Hansjörg Dittus- Testing Gravity in the Solar System

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Testing Gravity in theSolar System

Hansjörg DittusCentre of Applied Space

Technology and Microgravity

ZARM, University of Bremen

with thanks to: Claus Lämmerzahl, Eva Hackmann, Benny Rievers, Stefanie Bremer, ZARMPioneer Anomaly Explorer Team

with support from: German Science Foundation (DFG),German Space Agency (DLR)



DESY, 30.9.2008

Outline

Outline

• Introduction / Motivation

• Experimental confirmation of GR with space tests

• History of space tests und running projects

• Unexplained phenomena / Observations in the solar system

• Anomalies from satellite tracking

• Pioneer Anomaly

• Present status of analysis

• Thermal models

• Other attempts for explanation

• Fly-by Anomaly

• GRACE Anomaly

• Outlook

Outline

• Introduction / Motivation• Experimental confirmation of GR with space tests

• History of space tests und running projects

• Unexplained phenomena / Observations in the solar system

• Anomalies from satellite tracking• Pioneer Anomaly

• Present status of analysis

• Thermal models

• Other attempts for explanation• Fly-by Anomaly

• GRACE Anomaly

• Outlook



DESY, 30.9.2008

Motivation

Theoretical Background – Standard Model of Quantum Physics

– Special Relativity

– General Relativity

– Statistical Physics

But:

– Incompatibility of Quantum Theoryand Gravitation

Unexplained phenomena ?

- Space – a unique laboratory

- Do we see effects on satellites in deepspace orbits?

- Is gravity modified on larger scales?

Experimental proofs

– Experimental confirmation of theStandard Model makes quantization of

space and time a likely approach – Gravitational theory well confirmed by

experiments and observations

– Precision Cosmology (COBE, W-MAP,etc.)


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Experimental confirmation of GR

Predictions:

• Solar System Effects• Perihelion shift• Gravitational Redshift• Light deflection• Time delay• Gravitomagnetic effects

• Strong field observations• Binary systems• Black holes

• Gravitational waves

• Cosmology

Foundations:

• Universality of Free Fall

• Local Lorentz Invariance

• Universality of Gravitational

Redshift

( )

( )2

330

4

2

200

21

4

221

c

U g

r c

r J g

c

U

c

U g

ij

ii

γ

µ

β α

+=

×=

−+−=

ρρ

Tests in the Post-New tonian frame

(not yet confirmed)

Gravity Probe BSchiff effect

LAGEOS satellitesLense-Thirringeffect

Gravity Probe Agravitationalredshift

Cassini S/Ctime delay

Very Long BaselineInterference

light deflection

astronomical

observations

perihelion shift

4104.11 −⋅≤−α

( ) 43

13

2 101 −≤−−+ β γα

4101 −≤−γ

51021 −⋅≤−γ

3105 −⋅≤

1.0≤





DESY, 30.9.2008

Shapiro Time Delay

)

( )( )

( )( )

( ) ( ) ( )( )( ) ∑∑

∑ ∑

∑

≠≠

≠ ≠

≠

−

+++−+⋅−

−+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅−+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

⋅−−⋅

+−+++

−

−−

−

+−⋅

−

−

=

i ji j

j

jii ji j

i j

j

ji j

i j

j ji

ji

ji

ik jk k j

j

k i

j

i ji j

i j j

i

r r

m

c

γr γr γr r

r r

m

c

r r r cr r

r r r

cr r

c

γ

c

r γ

c

r γ

r r

m

c

β

r r

m

c

γ β

r r

r r m

r

ρρ&ρ&ρρρ

ρρ

&&ρρρρρ

&ρρρ&ρ&ρ

&ρ&ρ

ρρρρ

ρρ&&ρ

G

2

432122

G1

1

2

3221

G12G21

G

232

2

2

222

2

2

2

22

3

Einstein-Infeld-Hoffmann Equation

Numerical models based on an isotropic PPN - n-body metric

Planets and asteroids considered to be point masses

Accelerations calculated wrt the barycentre of the solar system.

