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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 84–95 | Cite as

Collecting solar power by formation flying systems around a geostationary point

  • F. J. T. SalazarEmail author
  • O. C. Winter
  • C. R. McInnes
Article

Abstract

Terrestrial solar power is severely limited by the diurnal day–night cycle. To overcome these limitations, a Solar Power Satellite (SPS) system, consisting of a space mirror and a microwave energy generator-transmitter in formation, is presented. The microwave transmitting satellite (MTS) is placed on a planar orbit about a geostationary point (GEO point) in the Earth’s equatorial plane, and the space mirror uses the solar pressure to achieve orbits about GEO point, separated from the planar orbit, and reflecting the sunlight to the MTS, which will transmit energy to an Earth-receiving antenna. Previous studies have shown the existence of a family of displaced periodic orbits above or below the Earth’s equatorial plane. In these studies, the sun-line direction is assumed to be in the Earth’s equatorial plane (equinoxes), and at \(23.5^{\circ }\) below or above the Earth’s equatorial plane (solstices), i.e. depending on the season, the sun-line moves in the Earth’s equatorial plane and above or below the Earth’s equatorial plane. In this work, the position of the Sun is approximated by a rectangular equatorial coordinates, assuming a mean inclination of Earth’s equator with respect to the ecliptic equal to \(23.5^{\circ }\). It is shown that a linear approximation of the motion about the GEO point yields bounded orbits for the SPS system in the Earth–satellite two-body problem, taking into account the effects of solar radiation pressure. The space mirror orientation satisfies the law of reflection to redirect the sunlight to the MTS. Additionally, a MTS on a common geostationary orbit (GEO) has been also considered to reduce the relative distance in the formation flying Solar Power Satellite (FF-SPS).

Keywords

Solar Power Satellite system Formation flying Microwave transmitting satellite Geostationary point Two-body problem Solar radiation pressure 

Mathematics Subject Classification

70M20 

Notes

Acknowledgements

First, authors thank the financial support of the FAPESP (São Paulo Research Foundation, Brazil), Grants 2011/08171-3, 2013/03233-6 and the CNPq (National Council for Scientific and Technological Development, Brazil), and the technical support of University of Glasgow. C.R.M. was support by an Engineering and Physics Research Council (EPSRC) Institutional Sponsorship Grant and a Royal Society Wolfson Research Merit Award.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.UNESP-Grupo de Dinâmica Orbital e PlanetologiaGuaratinguetáBrazil
  2. 2.School of EngineeringUniversity of GlasgowGlasgowUK

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