Testing Gravity with Lunar Laser Ranging

DoE Site Visit

James Battat

August 21, 2006

Testing Gravity with Lunar Laser Ranging

New Mexico, near White Sands. Note SDSS

3.5 m

APOLLO

UCSD:Tom Murphy - PIEric MichelsenAdam Orin

Harvard:Christopher StubbsJames Battat

U. Washington:Eric AdelbergerErik SwansonC. D. HoyleLarry Carey

JPL:Jim WilliamsJean DickeySlava Turyshev

Lincoln Lab:Brian AullBernie KosickiBob Reich

Northwest Analysis:Ken Nordtvedt

Mapping the lunar orbit to 1 millimeter

APD detectors

Ephemeris

Why Push Gravity Tests Further?

• Order of magnitude in constraints

• Dark energy, w

• Scalar field modifications to GR– Predict non-GR effects

• Brane-world cosmology– Gravitons leaking into bulk modify gravity at

large scales

LLR is a Powerful Test of Gravity

With one millimeter range precision:

• Weak EP a/a 10-14

• Strong EP 3×10-5

• Gravitomagnetism 10-4

• dG/dt 10-13•G/year• Geodetic precession 3×10-4

• Long range forces 10-11 × the strength of gravity

* In each case, LLR currently provides the best limit.

LLR is a Powerful Test of Gravity

With one millimeter range precision:

• Weak EP a/a 10-14

• Strong EP 3×10-5

• Gravitomagnetism 10-4

• dG/dt 10-13•G/year• Geodetic precession 3×10-4

• Long range forces 10-11 × the strength of gravity

* In each case, LLR currently provides the best limit.

Nordtvedt Effect

Nordtvedt, Phys Rev, 169, 1014, 1968

Nordtvedt, Phys Rev, 169, 1017, 1968

Nordtvedt, Phys Rev, 170, 1186, 1968

Synodic period = 29.35 days

r = 13 cos(D) meters

Avalanche Photodiode Array

= 30m

-Courtesy of MIT Lincoln Lab

3.5 meter telescope

Good seeing

APOLLO: Reaching 1 mm

Laser Ranging Apparatus: Transmit

2.3 Watt NdYAG laser2.3 Watt NdYAG laser20 Hz, 20 Hz, = 530 nm = 530 nm < 100 ps pulse width< 100 ps pulse width110 mJ per pulse110 mJ per pulse

APD arrayAPD array

START

3.5m primary3.5m primary

LASER

Corner cubeCorner cube

Laser Ranging Apparatus: Receive

2.3 Watt NdYAG laser2.3 Watt NdYAG laser20 Hz, 20 Hz, = 530 nm = 530 nm < 100 ps pulse width< 100 ps pulse width110 mJ per pulse110 mJ per pulse

APD arrayAPD array

STOP

3.5m primary3.5m primary

LASER

25 km

4 km

~1017 attenuation

MOON

Interpretation Requires Sophisticated Modeling

Measure telescope-to-reflector distanceWant center-to-center separationThrough the atmosphereNeed precise ephemeris information – JPL collaboration

MLRS: The Old Way

28 photons in 42 minutes

Enter APOLLO

1,500 photons in 13 minutes

1 mm statistical uncertainty

Current Status

Millimeter precision dataReturns from all 3 Apollo arraysRemote operations

• Enter campaign mode (October)1-2 hours every 2-3 nights

• Improve site coordinates

• New constraints on gravitational params

The End

THE END

EXTRA SLIDES

APOLLO: Reaching 1 mm

• Large-aperture, good seeing– Figure of merit goes like (D/)2

• Incorporate modern technology– Detectors, precision timing, laser

• Re-couple data collection to analysis/science

LLR Targets

Gravitational Self-Energy + SEP

Object mSE/m

1 kg sphere, 6” diam 5 x 10-27

Moon 0.2 x 10-10

Earth 5 x 10-10

APOLLO Random Error BudgetExpected Statistical Error RMS Error (ps) One-way Error (mm)

Laser Pulse (95 ps FWHM) 40 6

APD Jitter 50 7

TDC Jitter 15 2.2

50 MHz Freq. Reference 7 1

APOLLO System Total 66 10

Lunar Retroreflector Array 80–230 12–35

Total Error per Photon 105–240 16–37

Nordtvedt, Class. Quantum Grav., 15, 3363, 1998

Lunar Phase Coverage

• EP violation has a null at Quarter moon and maxima at Full and New Moons

• Same data, uniform coverage gives tighter

No measurements at max signal

Current PPN Constraints

1

0.998 10.999 1.001 1.002

1.002

1.001

0.999

0.998

Lunar Laser Ranging

Mercury Perihelion Shift

Mars Radar Ranging

VLBI & combined planetary data

Spacecraft range & Doppler

Basic phenomenology:

measures curvature ofSpacetime

measures nonlinearity of gravity

= (2.1 § 2.3) x 10-5

= (1.2 § 1.1) x 10-4

= (4.4 § 4.5) x 10-4

Solar System Parameters• Separation

– Moon-Earth 0.38 million km– Sun-Earth 150 million km

• Mass– Sun 2 x 10^30 kg– Earth 6.0 x 10^24 kg– Moon 0.073 x 10^24 kg

• Radius– Sun 695,000 km– Earth 6380 km– Moon 1740 km

• Gravitational Constant6.67 x 10^-11 m^3 kg^-1 s^-2

Testing Gravity with Lunar Laser Ranging

Historical Accuracy of LLR Data

30 cm

0 cm

1970 present

Laser Ranging Apparatus

2.3 Watt NdYAG laser2.3 Watt NdYAG laser20 Hz, 20 Hz, = 530 nm = 530 nm < 100 ps pulse width< 100 ps pulse width110 mJ per pulse110 mJ per pulse

APD arrayAPD array START

3.5m primary3.5m primary

LASER

Corner cubeCorner cube

2.3 Watt NdYAG laser2.3 Watt NdYAG laser20 Hz, 20 Hz, = 530 nm = 530 nm < 100 ps pulse width< 100 ps pulse width110 mJ per pulse110 mJ per pulse

APD arrayAPD array

3.5m primary3.5m primary

Laser Ranging Apparatus

LASER

STOP