Light sail technology is one of the most promising methods for interstellar travel, having passed the stage of orbital testing. This work, for the first time and based on radiation dynamics, systematically investigates the influence of incident, mirror-reflected, and diffusely scattered light on a relativistic sail (moving at near-light speed). It is established that due to the Doppler effect, the thrust of all three components decreases with increasing speed: the strongest is from incident light, weaker from mirror reflection, and weakest from diffuse scattering. A critical speed exists for the thrust from scattered light: exceeding it turns this component into a drag force, although the total radiation force continues to accelerate the craft. Equations of motion were constructed and numerically solved; it is shown that the main speed increase is concentrated in the initial phase of acceleration, and as speed grows, efficiency drops. The study provides a rigorous theoretical foundation for light sail dynamics.
Humanity has long dreamed of interstellar travel. Light sails are one of the most promising technologies, having already undergone orbital tests (IKAROS, LightSail 2). However, when a probe accelerates to speeds comparable to the speed of light, relativistic effects kick in: time dilation and light aberration, which drastically change the dynamics. This is especially important for projects like Breakthrough Starshot, targeting the nearest exoplanets in the Alpha Centauri star system. Understanding how thrust behaves at near-light speeds is critically necessary for calculating realistic trajectories.
The authors applied the apparatus of radiation dynamics in flat spacetime, using the energy-momentum tensor of radiation and Lorentz transformations. Three components were modeled: incident light, specularly reflected (with reflection coefficient ξ), and diffusely scattered (one-sided Lambertian scattering model). The diffuse component was described by a tensor constructed via the 4-velocity and the normal to the sail surface. The equations of motion were solved numerically after introducing dimensionless time T (in units of characteristic acceleration time τ). For verification, analytical solutions were obtained in limiting cases (pure reflection and pure absorption). Maxwell predicted light pressure a century and a half ago, and now his theory serves as the basis for calculating forces at such speeds. The calculations took into account the relativistic photometric shift (change in energy flux density) and angular redistribution of photons.
Main result: the thrust force from each component decreases monotonically with increasing speed due to relativistic redshift. For a perfectly reflecting sail (ξ=1), the thrust is proportional to (1-β)/(1+β), where β=v/c. Diffuse scattering gives an even weaker contribution, and at β > 0.75 it changes sign and starts to decelerate the craft — the effect of light aberration: scattered photons go forward along the course. Nevertheless, the total radiation force remains accelerating. Numerical integration showed that a speed of 0.75c is reached in 5τ (characteristic times), after which the acceleration rate sharply slows. For typical parameters of an interstellar probe with a powerful laser source, this could correspond to several hours or days. An important nuance: the role of cosmic dust and electromagnetic forces has not yet been taken into account, but in a real flight they may introduce disturbances.
Practical conclusion for designers: it is necessary to minimize diffuse scattering and strive for specular reflection with ξ→1. This reduces energy losses to heating and increases efficiency. Understanding the critical speed of 0.75c allows for more precise mission profiling: after this threshold, the diffuse glow of the sail turns into a parasitic brake. Theoretically, the inclusion of spacetime curvature (general relativity) may slightly correct the result, but the main features are correct in the flat approximation. The work also confirms that even with an ideal sail, acceleration to ultra-relativistic speeds requires exponentially growing energy expenditure — the speed of light remains an asymptotic limit.
Future research should include three-dimensional sail orientation, variable area, and complex scattering models (e.g., two-sided emission, blackbody). Accounting for gravity of massive bodies and resistance of the interstellar medium (dust, gas) will allow building fully self-consistent trajectories. It is also interesting to consider quantum effects at extreme photon densities. In the future, such calculations will form the basis of engineering design for probes to exoplanets and possibly to stars like the Sun for studying the heliosphere.
The results will directly impact interstellar mission projects (Breakthrough Starshot) and solar sails for deep space exploration. The developed formalism can be adapted for analyzing any photon engines, including stabilization and maneuvering.
It is planned to generalize the model to the three-dimensional case with an arbitrary normal vector and variable area, as well as to include the effects of scattering on surface irregularities.
The fundamental problem of relativistic mechanics of bodies under radiation lies at the heart of creating interstellar probes. The work clarifies how different channels of light reflection limit maximum speed, and connects this with aberration and the Doppler effect — key to understanding momentum transfer at near-light speeds.
🎯 A solar sail the size of a football field and the mass of a postage stamp, illuminated by a megawatt laser, could accelerate to 20% of the speed of light in a matter of days. However, when its speed exceeds 75% of light, its own diffuse glow will start to 'blow' in the opposite direction.
🎬 The idea of interstellar sailcraft harks back to Arthur C. Clarke's story 'The Wind from the Sun' (1964), where heroes compete in solar sail races from Earth to the Moon. The modern Breakthrough Starshot project, using laser propulsion, embodies this fantasy on a technological level.