( ) ( )

( )( )

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−−+

−++++⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

++−−+

++−++++

−=

E

s

E

t

E

t

E

s

E

s

E

t

E

t

E

s E

S

S

s

S

t

S

t

S

s

S

S

s

S

t

S

t

S

sS

C

s

C

t

r r

r r

c

mγ

c / mγr r

c / mγr r

c

mγ

c

r r t ρρ

ρρ

ρρ

ρρρρ

r r

r r ln

G1

G1r r

G1r r ln

G132

2

3 ∆

Time delay in space time curved by sun and earth

Cassini Conjunction Experiment (Bertotti et al. 2002):

Satellite – Earth distance: > 109 km

Ranging: X~7.14GHz & Ka~34.1GHz (dual band)

Result: γ = 1 + (2.1 ± 2.3) × 10−5



DESY, 30.9.2008

Gravitational redshift

Gravity Probe A experiment (Vessot etal., 1974): ballistic rocket flight

Confirmation of the Universaliy of theGravitational Redshift:All clocks run the same and experiencethe same frequency shift in gravitational

fields– independent of their physicalcharacteristics

GP-A: comparison of H-masers on earthand in a capsule on a ballistic flight path

Accuracy

k – wave vector

u – 4-velocity of observer

4

2

1 10−≤⎟⎟

⎠

⎞

⎜⎜⎝

⎛

f

f δ C. Lämmerzahl

( )( )

( )( )

( ) ( )⎟ ⎠

⎞⎜⎝

⎛ −−==

2

21

200

100

2

1

2

1 1c

xU xU

x g

x g

uk

uk

f

f



DESY, 30.9.2008

Lunar Laser Ranging

Retroreflectors on moon surface:

Installed between 1969 and 1973

with Apollo 11,14,15 and Luna 17,21

Resolution: ca. 2 cm (< 1 cm)

Laser pulse width: 150 – 300 ps

Pulse frequency: 10 HzIlluminated area on moon surface: 20 km2

1 of 1019 photons observed (1 photonper 10 pulses)



DESY, 30.9.2008

⎟⎟ ⎠

⎞⎜⎜⎝

⎛ −⎟⎟

⎠

⎞⎜⎜⎝

⎛ +⎟⎟

⎠

⎞⎜⎜⎝

⎛ ⎟ ⎠

⎞⎜⎝

⎛ −⎟ ⎠

⎞⎜⎝

⎛ +′−

=3333

ΩΩ

MS

MS

ES

ES S

M

passive

ES

ES S

M E EM

EM total d

r r m

m

m

r

m

mmη

r

m rrrr

a

3

2121 103

1

3

2

3

2

3

10

34 −≤−−+−−−−≤ ζ ζ ααξ γ β ηNordtvedt parameter

Lunar Laser Ranging

Fe-dominated

Si-dominated

Earth and moon are of different chemical composition

and freely falling in the sun´s gravitational field. Thisenables to perform tests of the Weak EquivalencePrinciple by ranging between earth and moon.

Dependent on the validity of the StrongEquivalence Principle:

Does self-gravitation Ω contributes the

same to inertial and gravitational mass?

für2

G

ES

S E d

r

mηa =13

10−≤ E η



DESY, 30.9.2008

Precise measurement of gyro prececcions due to space-time curvature of the

rotating earth. Geodetic Precession: 6,6 arcsec per year

Lense-Thirring precession (frame dragging, Schiff effect):0,042 arcsec pro Jahr für die Lense-Thirring-Präzession

Experiment already proposed 1959 (!) (G. Pugh)

Carried out: April 2004 to August 2005

Gravity Probe B

F. Everitt, Stanford University

S hU v av S t

S ρρρρρρρ×⎟

⎠

⎞⎜⎝

⎛ ×∇+∇×+×−=×=

2

3

2

1Ω

d

d



DESY, 30.9.2008

Precise gyroscopes

• Ideally round spheres made fromfused silica, Nb-coated forsupercondcutivity:deviation from sphericity max. 5 nm

• Electrostatic levitation, frictionlessbearing:spin-rate change: 1 % in 1000 years

• Accuracy:10

-11° /h-1

(1 revolution in 11,5 billion years)

16 km

0,001´´

a hair from 16 km distance



DESY, 30.9.2008

Precision-thruster for satellites

Drag free control: Satellit follows a freelyfalling test mass on a geodetic

Closed-loop control of test mass movement

Micropropulsion thrusters guide the satellite

Field Emission Electrical Propulsion (FEEP)

Residual acceleration: ca. 10-14 m / s2

Thrust-increment resolution: ca. 0.1 µNSpecific impuls: > 10,000 s



DESY, 30.9.2008

Satelliten attitude and orbit control

GP-B attitude and orbit control needs 4·10-12

ms2 of residual acceleration for frequenciesbetween 10-2 and 10-5 Hz

Helium outgas of the 2,4 m3 Satellite Dewarused as propellant for cold gas proportional

thrusters; laminar flow at Re ~ 10.

