The "Terrascope": On the Possibility of Using the Earth as an Atmospheric Lens
arXiv:1908.00490 · doi:10.1088/1538-3873/ab33c0
Abstract
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 , yielding an amplification of , where is the Earth's refractive scale height, is its geopotential radius and is the detector diameter. These estimates are verified through numerical ray-tracing experiments from optical to 30 micron 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 stratosphere 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 1 metre, or equivalent to a 150 metre optical/infrared telescope.
Accepted in PASP