The “Terrascope”: On the Possibility of Using the Earth as an Atmospheric Lens
David Kipping
(Submitted on 1 Aug 2019)
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 WHΔ/R, yielding an amplification of 8HΔ/W, where HΔ 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 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 (Δmag=10.9) for W=1 metre, or equivalent to a 150 metre optical/infrared telescope.
Comments: Accepted in PASP
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Earth and Planetary Astrophysics (astro-ph.EP)
Cite as: arXiv:1908.00490 [astro-ph.IM] (or arXiv:1908.00490v1 [astro-ph.IM] for this version)
Submission history
From: David Kipping [view email]
[v1] Thu, 1 Aug 2019 16:26:25 UTC (5,222 KB)