594.55 594.6 594.65 594.7 594.75

-2

-1

0

1

2

3

x 10-8

Day of Year, 2004

P r o o f m a s s a c c e l e a t i o n ( m - s e c - 2 )

Engagement of DF control on Gyro 1 (Z axis)

10-4

10-3

10-2

10-1

100

10-11

10-10

10-9

10-8

10-7

10

-6

Frequency (Hz)

C o n t r o l e f f o r t , m / s e c

2

Gyro 1 - Space Vehicle and Gyro Ctrl Effort - Inertial space (2005/200, 14 days)

X Gyro CE

X SV CE

2×Orbit

Drag-free on

A c c e l e r a t i o n

( m / s e c 2 )

A c c e l e r a t i o n

( m / s e c 2 )

Drag-free off

x10-8

Cross-axis avg.1.1 x 10-11 g

Gravitygradient Roll

rate

F. Everitt et al.



DESY, 30.9.2008

Tests of the Equivalence Principle

10-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

1700 1750 1800 1850 1900 1950 2000

Newton

Bessel

Dicke

Eötvös

Adelberger , et.al.

Lunar ranging

Little String

Theory

α varying

Runaway Dilaton Theory

Neutrino exchange forces -

Fischbach

STEP

µSCOPE

Free fall on Earth ηE < 10-10

Torsion BalanceExperiments

ηE < 5·10-13

Lunar Laser Ranging ηE ≤ 10-13

MICROSCOPE (Satellite) ηE < 10-15

STEP (Satellite) ηE < 10-18



DESY, 30.9.2008

WEP tests on satellites

md12

1 1031−

≈= E r r η

r 1

For weak mechanical coupling bothtest masses as well as the satelliteform a spring-mass system, whichamplitude varies periodically withorbit frequency. Can be measuredwith high precision..

Orbit radius difference too smallfor direct measurment



DESY, 30.9.2008

MICROSCOPE

X

Z

Y

x-axis: sensitive axis

z-axis: satllite spin axis

Micro-satelliteà Trainée Componsée pour

l´Observation du Principed´Equivalence

Missions parameter:

Sunsynchronous orbit: 660 km Orbit exzentricity: < 5 · 10-3

Spin rate: varying for modulation of theorbit-frequency

Signal frequenz:

( π +1/2) f orb und ( π +3/2) f orb

Missions duration: 6 to 12 months

Satellite mass: < 120 kg



DESY, 30.9.2008

MICROSCOPE design

• Cylindrical test masses

• Identical moments of inertia to avoidinfluences of theinhomogeneity of the

earth´s gravitationalfield

• Struktural elements madefrom zerodur glass ceramics

• Au-couated electordes

• Ultrahigh vacuum• Magnetic shielding

Vacuum System

Electrical

Connectors

Blocking System

Fixed Stops

Housing

Mobile Stops

Sole Plate

External AccElectrode Cylinders

External PM

(PtRh10 or TA6V)

Internal PM (PtRh10)

Internal AccElectrode Cylinders

l l



DESY, 30.9.2008

Differential-Accelerometer

2 Co-axial, co-centric cylindrical test masses Centres of mass conicide with ± 3 µm

accuracy

Testmasses centred by pairs of electrodes

Electrodes pairwise arrenged Capacitive measurment for all degrees of

freedom

Closed-loop control of all degrees of freedom

Potential control via an extremely thinAu-wire (Ø 5 µm)

MICROSCOPE i t t f



DESY, 30.9.2008

MICROSCOPE instrument perfomance

Instrument specifications Completely verified

Expected accuraca (in orbit): 10-15 m/s2 @ 10-3 Hz

Hz

f orb f spin

gold wire

damping

Elektronischer

Noise

capacitive

sensing

m/s2/Hz1/2

10-4 110-2

10-12

10-10

Inner sensor

Outer sensor

Requirement

thermal drift

Hz

Cl k i ACES / PHARAO



DESY, 30.9.2008

Clocks in space: ACES / PHARAO

PHARAO most precise clock in space Allan-Variance: 10-16

ACES enables Phase and Frequencycomparison between a Cs-atomic clock andearth bound clocks:

0.3 ps during ISS pass (~5min.) 7 ps during 1 day 23 ps during 10 days

Resolution of the time-link: common view: 1 ps non-common view:

3 ps for ∆t < 1,000 s

10 ps for ∆t < 10,000 s

in GNSS Orbits

Longitudinal Doppler effect 10-2 s per day

Transversal Doppler effekt 10-5 s per day

Sagnac effekt 3·10-7 s per orbit

1st ord. Gravitational redshift 8·10-5 s per day

2nd ord. Gravitational redshift 10-13 s per day

Gravitational time delay 4·10-11 s

Gravitomagentic clock effect 10-7 s per orbit

Time transfer (MWL)



DESY, 30.9.2008

Time transfer (MWL)

MWL (Microwave link to ISS)developed for transfers of timesignals between ISS and earth

Frequency comparison with arelative accuracy of 10-16 (230fs per pass, 5 ps per orbit)

2 symmetric 1-way links for ein

continuly pseudo-noise codedsignal

High Ku-band chip rate (100MChip/s) to improve the

resolution and to depresspossible multipath signals

1 W power (S- and Ku-band)

Enables additional ranging with λ /1,000 = 24 µm accuracy.

