Test di Precisione della Relatività Generale con Retroriflettori Lunari di Nuova Generazione
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1 Test di Precisione della Relatività Generale con Retroriflettori Lunari di Nuova Generazione!! Simone Dell Agnello (for the SCF_Lab Team) INFN-LNF, Via Enrico Fermi 40, Frascati (Rome), 00044, Italy Membro Collegio dei Docenti di SIACE" (Scienze e Ingegneria dell Ambiente, delle Costruzioni e dell Energia)! Coordinatore INFN-LNF/Cosenza della Ricerca Tecnologica e Interdisciplinare per la" Commissione Scientifica Nazionale 5 dell INFN (INFN-CSN5)! University of Calabria, Arcavacata di Rende (CS), 87036, Italy, November 28, 2013!
2 Precision Tests of General Relativity with! New Generation Lunar Retroreflectors!! Simone Dell Agnello (for the SCF_Lab Team) INFN-LNF, Via Enrico Fermi 40, Frascati (Rome), 00044, Italy Membro Collegio dei Docenti di SIACE" (Scienze e Ingegneria dell Ambiente, delle Costruzioni e dell Energia)! Coordinatore INFN-LNF/Cosenza della Ricerca Tecnologica e Interdisciplinare per la" Commissione Scientifica Nazionale 5 dell INFN (INFN-CSN5)! University of Calabria, Arcavacata di Rende (CS), 87036, Italy, November 28, 2013!
3 SCF_Lab Simone Dell Agnello, Delle Monache G., Vittori R., Boni A., Cantone C., Ciocci E., Lops C., Martini M., Patrizi G., Tibuzzi M., Maiello M., Currie D., Bianco G., Intaglietta N., Salvatori L., Contessa S., Porcelli, L., Tuscano, P., Mondaini, C.!! INFN-LNF, Frascati (Rome), Italy! SCF_Lab! Satellite/Lunar/GNSS! laser ranging and altimetry Characterization Facilities Laboratory!
4 Acknowledgments! We acknowledge important support/contracts from/with:! ASI,! ESA & Galileo,! Italian Ministry of Defense/Air Force,! ISRO! 4!
5 Outline! Lunar Laser Ranging to laser retroreflectors! SCF_Lab Research INFN-LNF! Science program and SCF_Lab Activities! Lunar mission opportunities! Applications to Physics/Mathematics research at UniCal! Collaboration on SIACE Doctoral project, FISICOM! HORIZON 2020 Space, INFN-CSN2 and other opportunities for collaboration! 5!
6 Main Science Activities and Goals! Improved Test of Gravity with refined analysis of, and LLR data from, Apollo and Lunokhod reflectors! Launched , NASA, ROSKOSMOS.! Uninterrupted LLR data since 69. By ILRS; also ASI-Matera from 2010! Accurate thermal-optical-orbital modeling. With Maryland! General Relativity analysis. PEP with CfA (USA)! New theories of gravity and Solar System constraints with IST Lisbon, Univ. Porto! Improved Tests of Gravity (up to x100) and improved Selenodesy (lunar interior) MoonLIGHT! New Enabling Technology for Gravity, Planetary Exploration and Geodesy - INRRI! Independent missions, though part of unitary program! 6!
7 Satellite Laser Ranging (SLR)" Lunar Laser Ranging (LLR)! " Time of Flight (ToF) measurements! 7!
8 Satellite/Lunar Laser Ranging (SLR/LRR)! Earth! GeoMetroDynamics (GMD) in space! Unambiguous position/distance measurement (so-called laser range ) to cube corner retroreflectors (CCRs) with short laser pulses and a time-of-flight technique! Time-tagging with H-maser clocks! Moon! Precise positioning (normal points at mm level, orbits at cm level)! Absolute accuracy (used to define Earth center of mass, geocenter, and scale of length)! Passive, maintenance-free Laser Retroreflector Arrays (LRAs)! 8!
