Abstract
The motion of a local source inducing small oscillations in the gravitational field is investigated and shown to exhibit pure rotational kinetic energy. Should the net affect of these slow, revolving oscillations cause large-scale rotations in spacetime it would certainly result in anomalous celestial accelerations. When this angular rotational frequency of spacetime is applied to the anomalous acceleration of the Pioneer 10/11 spacecrafts, the correlation is promising.
Similar content being viewed by others
References
The German mathematician Karl Weierstrass (1815–1897) showed in 1858 that the motion of a dynamical system could always be expressed in terms of normal coordinates
Misner, W., Thorne, K.S., Wheeler, J.: Gravitation, pp. 1022–1034. W. H. Freeman, San Fransisco (1973)
Byers, N.: Israel Mathematical Conference Proceedings, vol. 12 (1999)
Goldstein H., Poole C., Safko J. (2002) Classical Mechanics, p. 250. Addison-Wesley, Reading
Marion, J.B., Thornton, S.T.: Classical Dynamics of Particles and Systems, 3rd edn, p. 458. HBJ (1988)
Quick R.M., Miller H.G. (1985). Phys. Rev. D 31: 2682
Majid A., Allezy A., Dufour R. (2006). J. Vib. Acoust. 128: 50
Collins, H., Holdom, B.: Phys. Rev. D 65, 124014-1 (2002)
Private Communication with Prof. Alfonso Agnew, of California State University Fullerton, Mathematics Department independently confirmed the energy-momentum tensor result of Eq. (3.1)
Misner, W., Thorne, K.S., Wheeler, J.: Gravitation, Sect. 22.3. W. H. Freeman, San Fransisco (1973)
Goldhaber A.S., Nieto M.M. (1974). Phys. Rev. D 9: 1119
Anderson J.D., Laing P.A., Lau E.L., Liu A.S., Nieto M.M., Turyshev S.G. (2002). Phys. Rev. D 65: 082004
Bertolami, O., Parámos, J.: Phys. Rev. D 71, 023521-3 (2005)
Cooray A., Seto N. (2004). Phys. Rev. D 69: 103502
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Christensen, W.J. Normal coordinates describing coupled oscillations in the gravitational field. Gen Relativ Gravit 39, 105–110 (2007). https://doi.org/10.1007/s10714-006-0360-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-006-0360-8