Optical links for tracking



DESY, 30.9.2008

Optical links for tracking

Optical transponder (On-board-laser, telescope,

on-board.clock) Successfully demonstrated over 0,17 AU (24

million km) with Messenger S/C (2-way link) andMars Global Surveyor S/C(1-way link)

Nd:YAG-Laser, pulse frequency 8 Hz

Atmospheric correction; calibration via ranging tonear-earth satellites (e.g. LAGEOS) from differentstations

Echo transponderTime delay must beknown.

Asynchronous transponder fürsatellite laser rangingRepetition rate must be

known.

Messenger S/C MOLA on Mars

Global SurveyorS/C (1-way)

Distance 2.4·107 km 8·107 km

Pulse-width 10 ns (up), 6 ns (down) 5 ns

Pulse-energy 16 mJ (up), 20 mJ (down) 150 mJRepetition rate 240 Hz (up), 8 Hz (down) 56 Hz

Laser energy 3.84 W (up), 0.16 W (down) 8.4 W

Beam divergence 60 µrad (up), 100 µrad(down)

50 µrad

Mirror area 0.042 m2(up), 1.003 m2

(down)0.196 m2

John J. Degnan, in Lasers, Clocks, and Drag Free…

LISA: gravitational waves obs



DESY, 30.9.2008

LISA: gravitational waves obs.

Cluster of 3 S/C inheliocentric orbits at 1 AU

S/C form an equilateral

triangle with5 mio km arm length

Earth trailing orbit:20 °behind the Earth

Leaned 60° with respect tothe ecliptic

S/C contain laser and inertialtest masses

System forms a MichelsonInterferometer

Designed for galactic andcosmological sources

Launch 2014

K.Danzmann, MPI-AEI

Unexplained phenomena within GR



DESY, 30.9.2008


Cosmological phenomena

Dark Energy (Turner 1999):to describe the accelerated expansion of the universe seen from supernovaeobservations and CMB anisotropy measurements

Dark Matter (Zwicky 1933):to describe galactic rotation curves, gravitational lensing effects and early

structure formation in cosmological models

W-MAP and the Cosmic Questions



DESY, 30.9.2008

W-MAP and the Cosmic Questions

confirms cosmological model / inflation dark energy /dark matter only 5 % of the Universe consists of

„ordinary“ matter ??

Do we see effects in our olar system?




DESY, 30.9.2008


Cosmological phenomena

Dark Energy (Turner 1999):to describe the accelerated expansion of the universe seen from supernovaeobservations and CMB anisotropy measurements



Astronomical observationsIncrease of the Astronomical Unit (Pitjeva 2005, Krasinski 2005):length scale related to the earth-sun distance increasesby 7 ± 1 m per 100 years (confirmed by astronomical observations);

solar mass loss only explains ca. 1 m per centuryQuadrupole/Octopole Anomaly (Tegmark et al . 2005, Schwarz et al. 2005 ):Quadrupole and octopole of CMB are correlated with solar system ecliptic

Increase of the Astronomical Unit



DESY, 30.9.2008

Increase of the Astronomical Unit

Remarks and questions

dG/dt ≠ 0 exluded by Lunar Laser Ranging

Mass loss of Sun causes only 1 m / 100 a

Influence by cosmic expansion many orders of magnitude

too small

Increase of solar wind plasma on long time scales ?

Drift of clocks t → t + α t 2 with α ≈ 3 · 10-20 s-1 ?


dG/dt ≠ 0 exluded by Lunar Laser Ranging

Mass loss of Sun causes only 1 m / 100 a

Influence by cosmic expansion many orders of magnitude

too small

Increase of solar wind plasma on long time scales ?

Drift of clocks t → t + α t 2 with α ≈ 3 · 10-20 s-1 ?

Observations

Krasinsky and Blumberg (2005): 15 ± 4 m / 100 a

Pitjeva (in Standish (2005)): 7± 1 m / 100 a

Quadropole / octopole anomaly



DESY, 30.9.2008

Quadropole / octopole anomaly

Schwarz et al 2004, Copi et al. 2005

Observations

Anomalous behaviour of low ℓ contributions to CMB quadupole and octopolealigned to > 99.87 %

Quadrupole and octopole aligned to ecliptic to > 99 % No correlation with the galactic plane

(Oliveira et al (2004), Schwarz et al (2005))

Observations

Anomalous behaviour of low ℓ contributions to CMB quadupole and octopolealigned to > 99.87 %

Quadrupole and octopole aligned to ecliptic to > 99 % No correlation with the galactic plane

(Oliveira et al (2004), Schwarz et al (2005))


Influence of solar system on CMB observations ?

