Archives
 
English Issues
 
Vol 64, Issue 3, [06 - 2023] - Full papers

Effect of the low-order coefficients of the Earth gravity model in calculating the satellite orbit

DOI:10.46326/JMES.2023.64(3).10

  • Affiliations:

    Hanoi National University of Civil Engineering, Hanoi, Vietnam

  • *Corresponding:
    This email address is being protected from spambots. You need JavaScript enabled to view it.
  • Received: 3rd-Feb-2023
  • Revised: 1st-June-2023
  • Accepted: 26th-June-2023
  • Online: 30th-June-2023
Pages: 90 - 98
Views: 869
View onlineView online
Downloads: 9
Downdload PDF
★★★★★Rating: , Total rating: 0
  • ★
  • ★
  • ★
  • ★
  • ★
Yours rating

Abstract:

The Earth's gravity model is a crucial factor in determining satellite orbits. Scientific organizations such as GFZ Potsdam in Germany, GRGS Toulouse in France, and AIUB in Switzerland have established Earth gravity models with increasing precision of spherical harmonic coefficients. Low-order coefficients, including C ̅_21,( S) ̅_21, C ̅_10,C ̅_11,( S) ̅_11and C ̅_20, play a vital role in describing changes in the Earth's poles, geometric center, and flattening. To evaluate the impact of these coefficients and understand altimeter satellite orbital error, the Propagerror program was developed. This program calculates satellite orbital error from the differential components of Earth gravity model spherical harmonic coefficients (dC/Slm), which can be obtained from the difference between two gravity models or from seasonal and annual components of spherical harmonics. By separating appropriate low-order components in the Earth gravity models, the Propagerror program enables the estimation of satellite orbital error. In this study, we isolate C ̅_10,C ̅_11,( S) ̅_11, and C ̅_21,( S) ̅_21 coefficients in the EIGEN-GRGS.RL02bis.MF and EIGEN-6S gravity models to assess the geophysical impact on satellite orbits. The influence of the geometry center elements results in a 2 cm error in the Jason-2 satellite, while the rotational axis elements have no effect. The C ̅_31,( S) ̅_31 coefficient has a 6-7 mm impact on the accuracy of the Jason-2 satellite, as demonstrated by the satellite error map in two situations with and without the C ̅_31,( S) ̅_31 harmonic coefficient. This study highlights the significance of regulating function coefficients in satellite orbit determination, particularly the low-level harmonic parameters. The Propagerror program provides insights into the impact of each spherical harmonic parameter on satellite orbits, contributing to the improvement of orbit accuracy and the understanding of the Earth's gravity model.

How to Cite
Luong, D.Ngoc and Tran, T.Dinh 2023. Effect of the low-order coefficients of the Earth gravity model in calculating the satellite orbit. Journal of Mining and Earth Sciences. 64, 3 (Jun, 2023), 90-98. DOI:https://doi.org/10.46326/JMES.2023.64(3).10.
References

Barthelmes, F. (2013). Definition of functionals of the geopotential and their calculation from spherical harmonic models. Http://Publications. Iass-Potsdam. de/Pubman/Item/Escidoc, 104132(3), 902.

Bayen, A. M., and Siauw, T. (Eds.). (2015). An Introduction to MATLAB® Programming and Numerical Methods for Engineers. In An Introduction to MATLAB® Programming and Numerical Methods for Engineers (p. i). Academic Press. https://doi.org/https://doi.org/10.1016/B978-0-12-420228-3.00020-8

Bertiger, W., Desai, S. D., Dorsey, A., Haines, B. J., Harvey, N., Kuang, D., Sibthorpe, A., and Weiss, J. P. (2010). Sub-Centimeter Precision Orbit Determination with GPS for Ocean Altimetry. Marine Geodesy, 33(sup1), 363–378. https://doi.org/10.1080/01490419.2010.487800

Bois, E. (1994). First-order accurate theory of perturbed circular motion. Celestial Mechanics and Dynamical Astronomy, 58(2), 125–138. https://doi.org/10.1007/BF00695788

