Next-Generation Lunar Laser Ranging

Tom Murphy UCSD

Designing the Perfect Gravity Test

Gravity must be the dominant influence– Negligible frictional, electrostatic, radiation forces

Make test bodies large– Gravity dominates– Test Strong Equivalence Principle (SEP) by

having appreciable “self-energy”: how does gravity pull on gravity?

Place in vacuum environment

Precision Requirements

Order-of-Magnitude improvement over current measurements/tests of gravity– ~10-5 test of General Relativity

~10-14 measurement precision needed– Good clocks are 10-12

– Need leverage somehow

Earth-Moon System Fits the Bill

Earth “self-energy” is ~0.5×10-9 of total mass Moon is large, but only 0.02×10-9 in grav. energy

– Non-gravitational forces very small– Self-energy small compared to that of earth

Sun dominates for both bodies– Can test differential motion/acceleration to Sun

Leverage from proximity of moon to earth– Rearth-moon = 1/400 A.U. → test motion with respect to sun at 1

A.U. via much shorter (differential) measurement

Historical Accuracy of Lunar RangingW

eigh

ted

RM

S R

esid

ual (

cm)

1970 1975 1980 1985 1990 1995 2000 2005

30

25

20

15

10

5

0

Current PPN Constraints on GR

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

• Is the Parameterized Post-Newtonian (PPN) formalism still relevant?

• What fool would want to push this further? Isn’t GR obviously right?

Basic phenomenology:

measures curvature ofspacetime, measuresnonlinearity of gravity

Why Push Further: Aristotelian Analogy

1.5

-1.0 0-0.5 0.5 1.0

2.5

2.0

1.0

0.5

0.0

Trajectory Asymmetry

Tra

ject

ory

Pol

ynom

ial O

rder

Newtonian Gravity

Aristotelian“Gravity”

Einsteinian Departuresat ~10-8 level of precision

“Real” Rationale for Pushing Further

Gravity is incompatible with the Standard Model Cosmological departures from old GR model

– Acceleration of expansion of Universe

Fine structure constant, , possibly varying?– What about gravitational constant, Equivalence Principle

Scalar Field modifications to GR– Predictions of PPN departures from GR

Brane-world cosmological models– Gravitons leaking into bulk, modifying gravity at large scales

APOLLO: Next-Generation LLRrecipe for success:

Move LLR back to a large-aperture telescope– 3.5-meter: more photons!

Incorporate modern technology– Detectors, precision timing, laser

Re-couple data collection to analysis/science– Scientific enthusiasm drives progress

Devise brilliant acronym:– Apache Point Observatory Lunar Laser-ranging Operation

APOLLO Goals*:

One millimeter range precision Weak Equivalence Principle (WEP) to a/a ≈ 10-14

Strong Equivalence Principle (SEP) to ≈ 3×10-5

Gravitomegnetism (frame dragging) to 10-4

dG/dt to 10-13•G per year Geodetic precession ( ) to ≈ 3×10-4

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

* These 1 errors are simply ~10 times better than current LLR limits. In each case, LLR currently provides the best limits. Timescales to achieve stated results vary according to the nature of the signal.

The APOLLO Apparatus

Uses 3.5-meter telescope at 9200-ft Apache Point, NM

Excellent atmospheric “seeing”

532 nm Nd:YAG, 100 ps, 115 mJ/pulse, 20 Hz laser

Integrated avalanche photodiode (APD) arrays

Multi-photon capability Daylight/full-moon capability

APD Arrays

We have a working prototype courtesy MIT Lincoln Labs

4×4 format (LL has made much larger)

30m diameters on 100m centers

Fill-factor recovered by lenslet array

~30 ps jitter at 532 nm, ~50% photon detection eff.

Multiple “buckets” for photon bundle

Millimeter Range?!!

Seven picosecond round-trip travel time error Half-meter lunar reflectors at ±7° tilt → up to 35 mm

RMS uncertainty per photon 95 ps FWHM laser pulse → 6 mm RMS Need ~402 = 1600 photons to beat down error Calculate ~5 photon/pulse return for APOLLO “Realistic” 1 photon/pulse → 20 photons/sec →

millimeter statistics achieved on few-minute timescales

APOLLO Random Error Budget

Expected 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

APOLLO Systematic Errors

Various contributions to systematic error:– Atmospheric refractive delay (2-meter signal)– Ocean, atmosphere, and ground-water loading– Thermal expansion of telescope & reflectors

Will implement supplemental metrology on-site– Barometric transducer array– Superconducting gravimeter (<1 mm vertical displacements)– Precision GPS (0.5 mm horz., 2.3 mm vert. in 24 hr)

IMPORTANT: Science signals are narrow-band– Environmental factors will not mimic new physics

Laser Mounted on Telescope

Mounted June 2003

In thermal enclosure (“fridge”)

Timing Electronics Built/Verified

Timing System in Operation CAMAC Crate Inhabitants

APOLLO Command ModuleTiming/APD control, CPU interface

Calibration/Frequency Board

Future Laser Ranging Tests of GR

Interplanetary is next logical step Laser transponder on Mars measures to 4×10-6,

and to 10-5

Mercury orbiter (Messenger: launched) could be used to measure perihelion shift →

– May perform test-ranging from Apache Point this summer

LATOR (stay tuned for Turyshev talk) uses inter-spacecraft laser ranging to measure curvature of spacetime to unprecedented precision: to 10-8

APOLLO Collaboration

UCSD:Tom MurphyJohn GoodkindEric Michelsen

U. Washington:Eric AdelbergerJana StrasburgLarry Carey

Northwest Analysis:Ken Nordtvedt

JPL:Jim WilliamsJean DickeySlava Turyshev

Lincoln Labs:Brian AullBernie KosickiBob Reich

Harvard:Chris Stubbs

Joint NASA/NSF funding