Systematics ?


Influence of solar system on CMB observations ? Systematics ?




DESY, 30.9.2008

Cosmological phenomenaDark Energy (Turner 1999):to describe the accelerated expansion of the universe seen from supernovaeobservations and CMB anisotropy measurements



Astronomical observationsIncrease of the Astronomical Unit (Pitjeva 2005, Krasinski 2005):length scale related to the earth-sun distance increasesby 7 ± 1 m per 100 years (confirmed by astronomical observations);solar mass loss only explains ca. 1 m per century

Quadrupole/Octopole Anomaly (Tegmark et al . 2005, Schwarz et al. 2005 ):Quadrupole and octopole of CMB are correlated with solar system ecliptic


Satellite tracking effects

Pioneer Anomaly ( Anderson et al. 1998,2002/04)Fly-by Anomalies ( Antresian and Guinn 1998 , Anderson and Williams 2001 ,Morley 2005, Campbell 2006, Anderson et al., 2008)

GRACE-Anomaly (Bertiger et al 2003)

Satellite tracking effects

Pioneer Anomaly ( Anderson et al. 1998,2002/04)Fly-by Anomalies ( Antresian and Guinn 1998 , Anderson and Williams 2001 ,

Morley 2005, Campbell 2006, Anderson et al., 2008)GRACE-Anomaly (Bertiger et al 2003)

(1) Pioneer Anomaly



DESY, 30.9.2008

Doppler tracking of the Pioneer 10and 11 satellites showed a blue-shifted, anomalous frequency shift

Drift can be interpreted as anacceleration directed toward the sunof

( Anderson et al. 1998, 2002)

( ) s /Hz91001.099.5 −⋅±= pf &

( ) 2m/s101033.174.8 −⋅±= p

a

Acceleration has been observed asconstant for more than 16 years

Temporal and spatial variantions < 3%

Analyzed in detail with data from 1987to 1998 for distances between 20 and 70 AU by JPL

Effect observed when satellites had setfrom elliptic (bound) to hyperbolic

(escape) orbits

No indication about range in space

(1) Pioneer Anomaly

Reasons for Speculations



DESY, 30.9.2008

Reasons for Speculations

cH a p

≈

Surprising coincidence of PA acceleration and cosmic expansion rate

Extremely constant acceleration in space and timeCancels out nearly all systematics

Largest size experiment ever carried outFailed to proof Newton´s 1/r 2-law on large distances

Not the only anomaly observed in our solar system

Doppler Tracking in the expanding Universe Observer at rest in cosmic substrate S/C moves on geodesics and is slowed down Cosmic redshift of frequency Resulting Doppler effect (velocity of points of constantdistance wrt cosmic substrate

Red shift and Doppler cancel Only the satellite´s slow down ist left over.

( ) ( )( ) ( )1021222

1 t V t t H t tot νν −−−=

( ) ( ) ( )1221222

t t H V t t H t V tot tot −−−=

cH cH c

V HV a <<==

Pioneer 10 and 11 satellites



DESY, 30.9.2008

Pioneer 10 P ioneer 11

Launch 2.3.1972 5.4.1973

Planetary fly-bys Jupiter: 4.12.1973 Jupiter: 2.12.1974

Saturn: 1. 9.1979

Last data received 27.4.2002 (after 30years of operation)

@ 80.2 AU

1.10.1990

@ ca. 30 AU

Direction of orbit line Aldebaran Aquila constellation

Doppler

8 WTransmission power

ca. 13 cmRadio link wavelength

2.292 GHz (S-band)Down-link frequency

2.110 GHz (S-band)Up-link frequency

588.3 kg · m2Maximum moment of inertia

4.28 rpmSpin rate5.914 m

2

Maximum cross section

2.74 mHigh-gain antenna Ø

boom 6 m / mass 5 kgMagnetometer

boom 3 m / mass 13.6 kgPower: SNAP-19 RTGs

259 kgSatellite mass

Slava Turyshev, JPL.

The orbits of Pioneer 10 and 11



DESY, 30.9.2008

Elliptic (bound) orbits befor the last fly-by

Hyperbolic (escape) orbits after the last fly-by

Observed Anomalous Doppler Drift



DESY, 30.9.2008

pp

f

c

v

c v

f ⋅⎟

⎠

⎞⎜

⎝

⎛ −

−

=′ 1

/1

122

c

v

c v

c v

f

f f

21

/

2 −≈+−=

−′′

f c

v

c v f ′⋅⎟

⎠

⎞⎜⎝

⎛ −

−=′′ 1

/1

122

frequencyfrequency receivedreceived at S/C:at S/C:

frequencyfrequency sentsent back andback andreceivedreceived onon earthearth::((neglectingneglecting thethe transpondertransponder shiftshift))

t av v pelled observed

2mod

−=−

f f´

f´´ f´

Anderson et al.

