APOLLO - · • APOLLO is a millimeter-capable lunar ranging station with unprecedented performance • Given the order-of-magnitude gains in range precision, we expect order-of-magnitude

APOLLO

Testing Gravitation

via

Laser Ranging to the Moon

Tom Murphy (UCSD)

photo credit: Jack Dembicky

2012.05.17 Sackler Conf. on Theoretical Astrophysics 2

The Parameterized Post Newtonian (PPN) Metric

• Generalized metric abandoning many fundamental assumptions

– Will & Nordtvedt, 1972

– GR is a special case

– Allows violations of conservations, Lorentz invariance, etc.


Simplified (Conservative) PPN Equations of Motion

Newtonian piece

gravitomagnetic

pieces


Relativistic Observables in the Lunar Range

• Lunar Laser Ranging provides a comprehensive probe of gravity, currently boasting the best tests of: – Equivalence Principle (mainly strong version, but check on weak)

• a/a 10−13; SEP to 4 10−4 β to 10−4

– time-rate-of-change of G

• fractional change < 10−12 per year

– gravitomagnetism (origin of “frame-dragging”)

• to 0.1% (from motions of point masses—not systemic rotation)

– geodetic precession

• to 0.5%

– 1/r2 force law

• to 10−10 times the strength of gravity at 108 m scales

– APOLLO effort will improve by 10

• access new physics (e.g., DGP, etc.)


Equivalence Principle Flavors

• Weak EP – Composition difference: e.g., iron in earth vs. silicates in moon

– Probes all interactions but gravity itself • Currently tested by LLR to a/a < 10−13

• Comparable to best lab tests by Eöt-Wash group at UW – but better choices of mass pairs offer stronger WEP test than LLR

• Strong EP – Applies to gravitational “energy” itself

• Earth self-energy has equivalent mass (E = mc2) – Amounts to 4.6 10−10 of earth’s total mass-energy

• Does this mass have MG/MI = 1.00000?

– Another way to look at it: gravity pulls on gravity • This gets at nonlinear aspect of gravity (PPN )

– LLR provides the best way to test the SEP • pulsar timing is closest competitor


The Strong Equivalence Principle

• Earth’s energy of assembly amounts to 4.6 10-10 of its total mass-energy

The ratio of gravitational to inertial mass for this self energy is

The resulting range signal is then

Currently is limited by LLR to be ≤4.5 10-4


Equivalence Principle Signal

• If the Equivalence Principle (EP) is Violated: – In effect, gravitational mass and inertial

mass are not equal

– Earth and Moon would fall at different rates toward the sun

– Would appear as a polarization of the lunar orbit

– Range signal has form of cosD (D is lunar phase angle: 0 = new; 180 = full)

• If, for example, Earth has greater inertial mass than gravitational mass (while the moon does not): – Earth is sluggish to move

– Alternatively, pulled weakly by gravity

– Takes orbit of larger radius (than does Moon)

– Appears that Moon’s orbit is shifted toward sun: cosD signal

Sun

Nominal orbit:

Moon follows this, on average

Sluggish orbit


Measuring G-dot & Significance

• Quadratic sensitivity: – If G changes with time, Kepler’s law is broken

– Range signal (semi-major axis) and period (phase) no longer run in lock-step (separable from tidal dissipation)

– The rate of phase slippage grows linearly in time

– The phase offset grows quadratically in time

– LLR sensitivity now limits change to ≤10-12/yr variation

– Less than 1% change over age of Universe

• Extra-dimension–motivated explanations of Universe’s acceleration (AdS/CFT) result in evolution of G and equation-of-state parameter w – Steinhardt & Wesley (2010) claim that factor-of-two

improvements in G-dot and w’ over today’s limits will rule out AdS/CFT as mechanism for acceleration at >3

A Word on Gravitomagnetism

• Applied to a rotating mass current, gravitomagnetism produces Lense-Thirring or Schiff precessions – this is but one possible phenomenological manifestation

• Gravitomagnetism on the Earth-Moon system (in SSB frame)produces six meter range amplitudes in both cosD and cos2D

– measured/constrained to < 1 cm tested to 0.1%

• Gravitomagnetism is a necessary piece of frame invariance – already tested well enough that it must be present at well < 1%

– departures of LT tests would require exotic aspect of rotation


Inverse Square Law Performance

Adelberger, Heckel, & Nelson (2000)


