On the Possibility of Using the Earth as an Atmospheric Lens
Illustration of a detector of diameter W utilizing the terrascope. Two rays of different impact parameters, but the same wavelength, lens through the atmosphere and strike the detector. The ring formed by those two rays enables a calculation of the amplification. In this setup, the detector is precisely on-axis
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.
Read more at https://arxiv.org/pdf/1908.00490.pdf
Using Earth to See Across the Universe: The Terrascope with Dr. David Kipping:
Read also: “The Terrascope – Using Earth As A Lens“