in use.
- Center of Mass Corrections
- Satellite Maneuver, Attitude, and Mass Histories
- System-dependent centre-of-mass corrections for spherical geodetic satellites
- Montenbruck, O., Schmid, R., Mercier, F., Steigenberger, P., Noll, C., Fatkulin, R., Kogure, S., Ganeshan, A.S., GNSS satellite geometry and attitude models, Advances in Space Research, DOI: http://dx.doi.org/10.1016/j.asr.2015.06.019, June, 2015.