LLR through the decades Previously

200 meters


APOLLO: one giant leap for LLR

• APOLLO offers order-of-magnitude improvements to LLR by: – Using a 3.5 meter telescope

– Using avalanche photodiode array

– Gathering multiple photons/shot

• Achieving millimeter range precision

– Tightly integrating experiment and analysis

– Having a fundable acronym

• funded by NASA & NSF

• Initiated at UW (with Stubbs/Adelberger) – now spread across country

2012.05.17 Sackler Conf. on Theoretical Astrophysics 13 Photo by NASA


Lunar Retroreflector Arrays

Corner cubes

Apollo 14 retroreflector array




The Reflector Positions

• Three Apollo missions left reflectors

– Apollo 11: 100-element



• Two French-built, Soviet-landed reflectors were placed on rovers

– Luna 17: Lunokhod 1 rover

– Luna 21: Lunokhod 2 rover

– similar in size to A11, A14

• Signal loss is huge:

– 10−8 of photons launched find reflector (atmospheric seeing)

– 10−8 of returned photons find telescope (corner cube diffraction)

– >1017 loss considering other optical/detection losses

The Earth-End

3.5 meter

2.5 meter

laser

people

2012.05.17 16 Sackler Conf. on Theoretical Astrophysics


APOLLO’s Secret Weapon: Aperture

• The Apache Point Observatory’s 3.5 meter telescope

– Southern NM (Sunspot)

– 9,200 ft (2800 m) elevation

– Great “seeing”: 1 arcsec – Flexibly scheduled, high-class

research telescope • APOLLO gets 8–10 < 1 hour

sessions per lunar month

– 7-university consortium (UW NMSU, U Chicago, Princeton, Johns Hopkins, Colorado, Virginia)


Laser Mounted on Telescope


A Telescope in Reverse


Gigantic Laser Pointer


Killer Returns 2007.11.19 Apollo 15 Apollo 11

• 6624 photons in 5000 shots

• 369,840,578,287.4 0.8 mm

• 4 detections with 10 photons

• 2344 photons in 5000 shots

• 369,817,674,951.1 0.7 mm

• 1 detection with 8 photons

red curves are theoretical profiles: get convolved with fiducial to make lunar return

represents system

capability: laser;

detector; timing

electronics; etc.

RMS = 120 ps

(18 mm)

Fitting the Return & Reflector Trapezoid



Sensing the Array Size & Orientation 2007.10.28 2007.10.29 2007.11.19 2007.11.20

Grading the Astronauts’ Performance


Azimuth and tilt offsets of Apollo 15 reflector


APOLLO Data Campaign

• Steady accumulation of data; less reliance on Apollo 15 over time

• Found Lunokhod 1 in 2010

Somewhere on this slide…

…which is less than 1 kilometer across…

…lurks Lunokhod 1.

Hint: it looks like this…

…and I haven’t covered it up 100 m


Your discovery gives hope to all of us

who lost something during the seventies…

− Ed Leon

Apache Point Observatory



APOLLO Data Quality

• Uncertainties are per night, per reflector; pre-APOLLO sub-centimeter rare

• Medians are 2.4, 2.7, 2.4, 1.8, 3.3 mm for A11, L1, A14, A15, L2, resp.

• Combined nightly median range error is 1.4 mm

Branching Out to Other Reflectors


A11 A14

A15

A11 A14

A15 A11 A14

A15

L1 L2

Data Quality Example: Lunar Orientation


APOLLO data clearly call for orientation adjustments each night (vertical bands)

• Apollo 11

• Apollo 14

• Apollo 15

• Lunokhod 2

Re-orienting all the models


10 nrad

is 17 mm

at the Moon’s

surface

A closer look at the best model (JPL)


More weight to APOLLO data model does better on orientation


Next Step: Model Development

• Extracting science from LLR data requires a model that includes all the physics that can influence the Earth-Moon range

– N-body relativistic gravity in solar system

– body figure torques

– site displacement phenomena

• The best LLR models currently produce > 15 mm residuals

• Many few-millimeter effects are not yet included

– crustal loading phenomena from atmosphere, ocean, hydrology

– geocenter motion (center of mass with respect to geometry)