9 Satellite Laser Ranging (SLR)" Lunar Laser Ranging (LLR)" Time of flight measurements! Cube corner retro-reflectors! (CCRs)! Time of flight, atmospheric! corrections! LAGEOS Sector from NASA-GSFC! LAser GEOdynanics Satellite: h~6000km! Normal reflection! Retro-reflection! =60 cm ~400 Kg 426 CCRs! (Precise). AND. (cost-effective) distance measurement in space! 9!
10 Cube Corner laser Retroreflectors (CCRs)! LAS ER! IN! LASER! OUT! Triple total internal reflection around the corner! 10!
11 SLR concept: laser, receiving telescope; clock;! time of flight! Slide courtesy of G. Bianco! Δt = t stop t start d cδt 2 stop LASER start 11!
12 LLR/SLR vs ground survey/alignment! An ILRS station is like a gigantic total station theodolite measuring angles & distances of CCRs in ordinary surveys and alignements on Earth. For example to build large physics installations, like particle physics experiments (ATLAS, KLOE, CDF,..) and particle beam! accelerators (LHC, DAFNE, Tevatron, )"!!Leica TC2002. Great instrument:"!tof theodolite with IR laser!!!!! mm (after interferometer calibration)" few microrad accuracy" " However, surveys for particle physics usually done indoor at approximately isothermal conditions, over short baselines (2 to hundreds of meters). With LLR/SLR things are completely different!! TO BE THE SUBJECT OF A DOCTORAL CLASS..! 12!
13 Cube Corner laser Retroreflectors (CCRs)! So-called prisms used for ground measurements by geometers, for ex mounted inside opened spheres, with the corner coincident with the center of the sphere! Taylor-Hobson sphere for measurements of angles! 13!
14 On ground: theodolite (or laser tracker ), retroreflector, time-of-flight! Usato for positioning metrology of large physics installations and! Experiments like KLOE particle physics experiment at the LNF! DAΦNE accelerator and 14!
15 SLR concept" ILRS stations: Matera, Herstmonceux, Graz, OCR! Slide courtesy of G. Bianco! 15!
16 APOLLO 11, 14, 15! Apollo 11: 100 CCRs! Flight payload for 32 CCRs (property of Univ. Maryland)! LAGEOS I ( 76; NASA),! LAGEOS II ( 92; NASA/ASI)! 16!
17 Laser Geodynamics Satellites (LAGEOS)! LAGEOS I (1976; NASA), LAGEOS II (1992; NASA/ASI)! LAGEOS Sector, an engineering prototype proporty of NASA-GSFC, SCF-Tested at INFN-LNF! 17!
18 Space geodesy, GNSS, Gravitation! International Terrestrial! Reference Frame (ITRF):! Geocenter from SLR! Scale from SLR & VLBI! Orientation from VLBI! Distribution w/gnss! DORIS! LAGEOS! SLR CONSTELLATION:! LEO, GNSS, GEO, Moon! UniCal, 28/11/2013! S. Dell Agnello (INFN-LNF) et al! 18!
19 Int. Terrestrial Reference Frame (ITRF)! Space geodesy long-term goal:! Define and maintain an ITRF with an! accuracy of 1 mm and a stability of! 0.1 mm/year over a 10-year period! Now ITRF is about a factor (few to) 10! less accurate/stable! SLR CONSTELLATION! LAGEOS! UniCal, 28/11/2013! S. Dell Agnello (INFN-LNF) et al! 19!
20 LAGEOS (h ~ 6000 km): ToF ~ 0.05 sec! S L R 20!
21 SLR/LLR examples! S! L! R! LAGEOS! (h ~ 6000 km):! ToF ~ 0.05 sec! Apollo LRA! Moon! (d ~ km):! ToF ~ 2.5 sec! 21!
22 Current LLR arrays! Apollo 11! Re-discovered! Lunokhod 1! (Luna 17 lander)! Apollo 15! Apollo 14! 22!
23 Apollo Missions R. H. Dicke et al: laser tracking of Moon with traditional light pulses for gravity testsin the 50s Laser invented ~1960 MIT and URSS shoot laser light to Moon surface in the 60s Retroreflectors deployed by Apollo 11, 14, 15 Apollo: CCR arrays of fused silica with circular aperture of 3.8 cm diameter each Apollo 11 e 14: used 100 CCRs Apollo 15: 300 CCRs 23!
