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# Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

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### Abstract

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency $ν g$ is much smaller than the particle's orbital one n b. We make neither a priori assumptions about the direction of the wavevector $k ̂$ nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly undergo non-vanishing long-term changes of the form $d Ψ / d t = F ( K i j ; e , I , Ω , ω ) , Ψ = e , I , Ω , ϖ , ℳ$ , where $K i j , i , j = 1 , 2 , 3$ are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency n b is much larger than the frequency $ν g$ of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.

### Most cited references104

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### Discovery of a pulsar in a binary system

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### Constraints on generalized inflationary cosmologies

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### LIGO: the Laser Interferometer Gravitational-Wave Observatory

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### Author and article information

###### Contributors
(View ORCID Profile)
###### Journal
SOR-ASTRO
ScienceOpen Research
ScienceOpen
2199-1006
02 September 2014
: 0 (ID: 3b886ac9-0a65-4724-9ab2-ac23b174abcb )
: 0
: 1-13
###### Affiliations
[1 ]Ministero dell'Istruzione, dell'Università e della Ricerca (M.I.U.R.), Rome, Italy
###### Author notes
[* ]Corresponding author's e-mail address: lorenzo.iorio@ 123456libero.it
###### Article
1727:XE
10.14293/S2199-1006.1.SOR-ASTRO.AWXWIL.v2

This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

###### Page count
Figures: 0, Tables: 0, References: 87, Pages: 13
###### Categories
Original Article

I have revised the article according to the suggestions kindly provided by the referees
2014-09-19 07:19 UTC
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4 people recommend this
In this revised version, the author carefully addressed the points raised by this referee. The paper is now very good and it deserves both publication in scienceopen.com and the attention of the scientific community.
2014-10-02 05:31 UTC