MATHEMATICAL MODELING OF CARGO DELIVERY OVER LONG DISTANCES USING LIGHT SAILS

Abstract

The article examines the prospects of using light sail technology for the delivery of cargo and satellites over long distances in outer space. The physical principles of the light and laser sail, based on the pressure of light created by the flow of photons, are considered. An analysis of the current state of development in this field, including real missions (NASA Cosmos-1, LightSail, JAXA IKAROS), was conducted, as well as the technical and economic challenges of implementing this technology in practical space missions were studied. The purpose of the research is mathematical modeling of the process of acceleration of the satellite with the help of pho- tons, determination of the main limitations and ways of increasing the efficiency of light sails. The article examines the features of sail design and materials for their manufacture (polyamide, graphene, and metallized coatings), as well as ways to reduce their weight without losing reflectivity. Mathematical dependences for determining the pressure of light, traction, acceleration of the device, time and energy consumption to achieve a speed of 0.1c are given. It is shown that with a total laser power of 100 MW, a 2 kg satellite can reach this speed in approximately 1045 days, and the required energy is ≈2.5 TWh. Special attention is paid to the economic aspects of the project: the cost of energy consumption, the construction of laser installations, the expediency of launching small satellites (nano-satellites) instead of large devices. Options for braking the interstellar vehicle and the possibility of creating mirror systems to reflect the laser beam from the opposite side of the trajectory are considered. The potential risks associated with dust and micrometeorites in space were analyzed and alternative solutions for the protection of the device were proposed, including the use of dispersive lenses instead of armor. Also presented is the concept of using heat from laser radiation to power ion engines that can perform trajectory correction. The study concluded that the technology of light sails can become the basis for the creation of interplanetary and interstellar transport systems. Under the condition of large-scale support, development of laser infrastructure and materials science, the formation of cosmic light highways for cargo transportation and scientific missions becomes possible. The technology combines environmental friendliness, low fuel consumption and high speed potential, which makes it one of the most promising areas of modern space logistics.