Shooting
the Moon
Getting Down
With Gravity
Eric L. Michelsen, PhD
Tom Murphy, Principal Investigator
UCSD Center for Astrophysics and Space Science
Topics
Who?
 What?
 Why?
 How?
 Where?
 When?
 Little lost rover

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Support


Our research is funded jointly by NASA, and the
National Science Foundation.
Which means: You!

APOLLO is based at UCSD, California
This presentation is based on one by Tom Murphy, UCSD
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What Do We Do?

We trace out the orbit of the moon by measuring
the distance to it to 1 mm
• thickness of a dime
• The moon is ¼ million miles away (~400,000 km)
• like measuring the distance around the equator to the
thickness of a sheet of paper

Lunar Laser Ranging
Who Am I?

Eric L. Michelsen
• PhD from UCSD, June 2010

Thesis topic: Lunar Laser Ranging
• Center for Astrophysics and Space Science (CASS)
My One Sentence

The fundamental basis of all science is that
thinking (theory) and experiment go hand in
hand.
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Why Fundamental Research?



We don’t know
But we have some ideas
80 years ago, physicists
studied new subatomic
particles: positrons
• Today, positrons save
1000s of lives a year
through Positron Emission
Tomography



Newton’s gravity got us to the moon
Einstein’s General Relativity got us GPS
LLR: Space missions? Asteroids? Particles?
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Galileo’s Equivalence Principle


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Galileo is said to have
dropped different objects
from the Leaning Tower of
Pisa to see if they fell at the
same rate
Galileo concluded that
indeed they do
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Could We Have Guessed This?



Is it reasonable that heavy objects fall faster?
Thought Experiment
But the ultimate arbiter is real experiment
• Thinking (theory) and experiment go hand-in-hand
Is this one ball
or two?
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Einstein’s Remarkable Insight


Thought experiments lead to the
1915 revolution in gravity:
General Relativity
Spacetime is a fabric that stretches
and twists
• Mass-energy bends spacetime,
influencing the motion of nearby
objects

GR rigorously tested for years
• Mercury orbit precession
• Deflection of starlight
• Slowing of time (vital for
Global Positioning System!)
• Lunar Laser Ranging
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G  8 T
Curvature is proportional to mass
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Why Isn’t General Relativity Good Enough?


GR and Quantum
Mechanics don’t mix
The expansion of the
Universe is not
following the expected
rules
• it’s accelerating!
• most of the universe is in
forms unknown to us

Composition of the Universe
visible matter
and energy, 5%
dark
matter
25%
dark energy
70%
Did Einstein have the
last word on gravity?
• unlikely
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How Do We Test Theories of Gravity?





Drop canonballs from the Leaning Tower of
Pisa
Laboratory measurements: extremely delicate
(e.g., Eot-Wash)
Lunar Laser Ranging (LLR) traces the orbit of
the Moon by measuring its distance repeatedly
over time
Other orbits: planets
Space missions ($$$)
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What Are We Looking For?

New physics!
• That is, violations of General Relativity

E.g., what if we could drop the Earth and
Moon together onto the sun?
• Would they fall at the same rate?


Earth and Moon are different materials: iron
vs. silica (rock)
Earth and moon have different gravitational
binding energy
• Does E = mc2 apply to gravitational energy?
Einstein says yes!
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The Lunar Tower of Pisa
 What if Earth falls more
slowly than the Moon?
farther out
Earth orbit
closer in
Moon orbit,
on average
sun’s
gravity
• Earth is sluggish to
move (pulled weakly by
gravity)
• Then Earth orbit is
larger than Moon’s
• Appears that Moon’s
orbit is shifted toward
sun
Sun
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Because it’s
our closest,
cleanest,
biggest
example of
gravity in
action.
55 earth
radii
Earth
(to scale)
apogee
perigee
Why use the Moon?
65 earth
radii
Year 2003 orbits.
Weak Gravity Acceleration Law

Used to model the Solar System
ri -point-mass 

Newtonian
 j rˆij 
1
rij2 
j i


2   
c2
1
c2

k i
j
r
2
j  i ij
scalar perturbations modify magnitude
vj
2 1   
k
vi 2
2  1
3
 2
  2  1    2 
r

r

rˆ  r j
i
j
2
2 ij
rik
r
c k  j jk
c
c
c
2c
k

rˆij   2  2  ri  1  2  r j  rij 
velocity terms ~ 1/r2
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2
3  4
2c 2



