Relativistic Light Sails (1704.04310v3)

Abstract: One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light towards Proxima Centauri. For such a case, the combination of the sail's low mass and relativistic velocity render previous treatments formally incorrect, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail's acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail's motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this 'principle of ensemble equivalence' for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail's velocity curve. Using our results and adopting putative parameters for Starshot, we estimate that previous relativistic treatments underestimate the spacecraft's terminal velocity by ~50m/s for the same incident energy, sufficient to miss a target by several Earth radii. Additionally, we use a simple model to predict the sail's temperature and diffraction beam losses during the laser firing period, allowing us to estimate that for firing times of a few minutes and operating temperatures below 300C (573K), Starshot will require a sail of which absorbs less than 1 in 260,000 photons.

• The paper presents a refined analytical framework for calculating relativistic light sail velocity changes, correcting errors in previous treatments by considering finite sail mass.
• A key finding is the principle of ensemble equivalence, simplifying calculations by treating numerous photons as a single equivalent photon for predicting sail response at relativistic velocities.
• Thermal analysis shows that minimizing heat absorption is critical, requiring sail materials to absorb fewer than one in 260,000 photons to stay below 300°C during acceleration.

Overview of "Relativistic Light Sails"

The research paper, authored by David Kipping, addresses the dynamics of relativistic light sails, primarily in the context of interstellar travel initiatives like the Breakthrough Starshot project. The work presents an analytical framework for calculating the velocity changes and thermal effects of a sail accelerated by light to relativistic speeds. The conclusions challenge some classical treatments and offer new insights relevant to the development of high-speed spacecraft.

Acceleration of Light Sails

The paper contributes substantial advancements in the understanding of the physics behind relativistic light sails. It provides a comprehensive derivation of the equation governing the velocity change of a light sail, which experiences a push due to photon reflections. Unique to this paper is the correction of previous relativistic treatments that fall short, particularly the work originating from Einstein, which wrongly assumes an infinite mass for the sail. Kipping’s formulation considers finite mass, leading to adjustments in predicted speeds up to an error of approximately 50 m/s for the target speed of 0.2c, significant enough to alter interstellar targeting.

A particularly noteworthy result in the paper is the "principle of ensemble equivalence," which states that the combined effect of numerous photons can be treated as a single photon of equivalent total energy. This principle offers a simplification for understanding and predicting a sail's response, facilitating more straightforward calculations for relativistic velocities. This approach is analytically verified for both perfect and less-than-perfect reflection scenarios, thus broadening its applicability.

Thermal Effects on the Sail

Another significant portion of the paper explores thermal considerations, addressing the heat absorption by the sail during operation. Remarkable is the analysis showing that even slight imperfections in reflectivity necessitate a longer laser firing duration to prevent overheating. Using equations derived in the paper, Kipping predicts that to keep the sail's temperature below 300°C, the material must absorb fewer than one in 260,000 photons.

Thermal computations consider real-world challenges, such as achieving and maintaining low absorptivity with current or near-future material technologies. The accurate modeling of thermal effects ensures that the designs for a practical light sail include robust systems for dissipating and managing heat loads, securing both the structural integrity of the sail and the on-board electronics.

Implications and Future Research

The findings from this research have substantial implications for the practical design and deployment of light sails. Kipping's work suggests that careful consideration of the relativistic dynamics and thermal management is crucial in optimally designing light sails for projects like Starshot.

Practically, the paper emphasizes the need for sails to be constructed from materials with both high reflectance and low absorption to minimize energy losses and thermal impact. The theoretical framework offers potential pathways for enhancing the velocity predictions previously considered in error, ensuring future missions can achieve higher accuracy in targeting.

Theoretically, this research opens avenues for further paper in relativistic physics, suggesting the need to reassess other systems where classical assumptions might break down at high velocities. The mathematical approaches and principles derived here lay the groundwork for further exploration, potentially impacting fields related to photon propulsion and beyond.

In conclusion, David Kipping's paper on relativistic light sails presents critical revisions to classical views and offers advanced tools for engineers and physicists working in interstellar propulsion. By re-evaluating established assumptions, this work not only enhances scientific understanding but also plays a pivotal role in shaping the technological future of space exploration.