24 Lunar Laser Ranging: accurate at ~ of Earth-Moon distance! Relative sizes and separation of the Earth Moon.! An LLR pulse takes sec for the mean orbital distance.! Locations of" 1 st Gen. Lunar" Retroreflector Arrays! 24!
25 Centro di Geodesia Spaziale (CGS) Giuseppe Colombo " Matera, Italy" Tri-colocated within ITRF by SLR, VLBI, GNSS! Slide courtesy of G. Bianco! MLRO,! Matera Laser Ranging Observatory! LLR since March 2010! Led by G. Bianco, also! Chairman of ILRS Governing Board! Giuseppe Colombo, !
26 Slide courtesy of G. Bianco!
27 3-station colocation, OCA-CERGA, Obs. du Calern, France (courtesy of)
28 SCF_Lab! Two unique OGSE (Optical Ground Support Equipment) facilities, in clean room to characterize the thermal and optical behavior of laser retroreflectors in lab-simulated space environment (532, 633, 1064 nm)! 28!
29 Two world-unique OGSE (Optical Ground Support Equipment) facilities in a clean room to characterize the space segment of laser ranging altimetry. In INFN jargon : test beam of laser retroreflector detectors! SCF for SLR/LLR/ GNSS/ Altimetry! (RD-1, RD-2)! SCF-G for GNSS (RD-10)!! 29!
30 Two AM0/space Solar Simulators! 30!
31 Optical measurements: FFDP & Interferometry! GPS/Galileo laser Retroreflector Array! (GRA)! 31!
32 SCF: thermal IR testing and sw modeling! With SCF can measure/model subtle thermal effects, and optimize thermal conductance of retroreflector mounting! SCF-Test! IR Heat Flow Due to Tab Supports! Thermal modeling (noon on Moon)! 32!
33 SCF-Test/Revision-ETRUSCO-2 (ASI-INFN)! Laboratory-simulated space conditions. Concurrent/integrated:! Dark/cold/vacuum! Sun/Albedo AM0 simulators (2) and Earth IR simulator! Non-invasive IR and contact thermometry! Laser interrogation and sun perturbation at varying angles! Payload thermal control, roto-translations! Critical orbit configurations (worst-case thermal-optical behavior)! Deliverables / Retroreflector Key Performance Indicators (KPIs)! Thermal behavior (τ CCR, thermal relaxation time)! Optical response: Far Field Diffraction Patter, (near-field) Wavefront Fizeau Interferogram! Integrated thermal-optical simulations (upon request)! Note: reduced, partial, incomplete tests (compared to the realistic space environment) are randomly misleading (either optimistic or pessimistic)! 33!
34 The SCF-Test (background IP of INFN)! J. Adv. Space Res. 47 (2011) ! 34!
35 Setting CCR 35!
36 SCF-Test of MoonLIGHT prototype! No sun shade coating,! under optimization! by Currie s SW modeling to be validated by SCF-Test! MoonLIGHT proto under test in the SCF 36!
37 SCF: CCR Temperatures, optical FFDP (no sunshade)! 150 o C! excursions! SCF FFDP! SCF FFDP! SCF FFDP! 37!
38 SCF: Optical response of MoonLIGHT (no sun shade)! Sun angle on CCR: 0 o +30 o -30 o 0 o! Optical FFDP! *! Nominal,! unperturbed! FFDP = 25%! 38!
39 Experiment of INFN National Scientific Committee 2 (CSN2) for :" MoonLIGHT-2" Moon Laser Instrumentation for General relativity High accuracy Tests Phase 2! SCF_Lab! Satellite/Lunar/GNSS! laser ranging and altimetry Characterization Facilities Laboratory!
