Astronomer David Kipping proposes using the Earth’s atmosphere as the lens for an enormous space-based telescope.
Distant starlight passing through the Earth’s atmosphere is refracted by an angle of just over one degree near the surface. This focuses light onto a focal line starting at an inner (and chromatic)boundary out to infinity – offering an opportunity for pronounced lensing. It is shown here that the focal line commences at ?85% of the Earth-Moon separation, and thus placing an orbiting detector between here and one Hill radius could exploit this refractive lens. Analytic estimates are derived for a source directly behind the Earth (i.e. on-axis) showing that starlight is lensed into a thin circular ring of thickness W H?/R, yielding an amplification of 8H?/W, where H? is the Earth’s refractive scale height, R is its geopotential radius and W is the detector diameter. These estimates are verified through numerical ray-tracing experiments from optical to 30 µm light with standard atmospheric models. The numerical experiments are extended to include extinction from both a clear atmosphere and one with clouds. It is found that a detector at one Hill radius is least affected by extinction since lensed rays travel no deeper than 13.7 km, within the statosphere and above most clouds. Including extinction, a 1 metre Hill radius “terrascope” is calculated to produce an amplification of ?45, 000 for a lensing timescale of ?20 hours. In practice, the amplification is likely halved in order to avoid daylight scattering i.e. 22, 500 (?mag=10.9) for W =1 m, or equivalent to a 150 m optical/infrared telescope.