Lunar Laser Ranging Stephen M Merkowitz NASA Goddard Space Flight Center February 22 2007 Overview History and Background Ranging System Science Next Steps Lunar Ranging UMD 2 22 07 2 Bouncing Light Off The Moon First suggested by R H Dicke in early 1950s MIT and soviet Union bounced laser light off lunar surface in 1960s Retroreflectors proposed for Surveyor missions but not flown Finally flown on Apollo Retroreflectors will return light back to its source Array of reflectors provide high cross section Single photon detection required due to r4 signal loss 10 21 over the 2x385 000 km round trip Lunar Ranging UMD 2 22 07 3 Apollo Missions Lunar Ranging UMD 2 22 07 Apollo arrays used fused silica circular opening cubes 3 8 cm diameter each Apollo 11 and 14 arrays used 100 cubes Apollo 15 used 300 cubes 4 Lunar Ranging UMD 2 22 07 7 Lunar Ranging UMD 2 22 07 8 Soviet Luna Missions Lunokhod Lunokhod arrays consist of 14 triangular shaped cubes each side 11cm Only Lunokhod 2 is still visible Lunar Ranging UMD 2 22 07 9 35 Years of LLR Lick Observatory in California got first light in 1969 McDonald Observatory in Texas 1969 to present Other early ranges Crimean astrophysical observatory in the Soviet Union Orroral Observatory in Australia Air Force Cambridge Research Laboratories Lunar Ranging Observatory in Arizona The Pic du Midi Observatory in France Calame et al 1970 Tokyo Astronomical Observatory Orroral Observatory in Australia 1978 to 1980 Observatoire de la C te d Azur OCA in France 1984 to present Haleakala Observatory on Maui in Hawaii 1984 to 1990 Apache Point Observatory in New Mexico is starting operation Lunar Ranging UMD 2 22 07 10 History of LLR J G Williams et al gr qc 0507083 Lunar Ranging UMD 2 22 07 11 Satellite Laser Ranging SLR LAGEOS 35 stations in operation tracking over 100 satellites Satellite Laser Ranging began in 1964 at NASA Goddard Space Flight Center Lunar Ranging UMD 2 22 07 http ilrs gsfc nasa gov 12 Ranging System Lunar Ranging UMD 2 22 07 13 Measurement Statistical Error Source OCA Error ps Laser pulse width 30 Laser pulse leading edge variations 4 Start pulse detection 5 Return detector position response Timer precision and stability 10 ps 3 mm 35 50 5 Retroreflector orientation 0 350 Background light 0 300 Clock stability Allan variance 10 Calibration errors 4 Atmosphere 0 Best case total 60 E Samain et al Astron Astrophys Suppl Ser 130 235 1998 Lunar Ranging UMD 2 22 07 14 Measurement Accuracy Source OCA Error ps Clock accuracy 3 Calibration cube reference point 10 Calibration return detector accuracy 65 Atmosphere 15 70 Statistical 65 350 Best case total 350 Typical normal point averaged 160 10 ps 3 mm E Samain et al Astron Astrophys Suppl Ser 130 235 1998 Lunar Ranging UMD 2 22 07 15 Modeling Modeling orbit dynamics r Gravitational interaction between Sun Moon Earth Planets Includes masses and relativity parameters Asteroid attractions Newtonian attraction between bodies and gravitational harmonics Tidal effects Lunar rotation dynamics Torques from other bodies Dissipative torque from fluid core Effects at lunar reflector Tidal effects Relative lunar orientation Time delays Atmospheric Relativistic time delay Other effects Solar radiation pressure Thermal expansion of reflectors Effects at Earth station Plate motion Tidal effects Orientation of Earth s rotation axis J G Williams et al gr qc 0507083 Lunar Ranging UMD 2 22 07 16 Science of LLR Lunar ephemerides are a product of the LLR analysis used by current and future spacecraft missions Lunar ranging has greatly improved knowledge of the Moon s orbit enough to permit accurate analyses of solar eclipses as far back as 1400 B C Gravitational physics Tests of the Equivalence principle Accurate determination of the PPN parameter Limits on the time variation of the gravitational constant G Relativistic precession of lunar orbit geodetic precession Lunar Science Lunar tides Interior structure Lunar Ranging UMD 2 22 07 17 Testing the Equivalence Principle A violation of the Equivalence Principle would cause the Earth and Moon to fall at different rates toward the Sun resulting in a polarization of the lunar orbit This polarization shows up in LLR as a displacement along the Earth Sun line with a 29 53 day synodic period Torsion pendulum measurements at UW on Earth Moon like test bodies separates out composition dependence The current limit on the Strong Equivalence Principle MG MI EP 1 0 1 4 x10 13 4 4 4 5 x10 4 a M G M G a M I 1 M I 2 MG U 1 MI Mc 2 U 3GM Mc 2 5Rc 2 4 3 U Um a e 2 4 45 10 10 2 a M ec M mc r t 13 1 cos m s t J G Williams et al Phys Rev Lett 93 261101 2004 S Bae ler et al Phys Rev Lett 83 3585 1999 Lunar Ranging UMD 2 22 07 18 Time Variation of G The strength of gravity is given by Newton s gravitational constant G Some scalar tensor theories of gravity predict some level of time variation in G This will lead to an evolving scale of the solar system and a change in the mass of compact bodies due to a variable gravitational binding energy The current limit on the time variation of G is given by LLR G G 4 9 10 13 year J G Williams et al Phys Rev Lett 93 261101 2004 Lunar Ranging UMD 2 22 07 19 Geodetic de Sitter precession A gyroscope moving through curved spacetime will precess with respect to the rest frame Earth Moon system behaves as a gyroscope with a predicted geodetic precession of 19 2 msec year Observed using LLR by measuring the lunar perigee precession The current limit on the deviation of the geodetic procession is Kgp 1 9 6 4 x10 3 J G Williams et al Phys Rev Lett 93 261101 2004 Lunar Ranging UMD 2 22 07 20 Parameterized Post Newtonian Limits In weak field limit post Newtonian the metric can be parameterized to describe most metric theories indicates how much spacetime curvature is produced per unit mass indicates how nonlinear gravity is self interaction 1 in General Relativity Limits on can be set from geodetic procession measurements but the best limits come from measurements of the gravitational time delay of light Shapiro effect Ranging measurement to the Cassini spacecraft set the current limit on 1 2 1 2 3 10 5 combined with LLR data provides the best limit on 1 1 2 1 1 10 4 B Bertotti et al Nature 425 374 2003 J G Williams et al Phys Rev Lett 93 261101 2004 Lunar Ranging UMD 2 22 07 21 Lunar Science Lunar tides characterized by Love numbers are measured by LLR Love numbers give information on the elastic properties of the lunar interior k2 has an accuracy of 11