Analyzing the viability of satellite laser guide stars for breakthrough starshot

The Breakthrough Starshot team plans to launch ultra-lightweight nanocraft to Proxima Centauri at 20% the speed of light with the propulsion of a high-powered ground based laser at 1064 nm. The proposed laser projector’s aperture spans several kilometers and will require an adaptive optics (AO) pre-correction to properly focus through Earth’s turbulent atmosphere. To measure the turbulence induced aberration above the projector system we have suggested that the Doppler shifted return light from the nanocraft be used as a beacon. For this method to work, the return light must be separable from outgoing laser light that is Rayleigh scattered off the atmosphere. However, the craft’s speed during the first 30 seconds or so of launch will not be fast enough to impart an adequate frequency difference to the return light and thus another method of wavefront detection is required. This paper discusses the viability of using a nanocraft-releasing mothercraft satellite with an on-board laser guide star as a beacon for wavefront sensing. In order to assess if this beacon satellite would offer a viable wavefront sensing method, we explored orbital solutions that would keep the mothercraft within the isoplanatic angle of the nanocraft during the critical 30 second window. A parameterized astrodynamics model was created to track the angular separation of both objects in the sky as a function of time, arbitrary orbital parameters, and the laser’s radiation force vector. We found that for a sufficiently large orbital semi-major axis there exists an optimized orbital eccentricity which reduces the angular separation of the mothercraft and nanocraft in the sky to less than the isoplanatic angle during the first 30 seconds of launch. We also found that focal anisoplanatism was negligible during that period at the distance of the mothercraft’s apogee.