40 Lunar Laser Ranging (LLR) Science! Suite of precision tests of General Relativity (GR) with single experiment! Study of lunar geophysics (Selenodesy)! Lunar Geophysical Network (LGN)! ITRF:! ILRS,! IGS, IVS,! IDS stations! IMRF:! Apollo/Lunokohd,! MEX, Astrobotic, C-ILN/GLXP,! SELENE-2, Chandrayaan-2,! LGN! landers/rovers! ITRF/IMRF: International Terrestrial/Moon Reference Frame! 40!
41 LLR science GR and Selenodesy! Science with LLR Observable Ranges between Earth/lunar surface Lunar orbit Lunar GM Gravitational physics Rotation (difference from Cassini state) Total moment of inertia(moi) Dissipation by core-mantle coupling & oblate fluid core core MOI/mantle MOI ratio Lunar mantle c core Final goals: radius and state of the lunar core bulk composition of the Moon Tidal deformation Lunar Love numbers (k2, h2, l2) 4 41!
42 Δt! time! t 3! t 2! t 1! time! Pulse to Moon! Wide Pulse to Earth! Pulse to Moon! Pulses to Earth! Apollo or! Lunokhod! MoonLIGHT/ LLRRA21! Δt! 1 unresolved widened pulse! back to Earth due to multi-ccr and lunar librations! t 2! t 1! t 3! 3 separated! pulses back to Earth! Many small CCRs! Large, single, CCRs! 42!
43 Current LLR arrays! Apollo 11! Re-discovered! Lunokhod 1! (Luna 17 lander)! Apollo 15! Apollo 14! Lunokhod 2! 43!
44 MoonLIGHT / LLRRA21 (cartoon no to scale)! Apollo:! ~m 2 arrays of small 3.8cm CCRs! MoonLIGHT: single! large 10cm CCR! ROVER! Big one!!! LANDER!!!!! REGOLITH! Background image courtesy of Lockheed Martin.! Rover/lander image courtesy of NASA! 44!
45 MoonLIGHT cube corner reflector (CCR)! SUN/DUST! SHADE! SUN/ DUST! SHADE! INNER! CONFORMAL! THERMAL SHIELD! (Au-Ag coated)! Mass ~ 1.7 kg! Size ~ 150mm (r) x 300mm (h)! Sophisticated thermal design (sun heat shade,! 2 internal heat shields), tight optical specs! 45!
46 Current dominant error on LLR Libration rotations up to ~8 (effect of e and i of Moon orbit). Current accuracy of ~ 2 cm Past (Apollo) Laser Pulse fat laser pulse: return uncertainty dominated by pulse far corner Librating Multi-reflector array near corner Present (Apollo) Future (MoonLIGHT) medium laser pulse: return uncertainty dominated by array libration short laser pulse: return uncertainty dominated by pulse Shorter pulses can be done Slide courtesy of! S. Merkowitz! UniCal, 28/11/2013! S. Dell Agnello (INFN-LNF) et al! 46!
47 Sensing Array Size/Orientation of Apollo reflectors Effect of multi-ccr array orientation due to lunar librations Apollo 11! Apollo 15! ! ! ! ! Slide courtesy of T. Murphy! Apollo arrays: to get 2 cm range out of +/- 1 nsec ToF distribution, thousands of laser returns are needed. With MoonLIGHT: with just 1 return we get a mm/sub-mm range! 47!
48 LLR ToF residuals with PEP, the Planetary Ephemeris Program by CfA Data by station from 1969 to 2009 The model parameter estimates are refined by minimizing the residual differences, weighted leastsquares sense, between observations (O) & model predictions by PEP (C= Computation) O-C differences for each Julian Day (seconds) x O-C (seconds) JD relative to Within a single day, differences between (O-C)'s should have a very small variation. We study the quantity max(o-c)-min(o-c) for days where multiple measurements were recorded for Apollo 11, 14 and 15 48!
