Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

Battista, Emmanuele; Agnello, Simone Dell'; Esposito, Giampiero; Fiore, L. Di; Simo, Jules; Grado, A.

doi:10.1103/physrevd.92.064045

Cited by 20 publications

(30 citation statements)

References 68 publications

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“…However, by patiently applying the time derivative operator four times to Eq. (4.3) (see Appendix A for details) the fourth time derivatives x (4) r are found to solve a linear system of ordinary differential equations of the form…”

Section: Linear System Of Ordinary Differential Equations Associamentioning

confidence: 99%

On solar system dynamics in general relativity

Battista

Esposito

Fiore

et al. 2017

Int. J. Geom. Methods Mod. Phys.

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Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder-Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of celestial bodies, showing in detail under which conditions the effects of internal structure and finite extension get cancelled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth's orbit about the Sun, written down in detail for the Sun-Earth-Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies. Last, the evaluation of quantum corrections to location of collinear and noncollinear Lagrangian points for the planar restricted three-body problem is revisited, and a new set of theoretical values of such corrections for the Earth-Moon-planetoid system is displayed and discussed. On the side of classical values, the general relativity corrections to Newtonian values for collinear and noncollinear Lagrangian points of the Sun-Earth-planetoid system are also obtained.

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Section: Linear System Of Ordinary Differential Equations Associamentioning

confidence: 99%

On solar system dynamics in general relativity

Battista

Esposito

Fiore

et al. 2017

Int. J. Geom. Methods Mod. Phys.

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“…Considering that the distance between the two Lagrangian points L 1 and L 2 is y 1 + y 2 3 × 10 9 m, and assuming an impact parameter b of the order of the Earth's radius R ⊕ 6.4 × 10 6 m, for the propagation time of Eq. (8) we obtain: (9) where the contribution of each term has been highlighted. If we consider a round trip travel for the propagation time, the smaller contribution of the gravitomagnetic field cancels out when we consider the propagation on the same side of the Earth, and the quadrupole effect can be extracted after modelling the Shapiro delay and the larger effect of the propagation time in the flat spacetime of Minkowski.…”

Section: Time Delays For a Configuration Where Emitter And Receiver Amentioning

confidence: 99%

How to use the Sun–Earth Lagrange points for fundamental physics and navigation

et al. 2017

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We illustrate the proposal, nicknamed LAGRANGE, to use spacecraft, located at the Sun-Earth Lagrange points, as a physical reference frame. Performing time of flight measurements of electromagnetic signals traveling on closed paths between the points, we show that it would be possible: a) to refine gravitational time delay knowledge due both to the Sun and the Earth; b) to detect the gravito-magnetic frame dragging of the Sun, so deducing information about the interior of the star; c) to check the possible existence of a

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“…The deflection angle for a light beam evolving in Kerr geometry is given by [4] 15) where the first term is the same as in Schwarzschild spacetime, the second one is due to the oblateness of the body of mass M , whereas the last one is related to angular momentum and hence it represents a gravitomagnetic effect. From Eqs.…”

Section: Quantum Corrected Time Delaymentioning

confidence: 99%

“…(3.12), (3.13), and Unfortunately this deviation from the underlying classical theory has no chance to be tested, unlike, for example, the effects some of us predicted in Refs. [10,11,14,15], where it is shown that Earth-Moon Lagrangian points are expected to undergo a displacement of the order of few millimetres from their classical position. Furthermore, we have proved that the result reported in Eq.…”

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

Quantum time delay in the gravitational field of a rotating mass

Battista¹,

Tartaglia²,

Esposito³

et al. 2017

Class. Quantum Grav.

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We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system.

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Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

Cited by 20 publications

References 68 publications

On solar system dynamics in general relativity

On solar system dynamics in general relativity

How to use the Sun–Earth Lagrange points for fundamental physics and navigation

Quantum time delay in the gravitational field of a rotating mass

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