2


1
r

r
ij
j
2c 2

 jrj
vector perturbations modify
rij
direction & magnitude
j i
acceleration term ~ 1/r
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How Does Lunar Laser Ranging Work?
1.
2.
3.
4.
5.
Outbound pulse starts out 3.5 meters in diameter, 2 cm thick
Each pulse has 300 quadrillion (3 x 10 17) photons
Atmosphere causes pulse to diverge by 1 arc-second or more
At the moon, pulse is ~ 2 km across, still only 2 cm thick
Only ~1 in 30 million photons (= ~10 billion photons) in the 2
km disc hit the breadbox-sized reflector
Moon
Travels “faster than
light” from our earth
viewpoint
6.
Atmosphere
7.
8.
Telescope
Earth
Not to scale
9.
10.
11.
Return pulse expands ~8 arcseconds due to
corner-cube diffraction
Return pulse on earth is about 15 km across
About 3 of the returning photons hit the
3.5 m mirror, ~ 1 detected
APOLLO launches 20 pulses per second
Round trip time is about 2.5 seconds
There are ~50 pulses in-flight at any time
Right Back At Ya

Mirrors don’t work for us
• Reflection misses the Earth
Close up at mirror

Retroreflectors send light back exactly
the way it came in
• Back into our telescope
Close up at reflector
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Lunar Retroreflector Arrays
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Corner cubes
Apollo 11 retroreflector array
Apollo 14 retroreflector array
Apollo 15 retroreflector array
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Reflector Positions

Three Apollo missions left
reflectors
• Apollo 11: 100-element
• Apollo 14: 100-element
• Apollo 15: 300-element

Two French-built, Sovietlanded reflectors were placed
on rovers
• Luna 17, Lunakhod 1
(lost for 39 years, now found!)
• Luna 21, Lunakhod 2
• Similar in size to A11, A14
• Lunokhod 2 doesn’t work in
sunlight
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LLR Through the Decades

From U-Texas, France, and Italy
Uncertainty (cm)
Previously
100 meters
APOLLO
1mm
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The Next Big Thing In LLR
APOLLO offers 10x improvements in LLR with
1 millimeter range precision by:



Using a 3.5 meter telescope
Operating at 20 pulses/sec
12 simultaneous detectors
• other stations have only 1

Advanced detector technology
• 25 ps (3.5 mm resolution)
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Apache Point Observatory, NM


Southern NM (Sunspot)
3.5 meter telescope
• That’s big!
• High-grade research telescope

9,200 ft (2800 m) elevation
• Great “seeing”: 1 arcsec

New Mexico
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7-university consortium
•
•
•
•
•
•
•
U Washington
U Chicago
Johns Hopkins
Princeton
NMSU
Colorado
U Virginia
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Equipment Mounted on Telescope
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First Light: July 24, 2005
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World’s Biggest Laser Pointer
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Hunting for Airplanes
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Optical System
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APOLLO Laser



Nd:YAG mode-locked,
cavity-dumped
Frequency-doubled to
532 nm (green)
90 ps pulse width
• 1/10 of a billionth of a second


20 pulses per second
2.3 watt average power
• Less than a night light

1 gigawatt peak power!
• 1 billion watts

Beam expanded to 3.5
meters
• Less of an eye hazard
• Less damaging to optics
• Negligible diffraction
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Catching Some Rays


Image plane on
lenslet array

APD array
APD
APD
lenslet array
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Several photons per pulse
require multiple detectors to
time-tag each photon
44 array of .03 mm
circular detectors on 0.1
mm centers
Lenslet array in front
recovers all the light,
eliminating gaps between
APDs
• Focused image is formed at
lenslet
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16-channel APD Electronics
APD Package
daughter board
(magnified)
daughter
boards
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Gimme Some Latitude

APOLLO needs to know range to ~10m in advance
geocentric
latitude
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geodetic
latitude
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Example Data From an Early Run
Return photons
from reflector
width is < 0.5 m
2150 photons in
14,000 shots
Randomly-timed background photons (bright moon)
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Killer Returns
Apollo 15
represents system
capability: laser;
detector; timing
electronics; etc.
November 19, 2011
RMS = 120 ps
(18 mm)
6624 photons in 5000 shots
369,840,578,287.4  0.8 mm
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Apollo 11
2344 photons in 5000 shots
369,817,674,951.1  0.7 mm
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Lunokhod 1: Little Lost Rover

Soviet rover landed 17 November, 1970
• Attempt to blunt Apollo 11 victory in race
to the moon



Operated on surface for 10 months
Parked during lunar nights to allow
ranging attempts
Soviets and French both got returns
December 1970, on first lunar night
reflector
• But both failed in later attempts, even after
end of mission


Americans never convincingly found it
A 1976 report states that Soviets found
L1 again in May 1974
• Claims regular observations thereafter
• No substantiation

APOLLO tried occasionally, beginning
April 2008
• In hindsight, position was far off: no
chance of success
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Lost for 39 years
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The Lunokhod Reflectors





