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

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.

• The paper introduces the terrascope concept by modeling atmospheric refraction to amplify starlight up to 45,000 times with a strategically placed 1-meter detector.
• The study uses numerical ray-tracing across various wavelengths to verify that aligning a space-based detector along the focal line minimizes atmospheric extinction and maximizes signal collection.
• The approach provides a cost-effective alternative to constructing massive telescopes by leveraging natural atmospheric properties for enhanced astronomical observations.

An Analytical Examination of Utilizing Earth's Atmosphere as a Refractive Lens: The Terrascope

The concept of using the Earth's atmosphere as a refractive lens, termed the "terrascope," presents a novel and cost-effective approach to enhancing astronomical observations. This paper by David Kipping explores the theoretical underpinnings and potential practicalities of leveraging the Earth's atmospheric refractive properties to amplify and focus starlight onto space-based detectors. This analysis offers a comprehensive look into the mathematical models and simulations supporting this intriguing proposal.

Theoretical Framework and Numerical Verification

The terrascope concept hinges on the understanding that Earth's atmosphere refracts starlight, particularly at an angle of just over one degree near the surface. The paper delineates how this refraction can be harnessed, focusing light into a focal line that begins at approximately 85% of the Earth-Moon separation. By strategically placing a space-based detector along this focal line, significant amplification of incoming starlight can be achieved. Kipping provides a thorough analytical exposition, using models to estimate the refracted light's behavior and subsequent amplification.

The numerical ray-tracing experiments conducted across wavelengths from optical to 30 μm confirm the theoretical refractive models. These experiments validate the proposed amplification of up to 45,000 for a 1-meter detector placed at the Hill radius. Adjustments accounting for extinction—both through a clear atmosphere and a cloudy one—reveal that positioning a detector within this radius minimizes the impact of atmospheric extinction, thus maximizing signal amplification.

Practical Implications and Observational Benefits

The terrascope offers a compelling alternative to the prohibitively expensive and technically challenging pathway of constructing ever-larger telescopes. Traditional telescope scaling laws imply that the cost increases quadratically with size, leading to astronomical fiscal requirements for future ground-based and space telescopes. In contrast, the terrascope stands as a naturally occurring solution that could mimic the performance of telescopes with apertures hundreds of meters in diameter while leveraging the existing atmospheric infrastructure.

This approach brings forth several observational advantages. For instance, it allows for a feasible way to achieve high photon collection rates without the need for physically massive lenses. Furthermore, the ability to place detectors at varying distances along the focal line enhances observational flexibility, accommodating different wavelengths and minimizing the influence of atmospheric scattering and cloud cover.

Considerations for Implementation

While the terrascope project offers promising avenues for cost-effective astronomical observations, several practical considerations must be addressed for its realization. Atmospheric stability remains a critical concern, as local variations in atmospheric pressure and temperature can influence refraction unpredictably. Moreover, the presence of both thermal and scattered radiance from the Earth poses potential challenges in maintaining clean observational conditions.

Kipping's paper also discusses various positioning strategies and configurations for the space-based detector, emphasizing the importance of optimizing the observational distance to enhance signal-to-noise ratios while minimizing atmospheric interference. Additional studies, particularly around handling atmospheric turbulence and pointing stability, are essential for refining these theoretical constructs into operational systems.

Conclusion and Future Directions

Kipping's exploration into the terrascope opens up new possibilities for astronomical instrumentation that efficiently utilizes Earth's atmospheric properties. The theoretical models are robust, and the numerical verifications provide a solid basis for considering this approach as a viable method of enhancing our observational capabilities. Future advancements in the terrascope's development could significantly impact astrophysics, providing an innovative pathway towards higher sensitivity observations without the extensive financial and technical overhead associated with constructing massive new telescopes. This concept beckons further exploration and experimental validation, potentially revolutionizing our approach to gathering photonic information from the universe.