The Separation of Gravitation and Inertia in the First-Order Gradient

  • Wenbin Shen
  • Helmut Moritz
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 117)

Abstract

The authors explored the possibility of separating gravitation from inertia in the first-order gradients of the gravitational potential in the light of general relativity. It is proposed to choose an inertial platform as a tetrad and let the accelerometers be fixed with the inertial platform. The force experienced by the inertial platform can be directly measured by the accelerometers. Since the Riemannian tensor components R 0i0j could be locally measured by gradiometers, one can determine the first-order gradients of the gravitational potential.

Keywords

Geophysics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boedecker G (1985) Gravity Vector Recovery by Inertial Geodesy-Why and How Is It Possible? In: Schwarz K P (ed), Proc. 3th Intern. Symp. on Inertial Technology for Surveying and Geodesy, Calgary, Canada, pp. 85–103.Google Scholar
  2. Britting K R (1971) Inertial Navigation Systems Analysis. Wiley-Interscience, New York.Google Scholar
  3. Dahlquist B (1972) Numerische Methoden. R. Oldenbourg Verlag, München.Google Scholar
  4. Goldsborough R G, Fundak L T (1985) The Gravity Gradiometer Survey System. In: Schwarz K P (ed), Proc. 3th Intern. Symp. on Inertial Technology for Surveying and Geodesy, Calgary, Canada, pp. 653–656.Google Scholar
  5. Grafarend E W (1981) From Kinematical Geodesy to Inertial Positioning. Bull. Géod., V. 55, pp. 286–299.CrossRefGoogle Scholar
  6. Jekeli C et al. (1985) A Review of Data Processing in Gravity Gradiometry. In: Schwarz K P (ed), Proc. 3th Intern. Symp. on Inertial Technology for Surveying and Geodesy, Calgary, Canada, pp. 675–685.Google Scholar
  7. Jordan S K (1985) Status of Moving-Base Gravity Gradiometrey. In: Schwarz K P (ed), Proc. 3th Intern. Symp. on Inertial Technology for Surveying and Geodesy, Calgary, Canada, pp. 639–647.Google Scholar
  8. Mason M J (1987) Numerical Analysis ( second ed. ). Macmillan Publishing Company, New York.Google Scholar
  9. Moritz H (1967) Kinematical Geodesy. Report No. 92, Dept. of Geodesic Science, Ohio State University, Columbus.Google Scholar
  10. Moritz H (1968) Kinematical Geodesy. Reihe A: Höhere Geodäsie—Heft Nr. 59.Google Scholar
  11. Moritz H, Hofmann-Wellenhof B (1993), Geometry, Relativity, Geodesy. Wichmann, Karlsruhe.Google Scholar
  12. Mueller I I (1981) Inertial Survey Systems in the Geodetic Arsenal. Bull. Géod., V. 55, pp. 272–285.CrossRefGoogle Scholar
  13. Rummel R., Colombo 0 L (1985) Gravity Field Determination from Satellite Gradiometry. Bulletin Géodésique, V. 59, pp. 233–246.CrossRefGoogle Scholar
  14. Schwarz K P (1981) A Comparison of Models in Inertial Surveying. Bull. Géod., V. 55, pp. 300–314.CrossRefGoogle Scholar
  15. Schwarz K P (1985) Inertial Modelling—A Survey of Some Open Problems. In: Schwarz K P (ed), Proc. 3th Intern. Symp. on Inertial Technology for Surveying and Geodesy, Calgary, Canada.Google Scholar
  16. Shen W (1996) On the Separability of Gravitation and Inertia According to General Relativity. Dissertation, Graz University of Technology.Google Scholar
  17. Shen W, Moritz H (1996a) On the Separation of Gravitation and Inertia and the Determination of the Relativistic Gravity Field in the Case of Free Motion. Journal of Geodesy, V. 70, pp. 633–644.Google Scholar
  18. Shen W, Moritz H (1996b) On the Separation of Gravitation and Inertia in Airborne Gradiometry. Bollettino di Geodesia e Scienze Affini, V. 55, N. 2, pp. 145–159.Google Scholar
  19. Wang Y (1987) The Gradiometer-Gravimeter Equation in Various Coordinate Systems. Bull. Géod., V. 61, pp. 125–144.CrossRefGoogle Scholar
  20. Weinberg S (1972) Gravitation and Cosmology. John Wiley & Sons, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Wenbin Shen
    • 1
  • Helmut Moritz
    • 1
  1. 1.Section of Physical GeodesyGraz University of TechnologyGrazAustria

Personalised recommendations