The Effects of Gravitational Waves on the Orbital Elements of the Planets

Ismaiel, M.N.; Saad, Nadia A.

doi:10.2174/1874381101104010001

Cited by 27 publications

(11 citation statements)

References 21 publications

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“…From a practical point of view, in the most general case one has six unknowns: the two angles of the wavevector, the frequency of the wave, its two independent amplitudes, and a phase lag. In principle, it is possible to constrain all of them by determining 15 It is unclear if the figures in Table III of Ismaiel and Saad [61] refer to the rates of change of the Keplerian orbital elements, i.e. if they are m s 1 and deg s 1 , or to their shifts over one orbital period, i.e.…”

Section: Discussionmentioning

confidence: 99%

“…if they are m and deg. Also the units adopted in Table III of Ismaiel and Saad [61] are unspecified. the secular variations of some Keplerian orbital elements for, e.g., several planets of the solar system.…”

Section: Discussionmentioning

confidence: 99%

“…The general wave-binary system scenario adopted by Ismaiel and Saad [61] is analogous to that by, e.g., Ivashchenko [57]. However, after having written the components of the tidal-type wave acceleration in cartesian coordinates, Ismaiel and Saad [61] obtain a potential function R from them in order to use the perturbative scheme based on the Lagrange planetary equations [80] for all the Keplerian orbital elements, apart from M. Then, they evaluate R onto the unperturbed Keplerian ellipse, without fixing ω, and expand it to some, unspecified, order in e by using the mean anomaly a independent variable. In such a way, they obtain that the right-hand sides of the Lagrange equations depend only on t, which allows Ismaiel and Saad [61] to integrate them over one orbital period.…”

Section: Confrontation With Other Approaches In Literaturementioning

confidence: 99%

“…Concerning the possible existence of a background of gravitational waves dating back to the origin of the universe, see, e.g., Weber [42]; Wheeler [43]; Zel'dovich and Novikov [44]; Carr [45], and the discussion in Mashhoon et al [46]. The effects of incident gravitational waves on the orbital motion of gravitationally bound systems were inspected by several authors with a variety of approaches and approximations pertaining various features of both the waves and the orbits themselves [46,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. The idea of using the solar system to try to detect a stochastic background of gravitational waves of wavelengths much larger than about 1 au was first suggested by Bertotti [47].…”

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confidence: 99%

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

Efroimsky¹

2014

ScienceOpen Research

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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 n g is much smaller than the particle's orbital one n b . We make neither a priori assumptions about the direction of the wavevector b 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 M undergo non-vanishing long-term changes of the form dW=dt ¼ FðK ij ; e; I; X; xÞ; W ¼ e; I; X; -; M, where K ij ; i; j ¼ 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 Earthbased 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 n 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.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Confrontation With Other Approaches In Literaturementioning

confidence: 99%

mentioning

confidence: 99%

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

Efroimsky¹

2014

ScienceOpen Research

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“…The idea of using the solar system to try to detect gravitational waves was first suggested by [14]. In the case of studying the effect of gravitational waves it is often useful to utilize the perturbative or disturbing function which is analogous to the potential function U as in [15] [16] and [17]. The disturbing force of gravitational waves contains long, short and secular effects.…”

Section: Introductionmentioning

confidence: 99%

Numerical Studies of Resonance and Secular Effects of Gravitational Waves

Youssef¹

2018

WJM

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This work deals with the numerical solution of the gravitational waves effects on the orbital elements of the planets in case of commensurability between the wave's frequency n g and the planet's mean motion n p. Taking Mercury and Pluto as practical examples for low frequency and high frequency, the variations of the orbital elements of Mercury due to resonance of gravitational wave are different and small than the perturbation on Pluto. The amount of changing in the orbital elements under the effects of gravitational waves is different from planet to planet according to the planet's mean motion n p. For low frequency n g , the secular variation in orbital elements will be negative (i.e. decreasing) in the inclination, semi-major axis and the eccentricity (i, a, e) like as Pluto. For high frequency n g like Mercury, the secular variation in all the orbital elements will be positive (i.e. increasing). The perturbation on all the orbital elements of two planets is changing during each revolution except the eccentricity e of Mercury and the mean anomaly M of Mercury and Pluto during the time.

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The Exoplanet Handbook

Perryman¹

2018

172

149

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The Effects of Gravitational Waves on the Orbital Elements of the Planets

Cited by 27 publications

References 21 publications

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

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

Numerical Studies of Resonance and Secular Effects of Gravitational Waves

The Exoplanet Handbook

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