Abstract
Satellites are attracted not only by the central force of the earth, but also by the non-central force, the attraction forces of the sun and the moon, and the drag force of the atmosphere. They are also affected by solar radiation pressure, earth and ocean tides, general relativity effects (cf. Chap. 5), and coordinate perturbations. Equations of satellite motion must be represented by perturbed equations. In this chapter, after discussions of the perturbed equations of motion and the attraction forces, for convenience of the earth tide and ocean loading tide computations, the ephemerides of the sun and the moon are described. Orbit correction is discussed based on an analysis solution of the \( \overline{C}_{20} \) perturbation. Emphasis is given to the precise orbit determination, which includes the principle of orbit determination , algebraic solution of the variation equation, numerical integration, and interpolation algorithms, as well as the related partial derivatives .
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bate RR, Mueller DD, White JE (1971) Fundamentals of astrodynamics. Dover, New York.
Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modelling techniques at the CODE Processing Center of the IGS: Theory and initial results. Manuscr Geodaet 19:367–386.
Brouwer D, Clemence GM (1961) Methods of celestial mechanics. Academic Press, New York.
Cappellari JO (1976) Mathematical theory of the Goddard trajectory determination system.
Cui C (1990) Die Bewegung künstlicher Satelliten im anisotropen Gravitationsfeld einer gleichmässig rotierenden starren Modellerde. Deutsche Geodätische Kommission, Reihe C: Dissertationen, Heft Nr. 357.
Dow JM (1988) Ocean tides and tectonic plate motions from Lageos. Deutsche Geodätische Kommission, Rheihe C, Dissertation, Heft Nr. 344.
Fliegel HF, Gallini TE, Swift ER (1992) Global Positioning System radiation force model for geodetic applications. J Geophys Res 97(B1):559–568.
Heiskanen WA, Moritz H (1967) Physical geodesy. W. H. Freeman, San Francisco/ London.
Herrick S (1972) Astrodynamics, Vol. II. Van Nostrand Reinhold, London.
Kang Z (1998) Präzise Bahnbestimmung niedrigfliegender Satelliten mittels GPS und die Nutzung für die globale Schwerefeldmodellierung. Scientific Technical Report STR 98/25, GeoForschungsZentrum (GFZ) Potsdam.
Kaula WM (1966, 2001) Theory of satellite geodesy. Blaisdell Publishing Company, Dover Publications, New York.
Knudsen P, Andersen O, Khan SA, Hoeyer JL (2000) Ocean tide effects on GRACE gravimetry. IAG Symposia.
Liu L, Zhao D (1979) Orbit theory of the Earth satellite. Nanjing University Press, (in Chinese).
Liu DJ, Shi YM, Guo JJ (1996) Principle of GPS and its data processing. TongJi University Press, Shanghai, (in Chinese).
McCarthy DD (1996) International Earth Rotation Service. IERS conventions, Paris, 95 pp. IERS Technical Note No. 21.
Meeus J (1992) Astronomische Algorithmen. Johann Ambrosius Barth.
Melchior P (1978) The tides of the planet Earth. Pergamon Press.
Montenbruck O (1989) Practical Ephemeris calculations. Springer-Verlag, Heidelberg.
Montenbruck O, Gill E (2000) Satellite Orbits: Models, Methods and Applications. Springer.
Moritz H (1980) Advanced physical geodesy. Herbert Wichmann Verlag, Karlsruhe.
Nie WF, Du YJ, Gao F, Ji CN, Wang TH, Xu G (2016) Validation of the numerical algebra solution for the state transition matrix in precise orbit determination. In review.
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd Ed. Cam-bridge University Press, New York.
Rapp RH (1986) Global geopotential solutions. In: Sunkel H (ed) Mathematical and numerical tech-niques in physical geodesy. Lecture Notes inEarth Sciences, Vol. 7, Springer-Verlag, Heidelberg.
Scheinert M (1996) Zur Bahndynamik niedrigfliegender Satelliten. DGK, Reihe C, Heft 435, Verlag der Bayerischen Akademie der Wissenschaften,, DGK, Reihe C, Heft 435.
Seeber G (1993) Satelliten-Geodaesie. Walter de Gruyter 1989.
Sigl R (1989) Einführung in die Potentialtheorie. Wichmann Verlag, Karlsruhe.
Torge W (1989) Gravimetrie. Walter de Gruyter, Berlin.
Wenzel H-G (1985) Hochauflösende Kugelfunktionsmodelle für das Gravitationspotential der Erde. Wissenschaftliche Arbeiten der TU Hannover, Nr. 137.
Xu G (1992) Spectral analysis and geopotential determination (Spektralanalyse und Erdschwerefeldbestimmung). Dissertation, DGK, Reihe C, Heft Nr. 397, Press of the Bavarian Academy of Sciences, ISBN 3–7696–9442–2, 100 p, (with very detailed summary in German).
Xu QF (1994) GPS navigation and precise positioning. Army Press, Peking, ISBN 7-5065-0855-9/P.4, (in Chinese).
Xu G (2004) MFGsoft – Multi-Functional GPS/(Galileo) Software – Software User Manual, (Version of 2004), Scientific Technical Report STR04/17 of GeoForschungsZentrum (GFZ) Potsdam, ISSN 1610-0956, 70 pages, www.gfz-potsdam.de/bib/pub/str0417/0417.pdf.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Xu, G., Xu, Y. (2016). Perturbed Orbit and Its Determination. In: GPS. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-50367-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-50367-6_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-50365-2
Online ISBN: 978-3-662-50367-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)