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MS 1 MINISYMPOSIUM: ADVANCED IMAGING FOR INDUSTRIAL APPLICATION Read chapter Read first chapter

2016 | Supplement | Chapter

Post-Newtonian Orbital Equations for Fermi Frames in the Vicinity the Earth

Authors : J. M. Gambi, M. L. García del Pino, M. M. Tung

Published in: Progress in Industrial Mathematics at ECMI 2014

Publisher: Springer International Publishing

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Abstract

Synge’s equations for time-like geodesics in terms of Fermi coordinates are used to derive post-Newtonian equations for the relative motion of satellites in coplanar circular near orbits about the earth. The reference frame, co-moving with the base satellite, is assumed to be a Fermi frame, that is, inertial guided. The resulting system is autonomous, linear, and reduces to the equation of the geodesic deviation for nearby satellites. Hence, it can be used by some Acquisition, Pointing, and Tracking systems to increase the accuracy presently reached in locating passive radio-transmitters.

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previous chapter Post-Newtonian Geolocation of Passive Radio Transmitters by TDOA and FDOA
next chapter MS 37 MINISYMPOSIUM: STRUCTURED NUMERICAL LINEAR ALGEBRA IN IMAGING AND MONUMENT CONSERVATION
Footnotes
1
For any two events in E, \(P_{1}(x^{k_{1}})\), \(P_{2}(x^{k_{2}})\), for which there is a unique geodesic \(\varGamma _{P_{1}P_{2}}\) joining them with equations x k = ξ k (u) where u is an affine parameter ranging from 0 to 1, the world-function Ω(P 1, P 2) is defined by the line integral
$$\displaystyle{ \varOmega (P_{1},P_{2}) =\varOmega (x^{k_{1}},x^{k_{2}}) = \frac{1} {2}\int _{0}^{1}g_{ ij}U^{i}U^{j}du }$$
taken along \(\varGamma _{P_{1}P_{2}}\) where \(x^{k_{1}} \equiv \xi ^{k}(0)\), \(x^{k_{2}} \equiv \xi ^{k}(1)\) and U k = dξ k ∕du.
 
Literature
1.
Guelma, M., Kogan, A., Kazarian, A., Livne, A., Orenstain, M., Michalik, H., Arnold, S.: Acquisition and pointing control for inter-satellite laser communications. IEEE Trans. Aerosp. Electron. Syst. 40(4), 1239–1248 (2004)CrossRef
2.
Norton, T., Conner, K., Covington, R., Ngo, H., Rink, C.: Development of reprogrammable high frame-rate detector devises for laser communication pointing, Acquisition and Tracking. IEEE Aerospace Conference Paper No. 1414 (2008). doi:10.​1109/​AERO.​2008.​4526342
3.
Gambi, J.M., Rodriguez-Teijeiro, M.C., Garcia del Pino, M.L.: The post-Newtonian Geolocation problem by TDOA. In: Progress in Industrial Mathematics at ECMI 2010, p. 489. Springer, Berlin/Heidelberg (2012)
4.
Synge, J.L.: Relativity: The General Theory, Chap. 2 North-Holland, New York (1960)
5.
Adamy, D.L.: EW 102: A Second Course in Electronic Warfare. Artech House Radar Library, Chap. 6, p. 169. Horizon House Pub. Inc., Boston (2004)
Metadata
Title
Post-Newtonian Orbital Equations for Fermi Frames in the Vicinity the Earth
Authors
J. M. Gambi
M. L. García del Pino
M. M. Tung
Copyright Year
2016
Book
Progress in Industrial Mathematics at ECMI 2014

Print ISBN: 978-3-319-23412-0

Electronic ISBN: 978-3-319-23413-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-23413-7_129

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