Next-generation laser retroreflectors for GNSS, solar system exploration, geodesy, gravitational physics and earth observation

Dell’Agnello, S.; Boni, A.; Cantone, C.; Ciocci, E.; Martini, M.; Patrizi, G.; Tibuzzi, M.; Monache, G. Delle; Vittori, R.; Bianco, G. Lo; Currie, D. G.; Intaglietta, N.; Salvatori, L.; Lops, C.; Contessa, S.; Porcelli, L.; Mondaini, C.; Tuscano, P.; Maiello, M.

doi:10.1117/12.2304232

Cited by 3 publications

(3 citation statements)

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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%

“…Recent work by the authors [1][2][3][4], motivated, on the quantum side, by modern developments in effective field theories of gravity [5][6][7][8][9][10][11][12][13], and, on the classical side, by the beautiful discoveries in celestial mechanics , aerospace engineering [55][56][57][58][59][60][61][62] and (lunar) laser ranging techniques [63][64][65][66][67][68][69][70][71][72][73][74][75], has studied in detail the libration points of the restricted three-body problem in Newtonian gravity, general relativity and effective field theories of gravity. In particular, we have found (see Ref.…”

Section: Introductionmentioning

confidence: 99%

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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: )mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On solar system dynamics in general relativity

Battista

Esposito

Fiore

et al. 2017

Int. J. Geom. Methods Mod. Phys.

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First two-way laser ranging to a lunar orbiter: infrared observations from the Grasse station to LRO’s retro-reflector array

Mazarico

Sun

Torre

et al. 2020

Earth Planets Space

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We present the results of the first series of successful two-way laser ranging experiments from a ground station, the Lunar Laser Ranging (LLR) station in Grasse, France, to a spacecraft at lunar distance, the Lunar Reconnaissance Orbiter (LRO). A 15 × 18 × 5 cm, 650-g array of twelve 32-mm diameter solid corner cubes is mounted on its anti-nadir deck. Ranging to this small retro-reflector array onboard a lunar orbiter from a ground station was a challenge compared to ranging to larger lunar surface retro-reflectors. Grasse measured 67 returns in two 6-min sessions on September 4, 2018. Clear returns were also recorded during two additional sessions on August 23-24, 2019 for which active slewing by LRO was performed to bring the array in view of the station. The measured echos yielded range residuals less than 3 cm (two-way time-of-flight RMS < 180 ps) relative to the reconstructed LRO trajectory. This experiment provides a new method of verifying theories of dust accumulation over decades on the lunar surface. It also showed that the use of similar arrays onboard future lunar landers and orbiters can support LLR lunar science goals, particularly with landing sites near the lunar limbs and poles, which would have better sensitivity to lunar orientation.

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Ground-based corner cube retroreflector optimal design for the geolocation validation of satellite photon counting lidar

Zhang

Zhou

et al. 2021

Appl. Opt.

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The corner cube retroreflector (CCR) can be applied in the on-orbit geolocation validation of satellite photon counting lidar, which provides insight into the fidelity of laser footprint geolocation on the ground. A novel parameter optimization method, to the best of our knowledge, is proposed to enhance the performance of the CCR. Based on the velocity aberration effect of the satellite and the far-field diffraction pattern (FFDP) of the CCR, a mathematical model with respect to the received energy and design parameters of the CCR, including the aperture, the dihedral angle errors (DAE), and the curvature radius of the front face (CROF), is derived. We can achieve the optimal design parameters of the CCR through searching for the locations of the maximal and uniform FFDP on the circumference of the aberration position. We resolve the optimal aperture, the DAE, and the CROF of the CCR as 14.3 mm, 2.4 in., and 6000 m for the Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) lidar. The received energy derived from the derived parameters has a significant improvement of around 26 times compared with the CCR parameters employed in the ICESat-2. The results demonstrate that the proposed algorithm is effective, and the regression models of the optimal aperture and DAE for different satellite altitudes are conveniently employed in the design of the CCR for the geolocation validation of satellite photon counting lidar.

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Next-generation laser retroreflectors for GNSS, solar system exploration, geodesy, gravitational physics and earth observation

Cited by 3 publications

References 9 publications

On solar system dynamics in general relativity

On solar system dynamics in general relativity

First two-way laser ranging to a lunar orbiter: infrared observations from the Grasse station to LRO’s retro-reflector array

Ground-based corner cube retroreflector optimal design for the geolocation validation of satellite photon counting lidar

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