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Effects on satellite orbits in the gravitational field of an axisymmetric central body with a mass monopole and arbitrary spin multipole moments

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Abstract

Perturbations of satellite orbits in the gravitational field of a body with a mass monopole and arbitrary spin multipole moments are considered for an axisymmetric and stationary situation. Periodic and secular effects caused by the central gravitomagnetic field are derived by a first order perturbation theory. For a central spin-dipole field these results reduce to the well known Lense–Thirring effects.

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References

  • Bini, D., Cherubini, C., Chicone, C., Mashhoon, B.: Gravitational induction. Class. Quantum Gravity 25(22), 1–14 (2008)

    Article  MathSciNet  Google Scholar 

  • Blanchet, L., Damour, T.: Post-Newtonian generation of gravitational waves. Ann. Inst. H. Poincarè (A) Physique thèorique 50(4), 379–430 (1989)

    MathSciNet  ADS  Google Scholar 

  • Branham Jr, R.L.: Recursive calculation of Hansen coefficients. Celest. Mech. Dyn. Astron. 49(11), 209–217 (1990)

    Article  ADS  MATH  Google Scholar 

  • Ciufolini, I., Pavlis, E.: A confirmation of the general relativistic prediction of the Lense–Thirring effect. Nature 431(7011), 958–960 (2004)

  • Damour, T., Soffel, M., Xu, C.: General-relativistic celestial mechanics. I. Method and definition of reference systems. Phys. Rev. D 43(10), 3273–3307 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  • Damour, T., Soffel, M., Xu, C.: General-relativistic celestial mechanics. IV. Theory of satellite motion. Phys. Rev. D 49(2), 618–635 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  • Everitt, C., DeBra, D., Parkinson, B., Turneaure, J., Conklin, J., Heifetz, M. et al.: Gravity Probe B: final results of a space experiment to test general relativity. Phys. Rev. Lett., 106(22), 221101, 1–5 (2011)

  • Gradshtey, I., Ryzhik, I.: Table of Integrals, Series, and Products, 7th edn. Academic Press, London (2007)

    Google Scholar 

  • Hartmann, T., Soffel, M.H., Kioustelidis, T.: On the use of STF-tensors in celestial mechanics. Celest. Mech. Dyn. Astron. 60(1), 139–159 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Iorio, L.: An alternative derivation of the Lense–Thirring drag on the orbit of a test body. Il Nuovo Cimento B 116(7), 777–789 (2001)

    ADS  Google Scholar 

  • Iorio, L.: A gravitomagnetic effect on the orbit of a test body due to the Earth’s variable angular momentum. Gen. Relativ. Gravit. 11(5), 781–787 (2002)

    Google Scholar 

  • Iorio, L.: General relativistic spin-orbit and spinspin effects on the motion of rotating particles in an external gravitational field. Gen. Relativ. Gravit. 44(3), 719–736 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Iorio, L.: Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body. arXiv:1402.5947, pp. 1–60 (2015)

  • Iorio, L., Lichtenegger, H., Ruggiero, M.L., Corda, C.: Phenomenology of the Lense–Thirring effect in the solar system. Astrophys. Space Sci. 331(2), 351–395 (2011)

    Article  ADS  MATH  Google Scholar 

  • Kaula, W.: Analysis of gravitational and geometric aspects of geodetic utilization of satellites. Geophys. J. R. Astron. Soc. 5(2), 104–133 (1961)

    Article  ADS  MATH  Google Scholar 

  • Mashhoon, B., Hehl, F.W., Theiss, D.S.: On the gravitational effects of rotating masses: the Thirring–Lense papers. Gen. Relativ. Gravit. 16(8), 711–750 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  • Panhans, M., Soffel, M.: Gravito-magnetism of an extended celestial body. Class. Quantum Gravity 31(24), 1–11 (2014)

    Article  MathSciNet  Google Scholar 

  • Pugh, G.: Proposal for a satellite test of the coriolis prediction of general relativity. Weapons Syst. Eval. Group Res. Memo. N. 11, 414–426 (1959)

    Google Scholar 

  • Schiff, L.: Motion of a gyroscope according to Einsteins theory of gravitation. Proc. Natl. Acad. Sci. 46(6), 871–882 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Soffel, M., Klioner, S., Petit, G., Wolf, P., Kopeikin, S., Bretagnon, P., et al.: The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron. J. 126(6), 2687–2706 (2003)

    Article  ADS  Google Scholar 

  • Teyssandier, P.: Rotating stratified ellipsoids of revolution and their effects on the dragging of inertial frames. Phys. Rev. D 18(4), 1037–1046 (1978)

    Article  ADS  Google Scholar 

  • Thorne, K.: Multipole expansions of gravitational radiation. Rev. Mod. Phys. 52(2), 299–339 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  • Zimbres, M., Letelier, P.: Multipolar corrections for Lense–Thirring precession. arXiv:0803.4133 [gr-qc], pp. 1–6 (2008)

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Authors and Affiliations

  1. Institute of Theoretical Physics, Dresden University of Technology, BZW, Zellescher Weg 17, 01069, Dresden, Germany

    Jan Meichsner

  2. Department of Astronomy, Dresden University of Technology, Beyer-Bau, George-Bähr-Straße 1, 01069, Dresden, Germany

    Michael H. Soffel

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  1. Jan Meichsner
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  2. Michael H. Soffel
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Correspondence to Jan Meichsner.

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Meichsner, J., Soffel, M.H. Effects on satellite orbits in the gravitational field of an axisymmetric central body with a mass monopole and arbitrary spin multipole moments. Celest Mech Dyn Astr 123, 1–12 (2015). https://doi.org/10.1007/s10569-015-9626-3

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  • DOI: https://doi.org/10.1007/s10569-015-9626-3

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