The two-way Doppler residualsfor Pioneer 10 vs time

[1 Hz is equal to 65 mm/s rangechange per second].

Error budget of external effects



DESY, 30.9.2008

g

error budget constituentsbias

[10-10m/s2

uncertainty

[10-10 m/s2]sources of external systematics

solar radiation pressure ± 0.001

→ sol. rad. press. from mass uncertainties + 0.03 ± 0.01

solar wind ± 0.00001solar corona effects ± 0.02

Lorentz force (em-effects) ± 0.0001

Kuiper belt´s gravity ± 0.03

earth rotation ± 0.001

mechanical / phase stability of DSN antenna ± 0.001

clock effects on phase stability ± 0.001

DSN station location ± 0.00001

tropospheric and ionospheric effects ± 0.001

computational systematics

numerical stability of least-square estimation ± 0.02

accuracy of consistency / model tests ± 0.13

→ mismodelling of manoeuvers ± 0.01

→ mismodelling of solar corona ± 0.02

annual / diurnal terms ± 0.32

Sources of internal systematic error



DESY, 30.9.2008

y

error budget constituents bias[10-10 m/s2]

uncertainty[10-10 m/s2]

radio beam reaction force + 1.10 ± 0.11

thermal and propulsion effects from RTGs

→ RTG heat reflected off the S/C -0.55 ± 0.55→ differential emissivity of the RTGs ± 0.85

→ non-isotropic radiative cooling of S/C ± 0.16→ expelled He produced within the RTGs +0.15 ± 0.16

mass expulsion / gas leakage ± 0.56

variation between S/C determinations +0.17 ± 0.17

94Pu238 → 92U234 + 2He4

Half-life time: 87.74 yearsca. 2000 WRadioisotope ThermoelectricalGenerator (SNAP-19)

L. Scheffer

Electric Isolator

Thermal source

condcond. cond.

Electric isolator

Thermal sink (radiator)

-P+

-P+

-P+

+N-

+N-

+N-

∆V= S ∆T

S - Seebeck coefficient

Thermal history



DESY, 30.9.2008

1987 [97 W]

1998.8 [65 W]

2001

~32.8% reduction

On-board power decrease

60 W asymmetric IR-radiation (out of initial 2000 W) could explain the

anomaly

Symmetry breaking through high-gain antenna (Ø 2,3 m)

Spin rate change of both satellites shows, that thermal models are consistent.

Models include surface degradation effects (also worst-case scenarios)

60 W asymmetric IR-radiation (out of initial 2000 W) could explain theanomaly

Symmetry breaking through high-gain antenna (Ø 2,3 m)

Spin rate change of both satellites shows, that thermal models are consistent.

Models include surface degradation effects (also worst-case scenarios)

Thermal Information



DESY, 30.9.2008 23,8 cm

182 cm,not in scale

Temperature at the fin

(radiator) roots of the RTGsas function of the time forPioneer 10 (left) andPioneer 11 (right)

S. Turyshev et al.

Distribution of temperature

sensors in S/ C Temperature sensors at the

radiators (fins) of the RTGs Temperature sensors inside the

S/ C hydracine tanks Pressure sensors inside the S/ C

hydracine tanks

Thermal modelling



DESY, 30.9.2008

Method: Finite Element (FE) modelling FE model used to acquire the steady state temperature solution and

to calculate surface based forces Ray-tracing used to determine the amount of absorbed and reflected

radiation For each active element a hemisphere of ray vectors is initialised

Computation of intersection points with all other surface elementCheck if intersection point lies in receiving element by means of barycentric coordinate formulation

( ) ( )444 3444 21

44 344 214444 34444 21

&

heat Radiated

Spacei

heat Generated radiationsolar of Absorption

tot T T AT T A A

r

r S Q

44

21

2

cos −⋅⋅⋅−−⋅⋅⎟ ⎠

⎞⎜⎝

⎛ +⋅⋅⎟

⎠

⎞⎜⎝

⎛ ⋅⋅= ⊕

⊕σ ε

δ

λφα

0=⇒=tot out in

QQQ &&& 1: Heat radiation of Antenna facing sun

2: RTG Heat dissipation

3: Equipment/Experiment section waste heat

4: Heat radiation of antenna facing space

Questions:

To where is the overall force pointing? How sensitive is the force direction magnitude to changes in surface properties changes in heat sources and axis alignment?

