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, WH ∆/R, yielding an amplification of 8H ∆/W, where H ∆ 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 (∆mag = 10.9) for W = 1 m, or equivalent to a 150 m optical/infrared telescope.
Publications of the Astronomical Society of the Pacific
- Pub Date:
- November 2019
- Astrophysics - Instrumentation and Methods for Astrophysics;
- Astrophysics - Earth and Planetary Astrophysics
- Accepted in PASP