– tidal model needs improvement

– atmospheric propagation delay model needs updating

– Earth orientation models could better incorporate LLR data

– multipole representations of Earth and Moon mass distributions need improvement


Summary & Next Steps

• LLR is a versatile, comprehensive probe of gravitational physics

• APOLLO is a millimeter-capable lunar ranging station with unprecedented performance

• Given the order-of-magnitude gains in range precision, we expect order-of-magnitude gains in a variety of tests of fundamental gravity

• Now grappling with analysis in the face of vastly better data – much new stuff to learn, with concomitant refinements to data reduction

and to the analytical model

– plans to adapt open source LLR/planetary analysis code

• Some surprises along the way – found lost Lunokhod 1 reflector; now have 5

– degradation of reflectors (most likely dust; factor of ten impact)

Eclipse Pics

2012.05.17 Sackler Conf. on Theoretical Astrophysics 35 photo credits: Jack Dembicky


Gravitomagnetism

• A moving mass produces a gravitomagnetic field, which then couples to other masses through a Lorentz-like force

F = mv B

• Like any magnetic field, gravitomagnetism carries with it a strong frame dependence – as in electromagnetism, the magnetic field can be seen as a necessary

complement to the electric field to satisfy frame invariance

• True that magnetic fields from arbitrary mass currents cannot be transformed away by a frame change – a rotating collection of “charges” is a simple example

– but the inability to “kill” the resulting magnetic fields does not make these magnetic fields any more “real” than transformable varieties

• The earth moving in the Solar System Barycenter (SSB) frame produces a gravitomagnetic field through which the moon moves – resulting in deflections of the lunar orbit

– this field could be killed by shifting to the geocenter frame, but this is a poor choice of frame for analysis (not asymptotically flat)


Gravitomagnetic Effect

• The gravitomagnetic Lorentz acceleration term in the equation of motion looks like:

• If earth has velocity V, and moon is V+u, two terms of consequence emerge:

– One proportional to V2 with 6.5 meter cos2D signal

– One proportional to Vu with 6.1 meter cosD signal

• LLR determines cosD to 4 mm precision and cos2D to < 8 mm

– Constitutes a 0.1% confirmation of effect

• The same exact v v g term can be used to derive the precession of a gyroscope in the presence of a rotating mass current

– recovers the full effect sought by GP-B: this is not different physics

– see Murphy, Nordtvedt, & Turyshev, 2007, PRL 98, 071102


But isn’t this just transformation fluff?

• Since LLR is “performed” in the geocenter frame, where the gravitomagnetic field of the moving earth is nulled, can LLR really measure this physics?

• Actual process: – measure proper times in earth frame of photon transmit and receive

– transform these to SSB times using dt/d = 1 + ½v2

– perform least-squares fit of data to equation of motion

• In other words, we don’t apply phenomenological distortions to the orbit in moving to the SSB and then “magically” find we need them to fit our data (this would indeed be vacuous) – it is far more subtle: the simple time transformation is the only action

– there are small cosD effects in the v2 term, but at the few-mm level

• LLR needs the physics of gravitomagnetism to work correctly – if another experiment found an anomaly in gravitomagnetism at the 0.1%

level, LLR would stand in conflict and require resolution

– a conflict would indicate we don’t even understand time transformation sufficiently


APOLLO Laser

• Nd:YAG; flashlamp-pumped; mode-locked; cavity-dumped

• Frequency-doubled to 532 nm – 57% conversion efficiency

• 90 ps pulse width (FWHM)

• 115 mJ (green) per pulse – after double-pass amplifier

• 20 Hz pulse repetition rate

• 2.3 Watt average power

• GW peak power!!

• Beam is expanded to 3.5 meter aperture – Less of an eye hazard

– Less damaging to optics


Catching All the Photons

• Several photons per pulse necessitates multiple “buckets” to time-tag each one – Avalanche Photodiodes (APDs)

respond only to first photon

• Lincoln Lab prototype APD arrays are perfect for APOLLO – 4 4 array of 30 m elements on 100

m centers

• Lenslet array in front recovers full fill factor – Resultant field is 1.4 arcsec on a side

– Focused image is formed at lenslet

– 2-D tracking capability facilitates optimal efficiency


Superconducting Gravimeter Installed

• We care about millimeter displacements of floppy Earth crust – gravimeter has sub-millimeter height sensitivity

• Will help us characterize tides, measure loading of crust – fight gravity with gravity!