Raytracing and thermal force



DESY, 30.9.2008

∫ ∫ ∫ = A

A

e A

c

T P

π π

φ β β β π

σ ε 2

0

2

0

4

dddsincos

Thermal momentum flux

122

21

4

1

12dd

coscos

1 2

A Ar

T I

A A

E ∫ ∫ ⋅

=θ θ

π

σ

Flux between model elements

1θ

2θ

1n2n

1 A

2 A

Resulting force

nRay n

n

losstot V I F

,1,⋅= ∑

c

LF

globs

elemheat

,Re

,

ρ=∑=

i

elemheat net tot i F F )(

,,

refl tot losstot net tot tot F F F F

,,,+−=

Thermal force from RTGs only explains the anomalypartially (model dependent)Problems:

fin root temperatures do not fit completely

model only covers RTGs so far

problems: surface degration / louvers / spin rate changes etc.

Unexpected masses in the solar system



DESY, 30.9.2008

a[10-8 m/s2]

d[AU]

ring with mass density µ( ρ ) ~ 1/ ρ

needs ca. 40 Earth masses

Acceleration vs.distance fordifferent massdensity distribution(Nieto, 2005 )

Drag through dust



DESY, 30.9.2008

Interplanetary Medium – is a thinly scattered matter (neutral Hydrogen, microscopic particles)

with two main contributions, IPD and ISD:

– Interplanetary Dust (IPD), modelled:

– Interstellar Dust (ISD), measured on Ulysses S/C:

324

g/cm10

−

≤IPD ρ

326 g/cm10−≤ISD

ρ

Drag on a spacecraft( )

s

ss

sdrag m

Av r c a

ρ−=

The Pioneer Anomaly (between 20 and 70 AU) could only be

explained with an axially-symmetric dust distribution with a constant

uniform density of

( ) ( )ISDIPD

r ρ ρ ρ ρ +≈⋅=≤ − 000.300g/cm103 319

0

Yukawa modification



DESY, 30.9.2008

Ansatz

with Taylor extension andG0 = (1 + α)G as observed grav. constant for r →∞

( ) ...3

G12

G1

G202020 ++−++−=

λ λ α α

λ α α r M M

r M r a SunSunSun

( ) ( ) λα /1 r Sun

r M r V −⋅+= eG

Standard Newtonian case

log10 ( λ ) > 16 for log10 α = 1compatible with present experimentalresults in the solar system (includingplanetary orbits)

A viable model?

Pioneer Anomaly:log10 ( λ) > 16, α + 1 ≤ 10-5

Galaxy rotation curveslog10 ( λ) > 16, α + 1 ≤ 10-1

(2) Fly-by Anomaly



DESY, 30.9.2008

1st time measured Dec. 1990during GALILIEO´s 1stgravity assist manouever atEarth:

unexplained 2-way S-bandDoppler shift of 66 mHzwhich could be interpreted as

anomalous velocity increaseof 3.93 ± 0.08 mm/s

Antreasian & Guinn 1998, Anderson & Williams 2001,Morley 2005, Preuss 2006 Time [UTC]

D o

p p l e r r e s i d u a l s [ m H z ]

Closest approach

NEAR

2-way Doppler

S-band residuals

range residuals

Earth Fly-bys analyzed so far



DESY, 30.9.2008

Galileo(1st fly-by)

NEAR Cassini Rosetta Messenger

v ∞ [km/s] 8.949 6.851 16.01 3.863 4.056

v F [km/s] 13.738 12.739 19.03 10.517 10.389

h [km] 956 532 1,172 1,954 2,336

ε 2.47 1.81 5.86 1.31 1.13

Θ [°] 47.67 66.92 19.66 99.396 94.7

i [°] 142.9 108.0 25.4 144.9 133.1

Fly-by 8.12.1990 23.1.1998 18.8.1999 4.3.2005 2.8.2005

∆v ∞ [mm/s] 3.92 ± 0.08 13.46 ± 0.13 ~ 1 1.82 ± 0.05

∆v F [mm/s] 2.56 ± 0.05 7.24 ±0.07 |-0.2| (?) 0.67 ± 0.02 O (0)

Observed phenomena



DESY, 30.9.2008

( )( )

i earth

i sat kin

v v v v v mE

′−′=−=

0

22

0

2//∆

∆v∞ [mm/s]

12

10

8

6

4

2

∆v∞ [mm/s]

12

10

8

6

4

2

1 2 3 4 5 6 250 500 750 1000 1250 1500

h [km]

perigee

e

eccentricity

Rosetta

NEAR

Galileo

Cassini

Rosetta

NEAR

Galileo

Cassini

∆v decreases with increasingeccentricity and perigee height

∆v disappears at e = 1(as expected for bound orbits)

Error analysis



DESY, 30.9.2008

error budget constituents bias[10-5 m/s2]

Atmospheric drag - 0.0001

Ocean tides ± 0.1

Solid earth tides « |0.15|

S/C charging (modeled / analyzed for LISA;

for charging Q < 10-7 C

± 0.0001

Magnetic moments (< 2 · 10-7 G/m) ± 10-10

Earth albedo (1 t S/C) ± 0.00024

Solar wind ± 0.0003

Relativistic corrections not affecting

Spin rotation coupling (coupling of the helicity of radiowaves with S/C spin and Earth rotation ( only effective for2-way Doppler ranging)

not affecting

2022 10/ −≈⋅ c v U

Attempts to explain



DESY, 30.9.2008

Explanations by systematics failed so far.

