# Representation of light pressure resultant force and moment as a tensor series

## TL;DR

This paper introduces a tensor series approach using Chebyshev polynomials to accurately model light pressure forces and moments on complex space structures, accounting for shadowing and reflections.

## Contribution

It presents a novel tensor series method for calculating light pressure on complex geometries, including self-shadowing and reflection effects, with applications to space structures like solar sails.

## Key findings

- Derived tensor-based expressions for light pressure forces and moments.
- Validated the approach on flat, spherical, cylindrical bodies, and a space observatory.
- Enabled improved analysis of space structure dynamics under radiation pressure.

## Abstract

In this article we address a problem of determination of light pressure upon space structures of the complex geometric shape. For the surface element, we wrote a condition that this element can interact with light only from the front side, not from the back side. This condition To in the form of series of Chebyshev polynomials of the first kind. Chebyshev expansion lets us move to the series of tensors of increasing rank for the problem of determination of force and moment. We obtained expressions for the fiber method for determination of light pressure on space structures of complex geometry taking into account self--shadowing and reflections within the structure. We also give the expressions for tensor parametrization by the specularity coefficient in case of specular-diffuse reflection. For these expressions we calculated the principal moment and force upon two-sided flat solar sail, spherical and cylindrical bodies, and approximated light pressure upon a perspective space observatory Millimetron. The proposed expressions can be used in the ballistic analysis of solar sails and other space objects, which are significantly affected by the radiation pressure. Also, these results can be used to analyze the dynamics of movement of large-scale space structures around the center of gravity under the light pressure.