Fun with gravimetry

• One day saw three steps in gravity record

– unequal, within 10 minutes

• Turns out to have been giant concrete blocks used to load-test the observatory crane being moved away

– can tell which was moved first, second, third

• Also see telescope dome rotation as up to 5 nm/s2 offset

• See Earth ringing for a month after Chilean earthquake Feb. 2010 and Sendai in March 2011

– 20 minute period “breathing” mode

Gravity Signal from Dome

gravity dome azimuth



EarthScope GPS Pitching In

• The NSF-funded Plate Boundary Observatory (part of EarthScope) installed a GPS station 2.5 km away from APOLLO

• Resolution in monthly interval is 0.3 mm horizontal, 1.2 mm vertical

• Will help constrain crust motion, loading phenomena

90 180 270 360 0

100

50

0

10

Reflecto

r S

trength

(%

)

Lunar Phase

Reflector Degradation

what we expect

what we really get…

10% 1% : “the full moon curse”



APOLLO rates on Apollo 15 reflector

full

mo

on

background level


More on the deficit

• APOLLO system sensitivity is not to blame for full-moon deficit – background is not impacted

• Early LLR data trucked right through full-moon with no problem

• The deficit began to appear around 1979

• No full-moon ranges from 1985 until 2006, except during eclipse

1973 - 1976 1979 - 1984

What’s Wrong?

• The full-moon deficit, together with normal eclipse behavior, gives us the best clues: – thermal nature – absorbing solar flux

• Most likely: dust – Obviously could explain overall deficit

(10%)

• Full moon effect then due to solar heating of dust – sun comes straight down tube at

full moon – makes front hotter than vertex of

corner cube, leading to divergence of exit beam

– only takes 4°C (7°F) gradient to introduce 10× reduction

cool, quick route

warm, slow road


Modeling CCR Diffraction Patterns


Exploring Orientation & Thermal Gradients


Eclipse Opportunity

• On December 21, 2010 (UTC), a perfectly-positioned eclipse gave us a celestial light switch – verified that sunlight is responsible for full moon curse

– examine response time: is it thermal effect in corner cubes?

perfect eclipse for North America


Illu

min

ation; T

herm

al G

radie

nt;

Retu

rn S

trength

Time

Cartoon of Expectations


hot face

cold face

zero crossing

response peak

Preliminary Eclipse Results

full shadow

robust recovery initially, then down, and brief resurgence once light returns


Apollo 11

Apollo 14

(Apollo 15)/3.0

historical peak range @ F.M.


The Lunokhod 1 Reflector

• 14 triangular CCRs, 11 cm side length • Landed November 1970 • Sporadic early reports of Soviet and French ranging; no records persist • Identical design to later Lunokhod 2 reflector

– would expect L1 to be weak, like L2…or worse


Location Determination

• Range measurements at different librations allow us to pinpoint the reflector location

• Each range measurement is a slice intersecting the moon in a “small” circle centered on the sub-earth point

• For L1, the arcs cross at a maximum of ~20

• Our observations through June 2010 are enough to constrain the position in selenographic coordinates to about 0.1 m


Current Error Ellipse • Based on a few months of

observation at a limited sampling of librations, we have a centimeter-level position determination

• Error ellipses are 1 , 2 , 3

• Best-fit position, in DE421 Principal-Axis coordinates:

– r = 1734928.72

– lat = 38.3330784

– lon = -35.036674

• Location of L1 makes it especially valuable for science


Potential Impact on Science • L1 is the farthest reflector from the

apparent lunar center

• Offers best leverage on libration determination

– key for C.o.M. motion gravity

– also for lunar interior study

• Unlike Apollo reflectors, L1 (and L2) offer both latitude and longitude libration sensitivity

• More reflectors probe tidal deformation

Reflector from

center

libration

sensitiv.

longitude

sensitiv.

latitude

sensitiv.

A11 23.5 0.40 0.40 0.01

A14 17.9 0.31 0.30 0.06

A15 26.4 0.44 0.06 0.44

L1 50.0 0.77 0.45 0.51

L2 39.5 0.63 0.46 0.37

Documents

APOLLO - · • APOLLO is a millimeter-capable lunar ranging station with unprecedented performance • Given the order-of-magnitude gains in range precision, we expect order-of-magnitude