Confirmed by different codes

Real effect inherent to the tracking of S/C

Source unknown

( Anderson et al., PRL, 2008)

Empirical prediction formula ( Anderson et al., PRL, 2008)

( )out in

K V

V δδ coscos −=

∞

∞∆

r

G2//

2 E

C S C S

M v v V −⋅=∞

ϖϖ

withc

R K E E

ω2=

(3) GRACE Anomaly



DESY, 30.9.2008

Observed difference of a systematic time shifts of

0.056 ps/ s → 45.6 ns/d

independently determined by

(1) Ku-band ranging and

(2) GPS (Bertiger et al 2003)

Could be interpreted as a anomalousacceleration of the GRACE satellites:

0.2 · 10−4 m/s2

Same order of magnitude than fly-by anomaly!

How to investigate? - ODYSSEY



DESY, 30.9.2008

Heliocentric distance: > 13 AU (beyondSatrun orbit)

Trajectory includes several fly-bys On-board “DC-accelerometer” to measure

non-gravitational accelerations (superiororbit reconstruction)

Radio-mertric Doppler tracking and ranging(X- and Ka-band)

One-way laser ranging for the solarconjunction experiment After last fly-by: deployment of a radio-

beacon probe for the outer solar and deepspace gravity experiment

Hyperbolic escape orbit after last fly-by VLBI observation of the angular position

for main S/C and beacon probe

Bruno Christophe et al.

Radio beacon probe



DESY, 30.9.2008

Perfect gold platted, spherical, and spinning S/C Cylindrical spacecraft

(combines optimal thermal inertia properties and cross-section to solarradiation) Minimal extrusions: sun sensors, vent openings, dipole antenna on poles Spin axis perpendicular to earth line of sight Determination of the non-gravitational accelerations along the probe-sun,

probe-earth, and probe-velocity vector to 8.74·10-12 ms-2 over months rotational velocity ~ 30 mHz = 1.8 rpm Option: precise on-board clock RTG powered (8 x BIAPOS A-6 RTG); perfectly symmetric heat radiation Telecommunications/ranging equipment

– on 8 h / 4 weeks – single band (X-band)

Passive thermal control by RTG waste heat

No thrusters, AOCS by nutation damper + trim masses

µ-Star on-board accelerometer



DESY, 30.9.2008

Capacitive sensing

Calibration with due to flip mecahnism Additional mass trim mechanism

Cubic test mass: 18 g

Located @ S/C CoM

Accuracy: 1·10-11 ms-2 (Integration time:

1 d @ 0.1Hz sampling rate) Thermal stability: 10 mK / h

for 7·10-10 ms-2 / K

ONERA, Paris

Clocks as space-time sensors



DESY, 30.9.2008

Acceleration of S/C usually measured via Doppler-Ranging (Tracking)

Alternatively, one can measure the frequency red shift of clocksonboard S/C, e.g.:

Frequency shift only dependent on gravitational accelerations andindependent from inertial (disturbing) accelerations

Frequency shift is cumulative wrt gravity

Clocks discretisize gravitational from inertial accelerations

Clocks work like DC-accelerometers

13

90

20

210d

1 −≈= ∫ x ac

AU

AU

PAν

ν∆

Long term stabilityfor Deep Space

Missions

Allan-Variance

Summary



DESY, 30.9.2008

• Unexplained phenomena• Dark matter (does it affect solar system physics?)

• Dark energy

• Increase of AU

• Quadrupole / Octopole anomaly• Pioneer Anomaly

• Fly-by anomaly

• GRACE anomaly

• It´s worth to discuss the anomalies

• Try to find systematics

• Try to find conventional explanations

• Try to find relations between anomalies (Anomalies most probably arenot isolated phenomena.)

• Are there similar effects in other gravitating systems?• What´s about hyperbolic orbits?

• Observation of future fly-bys of satellites

• Rosetta Earth fly-by 11 / 2009 (orbital height: ca. 2,500 km)

• New Horizon Jupiter fly-by in 2008 ?

• Use clocks

Documents

Hansjörg Dittus- Testing Gravity in the Solar System