zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
GPS satellites orbits: resonance. (English) Zbl 1185.86023
Summary: The effects of perturbations due to resonant geopotential harmonics on the semimajor axis of GPS satellites are analyzed. For some GPS satellites, secular perturbations of about 4 m/day can be obtained by numerical integration of the Lagrange planetary equations considering in the disturbing potential the main secular resonant coefficients. Amplitudes for long-period terms due to resonant coefficients are also exhibited for some hypothetical satellites orbiting in the neighborhood of the GPS satellites orbits. The results are important to perform orbital maneuvers of GPS satellites such that they stay in their nominal orbits. Also, for the GPS satellites that are not active, the long-period effects due to the resonance must be taken into account in the surveillance of the orbital evolutions of such debris.

86A20Potentials, prospecting (geophysics)
86A30Geodesy, mapping problems
Full Text: DOI EuDML
[1] U. Hugentobler, “Astrometry and satellite orbits: theoretical consideration and typical applications,” Geodätisch-geophysikalische Arbeiten in der Schweiz, vol. 57, 1998.
[2] W. M. Kaula, Theory of Satellite Geodesy, Blaisdell, Waltham, Mass, USA, 1966. · Zbl 0973.86001
[3] G. Seeber, Satellite Geodesy: Foundations, Methods and Applications, Walter de Gruyter, Berlin, Germany, 2003.
[4] D. Ineichen, G. Beutler, and U. Hugentobler, “Sensitivity of GPS and GLONASS orbits with respect to resonant geopotential parameters,” Journal of Geodesy, vol. 77, no. 7-8, pp. 478-486, 2003. · doi:10.1007/s00190-003-0348-z
[5] D. Delikaraoglu, On Principles, Methods and Recent Advances in Studies Towards a GPS-Based Control System for Geodesy and Geodynamics, NASA Technical Memorandum 100716, Greenbelt, Md, USA, 1989.
[6] P. H. C. L. Lima Jr., Sistemas ressonantes a altas excentricidades no movimento de satélites artificiais, Doctoral thesis, ITA, São José dos Campos, 1998.
[7] P. H. C. L. Lima Jr., R. Vilhena de Moraes, and S. S. Fernandes, “Semi analytical method to study geopotential perturbations conssidering high eccentric resonant orbits,” in Dinamics of Natural and Artificial Celestial Bodies, H. Pretka-Ziomek, E. Wnuk, P. K. Seidelmann, and D. Richardson, Eds., pp. 407-413, Kluwer, Dordrecht, The Netherlands, 2001.
[8] J. K. S. Formiga, Study of resonances in the orbital motion of artificial satellites, Master dissertation, Faculdade de Engenharia do Campus de Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá, Brazil, 2005.
[9] R. Vilhena de Moraes, J. K. S. Formiga, P. H. C. L. Lima Jr., and H. K. Kuga, “Orbital perturbations: resonance effects,” in Proceedings of 6th International Symposium of the IAA on Small Satellites for Earth Observation, p. 8, Berlin, Germany, April 2007, paper IAA-B6-0717P.