49 LLR tests of General Relativity! Science measurement / Precision test of violation of General Relativity! Time scale! Apollo/Lunokhod few cm accuracy*! MoonLIGHT 1 mm 0.1 mm! Parameterized Post-Newtonian (PPN) β! Few years! β-1 < ! 10-5! 10-6! Weak Equivalence Principle (WEP)! Few years! Δa/a < ! 10-14! 10-15! Strong Equivalence Principle (SEP)! Few years! η < ! ! ! Time Variation of the Gravitational ~5 years! Ġ/G <9 10 Constant! -13 yr -1! ! ! Inverse Square Law (ISL)! ~10 years! α < ! 10-12! 10-13! Geodetic Precession! Few years! K gp < ! ! ! * J. G. Williams, S. G. Turyshev,and D. H. Boggs, PRL 93, (2004) Our measurement of the Geodetic Precession with Apollo/Lunokohd, including new APOLLO station, with Planetary Ephemeris Program (PEP) by CfA: ~1% accuracy!! Number of laser returns to make a standard ~2-cm LLR range:! - MoonLIGHT single, large reflector: ~1! - Apollo/Lunokhod/Luna-Glob multi-reflector array: few thousands! 49!
50 LLR measurement of geodetic precession 3-body effect (Sun, Earth, Moon) predicted by GR: precession of a moving gyroscope (the Moon orbiting the Earth) in the field of the Sun The precession due simply to the presence of a central mass is ~ (3.00± 0.02)m/M orbit ~ 2 /cy SUN MOON arcsec/anno DE SITTER EFFECT Relative deviation of geodetic precession from GR value: JPL: J. G. Williams et al 2004 PRL. 93, K GP = (-1.9 ± 6.4) x10-3 Our measurement with CfA s software (Planetary Ephemeris Program): ~ 1% accuracy LLR data give unique science products both in relativistic gravity AND in lunar geophysics. Ω G geodetic precession r 0 circular orbit radius v gyroscope velocity r position vector G gravitational constant M central body mass 50!
51 Limits on 1/r 2 deviations in the Solar System! MoonLIGHT designed to provide accuracy of 100µm or better on tspace segment (the CCR), if deployed by drilling the regolith (Lunar Google X Prize, Astrobotic mission) Limits on additional Yukawa potential:! α (Newtonian-gravity) e -r/λ If other error sources on LLR will improve with time at the same level, then MoonLIGHT CCRs will improve limits on α from ~10-10 to ~10-12 at scales λ of ~10 6 meters Untested regions! 51!
52 Unique to LLR: test Strong EP (and PPN β)! LLR test of EP sensitive to both composition-dependent (CD) and self-energy violations! University of Washington (UW) laboratory EP experiment with miniature Earth and Moon, measures only CD contribution:!!!!![(m G /M I ) earth - [(M G /M I ) moon ] WEP,UW = (1.0 ± 1.4) 10-13!!![(M G /M I ) earth - [(M G /M I ) moon ] WEP,LLR = (-1.0 ± 1.4) 10-13! Subtracting UW from LLR results one gets the SEP test:!!![(m G /M I ) earth - [(M G /M I ) moon ] SEP = (-2.0 ± 2.0) 10-13! Assuming Nordtvedt effect: limit PPN parameter β at 10-4 ) SEP can only be tested LLR! 52!! Williams et al, arxiv: gr-qc/ v2, 2 Jan 2009! UW: Baessler et al, PRL 83, 3585 (1999);! Adelberger et al Cl. Q. Gravity 12, 2397 (2001)!
53 LLR Time-of-Flight residuals with PEP! Data by station from 1980s to 2009 Red: dedicated APOLLO station, optimized performance! 53!