Cohen, S. C., and Smith, D. E. (1985). LAGEOS Scientific Results: Introduction. Journal of Geophysical Research, 90(B11), 9217. https://doi.org/10.1029/JB090iB11p09217

Couhert, A., Cerri, L., Legeais, J.-F., Ablain, M., Zelensky, N. P., Haines, B. J., Lemoine, F. G., Bertiger, W. I., Desai, S. D., and Otten, M. (2015). Towards the 1mm/y stability of the radial orbit error at regional scales. Advances in Space Research, 55(1), 2–23. https://doi.org/10.1016/j.asr.2014.06.041

Exertier, P., and Bonnefond, P. (1997). Analytical solution of perturbed circular motion: application to satellite geodesy. Journal of Geodesy, 71(3), 149–159. https://doi.org/10.1007/s001900050083

Flechtner, F., Dahle, C., Neumayer, K. H., König, R., and Förste, C. (2010). The Release 04 CHAMP and GRACE EIGEN Gravity Field Models. In F. M. Flechtner, T. Gruber, A. Güntner, M. Mandea, M. Rothacher, T. Schöne, and J. Wickert (Eds.), System Earth via Geodetic-Geophysical Space Techniques (pp. 41–58). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-10228-8_4

Gourine, B. (2012). Use of Starlette and LAGEOS-1and-2 laser measurements for determination and analysis of stations coordinates and EOP time series. Comptes Rendus Geoscience, 344(6–7), 319–333. https://doi.org/10.1016/j.crte.2012.05.002

Ince, E. S., Barthelmes, F., Reißland, S., Elger, K., Förste, C., Flechtner, F., and Schuh, H. (2019). ICGEM – 15 years of successful collection and distribution of global gravitational models, associated services, and future plans. Earth System Science Data, 11(2), 647–674. https://doi.org/10.5194/essd-11-647-2019

Kaula, W. M. (1966). Theory of satellite geodesy. Applications of satellites to geodesy. Waltham.

Lambin, J., Morrow, R., Fu, L.-L., Willis, J. K., Bonekamp, H., Lillibridge, J., Perbos, J., Zaouche, G., Vaze, P., Bannoura, W., Parisot, F., Thouvenot, E., Coutin-Faye, S., Lindstrom, E., and Mignogno, M. (2010). The OSTM/Jason-2 Mission. Marine Geodesy, 33(sup1), 4–25. https://doi.org/10.1080/01490419.2010.491030

Luong, N. D. (2015). Analyse d’erreurs de constellations de satellites en termes de positionnement global et d’orbitographie [Université Nice Sophia Antipolis]. https://theses.hal.science/tel-01294647/document

Rummel, R. (2020). Earth’s gravity from space. Rendiconti Lincei. Scienze Fisiche e Naturali, 31(S1), 3–13. https://doi.org/10.1007/s12210-020-00889-8

Seeber, G. (2003). Satellite Geodesy. Walter de Gruyter. https://doi.org/10.1515/9783110200089

Sośnica, K., Thaller, D., Jäggi, A., Dach, R., and Beutler, G. (2012). Sensitivity of Lageos Orbits to Global Gravity Field Models. Artificial Satellites, 47(2), 47–65. https://doi.org/10.2478/v10018-012-0013-y

Verron, J., Sengenes, P., Lambin, J., Noubel, J., Steunou, N., Guillot, A., Picot, N., Coutin-Faye, S., Sharma, R., Gairola, R. M., Murthy, D. V. A. R., Richman, J. G., Griffin, D., Pascual, A., Rémy, F., and Gupta, P. K. (2015). The SARAL/AltiKa Altimetry Satellite Mission. Marine Geodesy, 38(sup1), 2–21. https://doi.org/10.1080/01490419.2014.1000471

Zelensky, N. P., Lemoine, F. G., Chinn, D. S., Melachroinos, S., Beckley, B. D., Beall, J. W., and Bordyugov, O. (2014). Estimated SLR station position and network frame sensitivity to time-varying gravity. Journal of Geodesy, 88(6), 517–537. https://doi.org/10.1007/s00190-014-0701-4