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How to Measure Gravitational Aberration?

Published online by Cambridge University Press:  09 August 2007

Michal Křížek  and
Alena Šolcová
Michal Křížek
Affiliation:
Mathematical Institute, Academy of Sciences, Žitná 25, CZ-115 67 Prague 1, Czech Republic e-mail: [email protected]
Alena Šolcová
Affiliation:
Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 29 Prague 6, Czech Republic e-mail: [email protected]
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Abstract

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In 1905, Henri Poincaré predicted the existence of gravitational waves and assumed their speed equal to the speed of light. If additionally the gravitational aberration would have the same magnitude as the aberration of light, we would observe several paradoxical phenomena. For instance, the orbit of two bodies would be unstable, since two attractive forces arise that are not in line and hence form a couple. This will be modelled by a nonautonomous system of ordinary differential equations with delay. In fact, any positive value of the gravitational aberration increases the angular momentum of such a system and this may contribute to the expansion of the universe. We found a remarkable coincidence between the Hubble constant and the increasing distance of the Moon from the Earth.

In 2000, Carlip showed that in general relativity gravitational aberration is almost cancelled out by velocity–dependent interactions. We show how the actual value of the gravitational aberration can be obtained by measurement of a single angle at a suitable time t* corresponding to the perihelion of an elliptic orbit. We also derive an a priori error estimate that expresses how accurately t* has to be determined to obtain the gravitational aberration to a prescribed tolerance.

Keywords

gravitationcausalityclose binariesMoonHubble constantnumerical methods
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 2 , Symposium S240: Binary Stars as Critical Tools & Tests in Contemporary Astrophysics , August 2006 , pp. 670 - 677
Copyright
Copyright © International Astronomical Union 2007

References

Bradley, J. 1729, Phil. Trans 35, 637 Google Scholar
Burša, M. & Pěč, K. 1993, Gravity Field and Dynamics of the Earth, Springer, Berlin Google Scholar
Carlip, S. 2000, “Aberration and the speed of gravity”, Phys. Lett. A, 267, 81–87 CrossRefGoogle Scholar
Driver, R.D. 1977, “Ordinary and delay differential equations”, Appl. Math. Sci., vol. 20, Springer, BerlinGoogle Scholar
Křížek, M. 1995, “Numerical experience with the three-body problem”, J. Comput. Appl. Math., 63, 403–409 Google Scholar
Křížek, M. 1999, “Numerical experience with the finite speed of Gravitational interaction”, Math. Comput. Simulation, 50, 237–245 CrossRefGoogle Scholar
Laplace, P.S. 1966, A treatise in celestial mechanics, vol. IV, book X (translated by N. Bow-ditch), Chelsea, New YorkGoogle Scholar
Louisell, J. 1991, “A stability analysis for a class of differential-delay equations having time-varying delay”, in: S. Busenberg, M. Marteli (eds.), Delay Differential Equations and Dynamical Systems, LN in Math., vol. 1475, Springer, Berlin, 225–242Google Scholar
Marsh, G.E. & Nissim-Sabat, Ch. 1999, “Comment on ‘The speed of gravity’”, Phys. Lett. A, 262, 257–260 CrossRefGoogle Scholar
Meinardus, G. & Nürnberger, G.N. (eds.) 1985, “Delay equations, approximation and applications”, Internat. Ser. Numer. Math., vol. 74, Birkhäuser, BaselGoogle Scholar
Poincaré, H. 1905, “Sur la dynamique de l'électron”, C. R. Acad. Sci. Paris, 140, 1504–1508 Google Scholar
Ralston, A. & Rabinowitz, P. 2001, A First Course in Numerical Analysis, Dover Publications, New York Google Scholar
Rektorys, K. 1994, Survey of Applicable Mathematics, vol. I, Kluwer, Dordrecht Google Scholar
Ron, C. & Vondrák, J. 1986, “Expansion of annual aberration into trigonometric series”, Bull. Astron. Inst. Czechosl., 37, 96–103 Google Scholar
Said, S.S. & Stephenson, F.R. 1996 “Solar and lunar eclipse measurements by medieval Muslim astronomers”, J. Hist. Astronom., 27, 259–273 Google Scholar
van Flandern, T. 1998, “The speed of gravity – what the experiments say”, Phys. Lett. A, 250, 1–11 Google Scholar