Covering a sphere with retroreflectors

One of the future missions for Mars involves returning a soil sample from the Martian surface to Earth. The sample will be deposited in a spherical canister, shot into Mar´s orbit and then subsequently captured by a spacecraft for the return journey. This paper discusses how retroreflectors can be placed on the orbiting sample canister with the objective of maximizing returned light from a scanning laser system. The retroreflectors are vital for acquisition of the sample canister during the terminal rendezvous phase (<5 km) of the capture. The identification of a retroreflector configuration relies extensively on Monte Carlo simulations. Computer simulations show that a spherical t-design yields a strong return for a 50 retroreflectors constellation. The return is calculated utilizing formulas for Rayleigh-Sommerfeld diffraction, and integrating over the surfaces of the retroreflector apertures for the specific orientation of the spherical container. At a distance of 5 km, in simulation the chosen configuration produces a return signal that is at least 5% of the return of a single retroreflector head-on approximately 99.99% of the time. On average, the return signal is 1.36 times the signal of a single retroreflector head-on. The results of the model and empirical results collected at a shorter distance are consistent