Thermal-optical design of a geodetic satellite for one millimeter accuracy

The LAGEOS (LAser GEOdynamic Satellite) satellites use a 1.5 in. uncoated retroreflector (cube corner). Design studies done for LAGEOS-1 showed that using smaller cubes would result in greater accuracy and lower thermal gradients. However, this would require using a larger number of cubes. Simulations showed that the accuracy goal of 5 mm could be met using 1.5 in. cubes by adding a dihedral angle offset. The LARES (LAser RElativity Satellite) satellite launched in 2012 is a smaller version of LAGEOS using the same size cube corner and floating mount as LAGEOS.The recent development of COTS (Commercial Off-The-Shelf) cube corners has eliminated cost as an obstacle to using a larger number of smaller cubes. COTS cubes have no dihedral angle offset. However, no offset is needed if the size is chosen properly. The diffraction pattern of a 1.0 in. uncoated cube with no dihedral angle offset has 6 lobes around the central peak due to total internal reflection, The velocity aberration for LAGEOS is about 32–40 microradians. The OCS (Optical Cross Section) of a one inch uncoated COTS retroreflector is about 0.5 million sq m for the LAGEOS orbit.Testing of 10 inexpensive COTS cubes by Ludwig Grunwaldt and Reinhart Neubert shows good cross section (unpublished work done at GFZ Potsdam, Germany). Measurement of 50 COTS cubes at INFN (Mondaini et al., 2018), shows a loss of cross section of only 33% (Slide 10). Simulations show that systematic range errors on the order of a half millimeter are possible for a spherical geodetic satellite such as LARES. Adjustments for the holding and ejection system result in some loss of accuracy.