MoonLIGHT: A USA–Italy lunar laser ranging retroreflector array for the 21st century

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.

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“…The quantum gravity effect described in our paper can be studied with the tech- [ [57][58][59][60][61][62] …”

Section: Tiny Departure From the Equilateral Triangle Picture: Prmentioning

confidence: 99%

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

et al. 2015

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“…In this respect, the quantum corrections to general relativity values for noncollinear points L 4 and L 5 look encouraging in the case of (κ 1 , κ 2 ) values appropriate to scattering potential, because corrections just below a centimeter are comparable with the purely instrumental, time-of-flight uncertainty of the geodesic positioning techniques based laser-ranging [63][64][65][66][67][68][69][70][71][72][73][74][75]. However, the total error budget of satellite/lunar laser ranging [63][64][65][66][67][68][69][70][71][72][73][74][75] varies with the specific application and/or orbit, at the level of millimeter to centimeter. In the first part of our paper, to prepare the ground for future work, we have provided an original synthesis of the Levi-Civita analysis of the problem of motion of N bodies in general relativity, a very difficult problem that was studied, among the others, by Einstein himself with Infeld and Hoffman [17], Fock [18], Levi-Civita [19], Damour, Soffel and Xu [29][30][31][32].…”

Section: )mentioning

confidence: 99%

“…The new map (5.14) is such that the quantum corrected Lagrangian reads as [19,26,27], while 3 sets of quantum parameters κ 1 and κ 2 are conceivable in effective gravity [5,6,[11][12][13]. In this respect, the quantum corrections to general relativity values for noncollinear points L 4 and L 5 look encouraging in the case of (κ 1 , κ 2 ) values appropriate to scattering potential, because corrections just below a centimeter are comparable with the purely instrumental, time-of-flight uncertainty of the geodesic positioning techniques based laser-ranging [63][64][65][66][67][68][69][70][71][72][73][74][75]. However, the total error budget of satellite/lunar laser ranging [63][64][65][66][67][68][69][70][71][72][73][74][75] varies with the specific application and/or orbit, at the level of millimeter to centimeter.…”

Section: )mentioning

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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“…For the Earth-Moon system, the prediction about the discrepancy between classical and quantum corrected quantities is of the order of millimeters. This magnitude is comparable with the instrumental accuracy of point-to-point laser Time-of-Flight (ToF) measurements in space typical of the modern Satellite/Lunar Laser Ranging (SLR/LLR) techniques [19][20][21][22][23][24][25][26][27][28][29][30][31][32]). The full positioning error budget of the orbits of satellites equipped with laser retroreflectors and reconstructed by laser ranging depends also on other sources of uncertainty (related to the specific orbit, satellite and retroreflector array), in addition to the pure point-to-point laser ToF instrumental accuracy (related to the network of laser ranging ground stations of the ILRS, i.e., the International Laser Ranging Service [20].…”

Section: Introductionmentioning

confidence: 92%

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

et al. 2015

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We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L 4 and L 5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L 4 or L 5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L 4 or L 5 . It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L 4 and L 5 , the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the longdistance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. Finally, general relativity corrections to Newtonian position of collinear Lagrangian points turn out to be below the millimiter, whereas on stable equilibrium points they are of order of a few millimiters.

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MoonLIGHT: A USA–Italy lunar laser ranging retroreflector array for the 21st century

Cited by 15 publications

References 12 publications

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

On solar system dynamics in general relativity

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

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