54 Rotation/Librations: well measured by LNF! 1980s to 2009 Red: dedicated APOLLO station (T. Murphy)! 54!
55 Test of geodetic precession K GP with LLR! 5 th test of General Relativity! First measured at 2% accuracy in 1988 by Shapiro et al!! CfA+LNF current accuracy with PEP, Apollo arrays and APOLLO laser station: 1%! M. Martini et al, Planetary and Space Science 74 (2012) ! Comparable with accuracy by JPL =0.64%! J. G. Williams et al, PRL 93, (2004)!! Gravity Probe B final result on GP, accuracy: =0.28%! C.W. F. Everitt et al, PRL 106, (2011)! 55!
56 Other MoonLIGHT physics goals! Extend program to Mars, Jupiter, Saturn moons! New gravity predictions & solar system constraints! Already done: extension of GR to include spacetime torsion! Non-minimally coupled, modified gravity theories f 2 (R)! With O. Bertolami/J. Paramos, Porto/Lisbon, Portugal! 56!
57 New Gravity & Solar System Constraints! PRD 88, (2013)! Studying possible NMC contributions to Yukawa Potential! 57!
58 Sant Anna: ML Pointing System (MPS)! Two motors + CCD (to locate Earth and point it after landing)! Stowage screen (for dust protection during landing); ~1.3 kg! Group led by Co-I Calogero Oddo! Pointing requirement: about +/- 2 o! MoonLIGHT Needs an Automatic Pointing System! Needs Only a Start Pulse! Operational Sequence (at equator site)! Point to Zenith! Take a Camera Exposure! Fit Earth Image (On-Board)! If Missing -Search off Zenith! Lock Brakes! 58!
59 Moon Express-1 Mission to the Moon 59!
60 Moon Express-1 Mission Concept 60!
61 MoonLIGHT on MEX-1 top deck Launch by Dec !
62 Astrobotic Landing-Roving Mission to the Moon Griffin lander. Launch by Space X with Falcon 9! On October 2015! Deployment on regolith! From! Payload User Guide 3.0! 62!
63 Passive, 25 gr, 60 mm 20 mm, no pointing! INRRI :! INstrument for landing-roving laser ranging/altimetry Retroreflector Investigations! Perfect for Lander, Rovers on moons and (Exo)Mars 2018! ExoMars is strategic, cornerstone, super-approved, ESA- Roskosmos mission! UniCal, 28/11/2013! S. Dell Agnello (INFN-LNF) et al! 63!
64 INRRI on ExoMars and other moon Rovers! Laser-positioned by Orbiter during exploration! Orbiter radio-positioned by Earth! Curiosity, Opportunity, Spirit do not have reflectors! INRRI on ExoMars 2018 will be a first! Beyond INRRI: new generation gravity mission! GETEMME: Gravity, Einstein s Theory, and Exploration of Martian Moons Environment! Orbiter deploys two reflector arrays on Phobos and Deimos! Orbiter laser-ranged by Earth! Orbiter laser-ranges arrays! 64!
65 INRRIs at: Moon; Mars, Jupiter/Saturn moons! Cartoon not to scale! Laser altimeter! Laser! ranging! Planet/asteroid/ icy-rocky moon! rover at EoL! Petit Poucet rover:! arm, CCR, camera!!! 1064! nm! Planet/asteroid/icy-rocky moon! rock! or iceberg! VIS! camera! Crater or canyon or iced sea?! Selenolocate rover activity from orbiters thanks to CCR (reflector):! Laser altimetry at nadir (LRO-like) to rovers at poles of moons! Laser ranging with pointing capability to CCRs anywhere (GETEMME-like)! Deploy CCR networks! Also on far side of Earth s Moon! UniCal, 28/11/2013! S. Dell Agnello (INFN-LNF) et al! 65!
