The Lense—Thirring Effect: From the Basic Notions to the Observed Effects

  • Claus Lämmerzahl
  • Gernot Neugebauer
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 562)


A pedagogical derivation is given of the Lense-Thirring effect using basic notions from the motion of point particles and light rays. First, the notion of rotation is introduced using the properties of light rays only. Second, two realizations for a non- rotating propagation of space-like directions are presented: the gyroscope and the spin of elementary particles. Then the gravitational field around a rotating body is specified which is taken for determining the various effects connected with a point particle or a gyroscope: the deSitter precession (geodesic precession) and the Lense-Thirring effect (‘frame dragging’). The results are applied to the precession of gyroscopes and to the motion of satellites around the earth.


Angular Momentum Wave Packet Momentum Tensor Point Particle Geodesic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F.A.E. Pirani: A note on bouncing photons, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astr. Phys. 13, 239 (1965).MathSciNetGoogle Scholar
  2. 2.
    A. Papapetrou: Spinning test-particles in general relativity I, Proc. Roy. Soc. (London) A, 248 (1951).ADSMathSciNetGoogle Scholar
  3. 3.
    E. Corinaldesi and A. Papapetrou: Spinning test-particles in general relativity II, Proc. Roy. Soc. (London) A, 259 (1951).ADSMathSciNetGoogle Scholar
  4. 4.
    W.G. Dixon: Dynamics of extended bodies in General Relativity III: Equations of motion, Phil. Trans. R. Soc. London A 277, 59 (1974).CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    J. Ehlers and E. Rudolph: Dynamics of extended bodies in general relativity: center-of-mass description and quasirigidity, Gen. Rel. Grav. 8 197 (1977).zbMATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    J. Ehlers: Beiträge zur relativistischen Mechanik kontinuierlicher Medien, Akad. Wiss. Lit. Mainz Abh. Math.-Nat. Kl., Seite 793 (1961).Google Scholar
  7. 7.
    J. Stachel und J. Plebanski: Classical particles with spin I: The WKBJ approximation, J. Math. Phys. 18, 2368 (1977).CrossRefADSGoogle Scholar
  8. 8.
    J. Audretsch: Trajectories and Spin Motion of Massive Spin 1/2 Particles in Gravitational Fields, J. Phys. A: Math. Gen. 14, 411 (1981).CrossRefADSGoogle Scholar
  9. 9.
    J.D. Bjorken and S.D. Drell: Relativistic Quantum Mechanics, McGraw-Hill, New York (1964).Google Scholar
  10. 10.
    P.B. Yasskin and W.R. Stoeger: Propagation equations for test bodies with spin and rotation in theories of gravity with torsion, Phys. Rev. D 21, 2081 (1980).ADSMathSciNetGoogle Scholar
  11. 11.
    S. Schlamminger, E. Holzschuh, W. Kündig, F. Nolting, and J. Schurr: Determination of the Gravitational Constant, this volume p. 15.Google Scholar
  12. 12.
    C.W. Misner, K.S. Thorne, J.A. Wheeler: Gravitation, Freeman, San Francisco 1973.Google Scholar
  13. 13.
    G. Neugebauer and R. Meinel: General Relativistic Gravitational Field of a Rigidly Rotating Disk of Dust: Solution in Terms of Ultraelliptic Functions, Phys. Rev. Lett. 75, 3046 (1995).zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    I. Ciufolini and J.A. Wheeler: Gravitation and Inertia, Princeton Series in Physics, Princeton University Press, Princeton 1995.zbMATHGoogle Scholar
  15. 15.
    W. De Sitter: On Einstein’s theory of gravitation and its astronomical consequences, Mon. Not. Roy. Astron. Soc. 77, 155 and 481 (1916).ADSGoogle Scholar
  16. 16.
    I.I. Shapiro, R.D. Reasenberg, J.F. Chandler, R.W. Babcock: Measurement of the deSitter perecession of the Moon: A relativistic three-body effect, Phys. Rev. Lett. 61, 2643 (1988).CrossRefADSGoogle Scholar
  17. 17.
    J.G. Williams, and X.X. Newhall, J.O. Dickey: Relativity parameters determined from lunar laser ranging, Phys. Rev. D 53, 6730 (1995).ADSGoogle Scholar
  18. 18.
    J. Lense and H. Thirring: Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie, Physik. Zeitschr. 19, 156 (1918).ADSGoogle Scholar
  19. 19.
    I. Ciufolini, D. Lucchesi, F. Vespe, and F. Chieppa: Measurement of gravitomagnetism, Europhys. Lett. 39, 359 (1997).CrossRefADSGoogle Scholar
  20. 20.
    I. Ciufolini, F. Chieppa, D. Luccesi, and F. Vespe: Test of Lense-Thirring orbital effect due to spin, Class. Quantum Grav. 14, 2701 (1997).zbMATHCrossRefADSGoogle Scholar
  21. 21.
    I. Ciufolini, E. Pavlis, F. Chieppa, E. Fernandes-Vieira, and J. Pérez-Mercader: Test of General Relativity and measurement of the Lense-Thirring effect with two Earth satellites, Science 279, 2100 (1998).CrossRefADSGoogle Scholar
  22. 22.
    M. Schneider: Himmelsmechanik (Band 4: Theorie der Satellitenbewegung, Bahnbestimmung) (Celestial Mechanics, Volume 4: Theory of Satellite Motion, Determination of Paths, in German), Spektrum Akademischer Verlag, Heidelberg, Berlin 1999.Google Scholar
  23. 23.
    C.W.F. Everitt et al.: this volume, p. 52.Google Scholar
  24. 24.
    R.J. Adler, A.S. Silbergleit: A General Treatment of Orbiting Gyroscope Precession,
  25. 25.
    T.L. Gustavson, P. Boyer, M. Kasevich: Precision rotation measurements with an atom interferometer gyroscope, Phys. Rev. Lett. 78, 2046 (1997).CrossRefADSGoogle Scholar
  26. 26.
    B.J. Venema, P.K. Majumder, S.K. Lamoreaux, B.R. Heckel, and E.N. Fortson: Search for a Coupling of the Earth’s Gravitational Field to Nuclear Spins in Atomic Mercury, Phys. Rev. Lett. 68, 135 (1992).CrossRefADSGoogle Scholar
  27. 27.
    B. Mashhoon: On the coupling of intrinsic spin with the rotation of the earth, Phys. Lett. A 198, 9 (1995).ADSGoogle Scholar
  28. 28.
    B. Mashhoon: Neutron Interferometry in a Rotating Frame of Reference, Phys. Rev. Lett. 61, 2639 (1988).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Claus Lämmerzahl
    • 1
  • Gernot Neugebauer
    • 2
  1. 1.Fakultät für PhysikUniversität KonstanzKonstanzGermany
  2. 2.Istitut für Theoretische PhysikFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations