Celestial Mechanics and Dynamical Astronomy

, Volume 128, Issue 4, pp 483–513 | Cite as

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

  • Nikolay NerovnyEmail author
  • Vladimir Zimin
  • Sergey Fedorchuk
  • Evgeny Golubev
Original Article


In this article, we address the problem of the determination of light pressure upon space structures with a complex geometric shape. For each surface element, we enforce a condition that it can interact with light only from its front side, a condition represented in the form of series of Chebyshev polynomials of the first kind. This Chebyshev expansion enables the use of a series of tensors of increasing rank for determination of the force and moment acting on the sail. We obtain expressions for the 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 using 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 the proposed space-based observatory Millimetron. The proposed expressions can be used in the ballistic analysis of solar sails and other space objects significantly affected by radiation pressure. Also, these results can be used to analyze the dynamics of large-scale space structures around their center of gravity under light pressure.


Solar sail Light pressure Resultant force Resultant moment SRP Millimetron 



Authors would like to thank assistant professor Marchevsky I.K. from department “Applied Mathematics” of BMSTU, assistant Kotsur O.S. from department “Aerospace Systems” of BMSTU, and assistant Goncharov D.A. from department “Theoretical Mechanics” of BMSTU for their valuable advice and discussions which led to the creation of the explained method.


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Bauman Moscow State Technical UniversityMoscowRussian Federation
  2. 2.Astro Space Center of P.N. Lebedev Physical InstituteMoscowRussian Federation

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