66 ExoMars 2018:" strategic, cornerstone ESA mission! 66!
67 Other collaboration opportunities! In addition to proposed SIACE Doctorate project:! HORIZON 2020 Space event yesterday 27/11/2013 in Rome Excellent Science! LEIT (Leadership in Enabling Industrial Innovation)! Participation in INFN-CSN2 experiment MoonLIGHT-2! Regional funding calls! MIUR funding calls!.! INFN-LNF School & Confs! LTL-2014 Cosenza-Rome Doctoral Laboratory Test facilities at INFN-LNF (SCF_Lab; and particle accelerators)! LFN Spring School! Vulcano 2014 workshop: astroparticle, astrophysics, gravity, cosmology! 67!
68 Acronyms and definitions! 1. AM0: Air Mass Zero! 2. ASI: Agenzia Spaziale Italiana! 3. BT: Break Through! 4. CCR: Cube Corner Retroreflector! 5. EO = Earth Observation! 6. ESA: European Space Agency! 7. ETRUSCO: Extra Terrestrial Ranging to Unified Satellite Constellation! 8. FFDP: Far Field Diffraction Pattern! 9. FOC: Full Orbit Capability! 10. GCO: GNSS Critical half Orbit! 11. GMES = Global Monitoring for Environment and Security! 12. GNSS : Global Navigation Satellite System! 13. GPS: Global Positioning System! 14. GRA: GNSS Retroreflector Arrays! 13. GTRF: Galileo Terrestrial Reference Frame! 14. ILRS: International Laser Ranging Service! 15. IOV: In Orbit Validation! 16. IPR: Intellectual Property Rights! 17. ITRF: International Terrestrial Reference Frame! 18. ITRS: International Terrestrial Reference System! 19. KPI: Key Performance Indicator! 20. OCS: Optical Cross Section! 21. LAGEOS: LAser GEOdynamics Satellite! 22. SCF: Satellite/lunar/GNSS laser ranging and altimetry Characterization Facility! 23. SCF-G: Satellite laser ranging Characterization Facility optimized for GNSS! 24. SLR: Satellite Laser Ranging! 25. TIR: Total Internal Reflection! 26. WI: Wavefront Interferogram! 68!
69 Main Reference Documents! [RD-1] Dell Agnello, S., et al, Creation of the new industry-standard space test of laser retroreflectors for the GNSS and LAGEOS, J. Adv. Space Res. 47 (2011) [RD-2] P. Willis, Preface, Scientific applications of Galileo and other Global Navigation Satellite Systems (II), J. Adv. Space Res., 47 (2011) 769. [RD-3] D. Currie, S. Dell Agnello, G. Delle Monache, A Lunar Laser Ranging Array for the 21st Century, Acta Astron. 68 (2011) [RD-4] Dell Agnello, S., et al, Fundamental physics and absolute positioning metrology with the MAGIA lunar orbiter, Exp Astron, October 2011, Volume 32, Issue 1, pp ASI Phase A study. [RD-5] Dell Agnello, S. et al, A Lunar Laser Ranging Retro-Reflector Array for NASA's Manned Landings, the International Lunar Network and the Proposed ASI Lunar Mission MAGIA, Proceedings of the 16th International Workshop on Laser Ranging, Space Research Centre, Polish Academy of Sciences Warsaw, Poland, [RD-6] International Lunar Network ( Core Instrument and Communications Working Group Final Reports. [RD-7] Yi Mao, Max Tegmark, Alan H. Guth, and Serkan Cabi, Constraining torsion with Gravity Probe B, Physical Review D 76, (2007). [RD-8] March, R., Bellettini, G., Tauraso, R., Dell Agnello, S., Constraining spacetime torsion with the Moon and Mercury, Physical Review D 83, (2011). [RD-9] March, R., Bellettini, G., Tauraso, R., Dell Agnello, S., Constraining spacetime torsion with LAGEOS, Gen Relativ Gravit (2011) 43: [RD-10] ETRUSCO-2: An ASI-INFN project of technological development and SCF-Test of GNSS LASER Retroreflector Arrays, S, Dell Agnello, 3 rd International Colloquium on on Scientific and Fundamental Aspects of the Galileo Programme, Copenhagen, Denmark, August !
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