On the Problem of Optimizing the Orbital Formation of Multi-Tiered Satellite Constellations for Continuous Near-Earth Space Coverage

The development of methods for the design of satellite constellations for continuous coverage is reviewed in this paper. The main notions and definitions involved in solving the problem of multifold continuous coverage of Earth and near-Earth space are described. The region to be observed is represented by a spherical layer, with the problem of continuous L-fold coverage of the layer reduced to continuous no-less-than-L-fold coverage of each of its spheres by the coverage areas. The mathematical setting and methodological principles for solving the problem of optimizing the orbital formation of multi-tiered satellite constellations for continuous coverage of near-Earth space are examined. The location of this problem in the general scheme of ballistic substantiation of space system design is indicated. A methodological solution pattern for optimizing the orbital formation of satellite constellations for continuous multifold coverage of near-Earth space within the class of kinematically regular mono-structures is proposed. It is shown that the solution of these constellation optimization problems is reduced to obtaining α-parameters of the systems and optimizing them for inclination, where the α-parameter is understood to be the minimal angular radius of the coverage areas that provide continuous L-fold coverage of the sphere.

References

[1] Walker J.G. Satellite Constellations. Journal of the British Interplanetary Society, 1984, vol. 24, pp. 369–384.

[2] Ballard A.H. Rosette constellations of Earth satellites. Aerospace and electronic systems, 1980, vol. 16, no. 5, pp.

[3] Mozhaev G.V. Zadacha o nepreryvnom obzore Zemli i kinematicheski pravil’nye sputnikovye sistemy. I [The problem of continuous review of Earth and kinematically correct satellite system. I]. Kosmicheskie issledovaniia [Cosmic Research]. 1972, vol. 10, is. 6, pp. 833–840.

[4] Mozhaev G.V. Zadacha o nepreryvnom obzore Zemli i kinematicheski pravil’nye sputnikovye sistemy. II [The problem of continuous review of Earth and kinematically correct satellite system. II]. Kosmicheskie issledovaniia [Cosmic Research]. 1973, vol. 11, is. 1, pp. 59–69.

[5] Mozhaev G.V. Sintez orbital’nykh struktur sputnikovykh sistem (teoretiko-gruppovoi podkhod) [The synthesis of the orbital structures of satellite systems (group-theoretic approach)]. Moscow, Mashinostroenie publ., 1989. 304 p.

[6] Mozhaev G.V. Capabilities of kinematically regular satellite systems with symmetry groups of the second type in the problem of continuous single coverage of the earth. Cosmic Research, 2005, vol. 43, no. 3, pp. 205–212.

[7] Mozhaev G.V. Problemy optimizatsii dvizheniia sputnikovykh sistem: sostoianie issledovanii i perspektivy [Problems of optimization of satellite systems motion: state of research and perspectives]. Trudy MAI [Proceedings of MAI]. 2009, is. 34. Available at: http://trudymai.ru/upload/iblock/a1c/problemy-optimizatsii-dvizheniya-sputnikovykh-sistem-sostoyanie-issledovaniy-i-perspektivy.pdf (accessed 14 December 2017).

[8] Lang T.J. Symmetric circular orbit satellite constellations for continuous global coverage. Astrodynamics 1987: Proceedings of the AAS/AIAA Astrodynamics Conference, Kalispell, 1987, no. 87-499, 12 p.

[9] Lang T.J. Optimal low earth orbit constellations for continuous global coverage. AAS/AIAA Astrodynamics Specialist Conference, 1993, Victoria, BC, Aug. 16–19 1993, no. 597, 17 p.

[10] Lang T.J. A Parametric Examination of Satellite Constellations to Minimize Revisit Time for Low Earth Orbits Using a Genetic Algorithm. AAS/AIAA Astrodynamics Specialist Conference, Quebec, Canada, 30 July–2 August 2001, vol. 109, pp. 625–640.

[11] Lang T.J. Walker Constellations to Minimize Revisit Time in Low Earth Orbit. 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico, 9–13 February, 2003, paper AAS 03-178.

[12] Razoumny Yu.N. Fundamentals of the Route Theory for Satellite Constellation Design for Earth Discontinuous Coverage. Part 1: Analytic Emulation of the Earth Coverage. Acta Astronautica, 2016, vol. 128, pp. 722–740.

[13] Razoumny Yu.N. Fundamentals of the Route Theory for Satellite Constellation Design for Earth Discontinuous Coverage. Part 2: Synthesis of Satellite Orbits and Constellations. Acta Astronautica, 2016, vol. 128, pp. 741–758.

[14] Razoumny Yu.N. Fundamentals of the Route Theory for Satellite Constellation Design for Earth Discontinuous Coverage. Part 3: Low-Cost Earth Observation with Minimal Satellite Swath. Acta Astronautica, 2016, vol. 129, pp. 447–458.

[15] Razoumny Yu.N. Fundamentals of the Route Theory for Satellite Constellation Design for Earth Discontinuous Coverage. Part 4: Compound Satellite Structures on Orbits with Synchronized Nodal Regression. Acta Astronautica, 2016, vol. 129, pp. 459–465.

[16] Razumnyi Iu.N. Mashinostroenie. Entsiklopediia. Tom 4-22. Raketno-kosmicheskaia tekhnika. Kniga 1 [Engineering. Encyclopedia. Volume 4-22. Rocket and space technology. B. 1]. Moscow, Mashinostroenie publ., 2012, pp. 180–225.