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On tidal resonance
Mashhoon, B.
AA(Utah, University, Salt Lake City, Utah)
Astrophysical Journal, Part 1, vol. 223, July 1, 1978, p. 285-298. (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Gravitation Theory, Gravitational Waves, Resonance, Tidal Waves, Wave Interaction, Approximation, Binary Stars, Charged Particles, Perturbation Theory, Relativity, Secular Variations, Two Body Problem
Bibliographic Code:


An approximate theory of the interaction of a weak gravitational wave with a Newtonian self-gravitating two-body system is presented within the framework of Einstein's theory of gravitation. The first-order orbital variation due to the external wave is thus determined. The existence of certain resonances that may possibly lead to the 'ionization' of the system is investigated. If the orbit is initially a circle, such secular ('resonance') terms can occur in the solutions of the first-order perturbation equations for xi = 1, 2, 3, where xi is the ratio of the frequency of the wave to the orbital frequency of the unperturbed system. If the initial orbit is an ellipse, resonance can occur for any value of xi consistent with the approximation scheme employed. Moreover, (extra) secular terms appear in the solutions whenever xi is a positive integer. The polarization dependence of the resonances and some of the astrophysical implications of tidal resonance are explored.

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