# The "Terrascope": On the Possibility of Using the Earth as an Atmospheric Lens

## TL;DR

This paper explores the concept of using Earth's atmosphere as a natural lens for distant starlight, proposing a 'terrascope' detector placed near the Hill radius to achieve significant amplification of signals.

## Contribution

It introduces a novel idea of Earth's atmosphere acting as a lens and provides analytic and numerical estimates for a potential Earth-based or orbital detector's performance.

## Key findings

- Focal line begins at ~85% of Earth-Moon distance.
- A 1-meter Hill radius terrascope could achieve amplification of ~45,000.
- Extinction effects are minimized at the Hill radius, enhancing detection capability.

## 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 $W H_{\Delta}/R$, yielding an amplification of $8 H_{\Delta}/W$, where $H_{\Delta}$ 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 ($\Delta$mag=10.9) for $W=$1 metre, or equivalent to a 150 metre optical/infrared telescope.