14 triangular CCRs, 11 cm side length
At 532 nm, expect brightness between A11/A14 and A15
However, L2 was once similar in strength to A15
But now L2 is 1/10th the strength of A15
So we expected L1 to be similar in strength to L2, at best
• Or maybe lack of returns meant L1, if found, would be weaker than L2
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Enter Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) helped three ways:
• LROC imaging (March 2010) found the rover and provided coordinates
• LOLA altimetry fixed the site radius
• A corner-cube-reflector array on LRO prompted APOLLO to develop a
wide-gate capability, making L1 searches easier (~80 m window vs
usual 10 m)
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“X” Marks the Spot
laser
pulses
to earth
sub-earth
point





We found it, and it’s strong!
Each range measurement is
a slice intersecting the lunar
surface in a circle, centered
on the sub-earth point
Range measurements at
different librations allow us
to pinpoint the reflector
Our observations through
June 2010 constrain the
position to about 0.1 m
Our lunar radius is ~1 m
larger than LOLA! Why?
5/28/2016
Reflector found April, 2010
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APOLLO Superlatives

APOLLO beats previous records by far
• Best 1-hour night (Oct 17 2008):




66,000 photons
more than Texas station in 38 years
four years-worth of French station
(who held previous records)
Detection rates up to 0.5 - 1 photons per pulse (10 20 per second)
• As high as 12 detected in a single pulse

Range with ease at full moon
• Current stations can’t fight the background

Our data precision exceeds the JPL model
• That’s expected: the model is based on data!

Precisely located the 39-year-lost rover Lunokhod 1
• Substantially improves gravity and lunar interior science
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Science on a Budget

APOLLO to date: $2 million
• Ground experiment

Allows repairs and upgrades
• Previous LLR claims 0.1% accuracy
on “gravitomagnetism”
• APOLLO aims to make that 0.01%

Gravity Probe B: $1 billion
• Space mission: implies high risk
• Targeting 1% accuracy on gravitomagnetism
• Sad failure: Unexpected noise in measurement


5/28/2016
no results
no hope of repair
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Project Status and Plans

Operating 7-9 nights per month
• ~1 hour each



Frequently achieve 1 mm precision in a night
Sufficient data for 10x tighter bounds on gravity
parameters in coming years
Eliminate remaining sources of systematic error
•
•
•
•

Earth tides (crustal deformation, few mm out of ~0.5 m)
Atmospheric delay (several mm out of 2 m)
Telescope thermal expansion (~3 mm)
First photon bias (~2 mm)
Acquire in-project solar system model
• Rapid analysis => rapid debugging of problems
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The End

Questions?
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New Ideas

Finding Lunokhod 1
• Reflector is 1 m above surface

We can detect size of reflectors from earth
• Like resolving .5m/400 Mm

Push benchtop detector ~1”, see histogram
jump
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Abstract
The APOLLO Lunar Laser Ranging operation measures the orbit of the moon
to 1 mm. It provides 10x improvements in precision over previous laser
ranging, as a new test of all major aspects of gravity. APOLLO is an
example of a world-class, high-precision physics experiment that operates
on a comparatively small budget. The keys to APOLLO’s improvements
are large aperture, multiple photon detector array, high laser output, and
good seeing at the telescope site. We present an overview of APOLLO’s
design, operation, and history, as well as examples of its theoretical
implications. We provide a rare, behind-the-scenes look at the reality of a
modern physics experiment, including its successes, some gaffes, and
unexplained results.
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What’s Happening Where
Lunokhod 1
Apollo 15
Lunokhod 2
Apollo 11
Apollo 14

Three Apollo missions left reflectors
• Apollo 11: 100-element
• Apollo 14: 100-element
• Apollo 15: 300-element

Two French-built, Soviet-landed reflectors were placed on rovers
•
•
•
•
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Luna 17, Lunokhod 1 (lost 39 years, now located by LRO and APOLLO)
Luna 21, Lunokhod 2
Similar in cross-section to A11, A14
Lunokhod 2 doesn’t work in sunlight
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Sensing the Array Size & Orientation
2007.10.28
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2007.10.29
2007.11.19
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APOLLO Return Rates
Reflector
APOLLO max APOLLO max APOLLO max APOLLO max
photons/shot
photons/run
photons/5-min photons/shot
(15 sec avg)
(5 min avg)
Apollo 11
4497 (26)
5395 (65)
0.90
1.4
Apollo 14
7606 (36)
9125 (69)
1.52
2.0
Apollo 15
15730 (26)
18875 (67)
3.15
4.5
750 (11)
900 (31)
0.15
0.24
Lunokhod 2
(relative to pre-APOLLO record)

APOLLO firmly into multi-photon-per-pulse regime
• French station record ~0.1; Texas ~0.02
• Some shots get 12 photons (out of 12 working detector
elements)
• Having a detector array is crucial: multiple buckets for
photons
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