The Study of the Anomalous Acceleration of Pioneer 10 and 11

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Satellite system OPTIS A platform for precision
experiments
OPTIS
Hansjörg Dittus, C.Lämmerzahl, S. Scheithauer
ZARM, University of Bremen, Germany, Achim
Peters, Humboldt University , Berlin,
Germany Stephan Schiller, Andreas Wicht
Institute of Experimental Physics,
Heinrich-Heine- University, Düsseldorf, Germany
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Motivation

• Test of SR implies
• Probing the structure of space-time
• Test of Maxwell equations
• Test of quantum gravity theories Prediction of
  modified Maxwell equations

• Test of GR implies
• Test of quantum gravity theories
• Tests of predicted violation of Weak Equivalence
  Principle
• Tests of predicted violation of Universality of
  Gravitational Red Shift

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Scientific objectives

• OPTIS Improved Optical Tests for the Isotropy of
  Space
• Improved experimental tests of

• Isotropy of light propagation
• Independence of velocity of light from velocity
  of laboratory
• Universality of Gravitational Redshift
• comparison of clocksoptical resonator atomic
  clock optical clock
• Test of Lense-Thirring effect
• Absolute gravitational redshift
• Doppler effect
• Perigee advance
• Newtonian potential (Yukawa-like terms)

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Experimental goals
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Mission Outline 1 (Baseline scenario)
apogee 40000 km
to sun
perigee 10000 km
ASTROD-Symp, Beijing, 14.7.2006
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Mission Outline 2

• Lense-Thirring effect (orbit precession)
• Perigee shift
• Test of Yukawa part in Newtonian potential

High precision tracking by laser rangingin
combination with drag free AOCS
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Mission main characteristics

• Space conditions
• Long integration time
• Large velocity changes
• Large potential differences

• Noise reduction
• Drag-free AOCS ( lt 10-13 m/s2 _at_ 10-2 Hz)
• First time combination of drag-free AOCS and
  laser ranging
• Monolithic resonator
• Systematic elimination of distortions

• New technologies in space
• Ultrastable lasers
• Optical frequency comb
• Resonators with narrow linewidth
• Micro-Propulsion systems (e.g. FEEPs, Colloidal
  thruster)
• Laser Link Platform
• Ultrastable atomic clocks

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Basic principle to measure the isotropy of c
Usual 2nd-order approximation
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Michelson-Morley (MM) experiment
Phase shift measurement
Best measurement on Earth
Brillet and Hall (1976)
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Kennedey-Thorndike (KT) experiment
Frequency change measurement
v
v
v
Best measurement on Earth
v0
v
Braxmaier, Müller, Pradl, Mlynek,Peters, and
Schiller (2002)
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Test of Universality of Gravitational Red Shift
(2)
Frequency difference measurement
U2(r)
Best measurements
for H-maser
Cs-clock
Signal signature of Red Shift violation differs
from that of SRT violation due to velocity
indepence !!!
Bauch and Weyers (2002))
Cs-clock
for cavity
U1(r)
Turneaure and Stein (1987)
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Effects measured by precise tracking
Lense-Thirring effectPrecession rates of knots
Perigee shift
Test of the Newtonian potential
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Mission Requirements

• Variable spin rates(elimination of systematic
  errors)
• TSpin 100 to 1,000 s
• Cavity length variation requirement dc/c lt
  10-18 s?L (TSpin) / L lt 10-18
• Laser frequency lock instability dc/c lt 10-18
  slock(TSpin) / f lt 10-18
• Temperature stability for cavities ?Trandom lt
  200 µK, ?T (7 h) lt 10 µK
• Independent clock reference for KT-
  experiment reason for Gravitational Red shift
  experiment
• Comb generator must be used for comparison
  between atomic clock and cavity df/f lt 10-15
• Residual acceleration on board spacecraft da lt
  10-13 m/s2 _at_ 10-2 Hz
• Laser ranging dr lt 1mm

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Key technology Optical cavity
single cavity fused silica

• Cavities length 5 cm (finesse
  100,000) effective length 5000 m
  better than interferometers 10 m
• Material fused silica
• Length stability
• ?L 10-16 m
• Temperature stability ?T lt 10-8 K / vHz
  but for MM common mode rejection due to
  monolithic design ?T lt 10-6 K / vHz
• Residual accelerations
• Gravity gradient

10-13 m/(s2 ?Hz)
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Resonator model
Elastic deformations under tidal forces
analytical solution by S. Scheithauer and C.
Lämmerzahl
Displacements for a 7000 km orbit
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OPTIS resonator (FEM analysis)
calculated for a 7,000 km orbit
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Mirror displacements during orbit
relative displacement between 2 opposing mirrors
displacements at mirror midpoints
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Resonators and spin
Relative mirror displacements dx on
x-axis Orbital rotation around y-axis Spin around
z-axis
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Thermal gradients
Thermal gradient along z- axis 10-9 K/L
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Key technology Lasers and electronics

• Lasers langth, energy levels -gt frequency
• Diode-pumped NdYAG laser (1064 nm)
• Narrow linewidth
• High intensity stability
• High frequency stability
• Ultrastable frequency lock on long time scales to
  cavities (Ruoso et al 1997, Braxmaier et al.
  2002)

RAV 310-15 _at_ 100 s 10-5 of cavity linewidth

• Also used for Earth-based GW interferometers
• Lasers already space-qualified (Bosch)
• Will be used for LISA-Pathfinder

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Clocks
Allan variance
Integration time
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Key technology Frequency comb

• Purpose comparison of atomic clock frequency
  1010 Hz
• with optical frequency 1015 Hz
• Accuracy 10-15 Hz

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Spacecraft and orbit (baseline scenario)
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OPTIS Summary

• Improved tests of isotropy and velocity-independen
  ce of c, universality of red shift, and
  gravitomagnetic tests
• up to 1,000 times more accurate
• Use of state-of-the-art technology
• Ultrastable optical cavities
• Lasers
• Optical frequency comb
• Electronics and stabilization
• Micro-propulsion system
• Laser ranging
• High precision atomic clocks
• Optimal use of space conditions
• Drag-free satellite control
• Long integration time
• High velocity
• Large gravitational potential changes