The “terrascope”: On the possibility of using the earth as an atmospheric lens

Abstract

Distant starlight passing through 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, 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 Earth (i.e., on-axis) showing that starlight is lensed into a thin circular ring of thickness, WHΔ/R, yielding an amplification of 8HΔ/W, where HΔ is 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, as lensed rays travel no deeper than 13.7 km, within the statosphere and above most clouds. Including extinction, a 1-m Hill radius “terrascope” is calculated to produce an amplification of ∼45,000 for a lensing timescale of ~20 hr. In practice, the amplification is likely halved to avoid daylight scattering i.e., 22,500 (Δmag = 10.9) for W = 1 m, or equivalent to a 150 m optical/infrared telescope.