March 31 2006 Birmingham

GR tests and micro-GR tests and micro-arcsecond light bending arcsecond light bending

parameters by global and parameters by global and differential Gaia differential Gaia mesurementsmesurements

Maria Teresa Crosta Maria Teresa Crosta

Astronomical Astronomical ObservatoryObservatory of of TurinTurin

INAFINAF - - OAToOATo

March 31 2006 Birmingham

SummarySummary

1 PPN 1 PPN γγ measurement through measurement through global astrometry global astrometry

2 PPN 2 PPN γγ and detection of the and detection of the quadrupole effect due to a planet quadrupole effect due to a planet with differential astrometric with differential astrometric measurementsmeasurements

3 Conclusions amp perspectives3 Conclusions amp perspectives

March 31 2006 Birmingham

Why

-arcsecond accuracy

Relativistic models ofLight propagation

Tests of General Relativity(and alternative theories)

Relativistic AstrometryRelativistic Astrometry

March 31 2006 Birmingham

Gaia relativity tests within the Gaia relativity tests within the Solar SystemSolar System

Light deflection

Global astrometry PPN parameter amount of curvature by unit rest mass]

Small field astrometry Eddington-like experiments

Local relativistic effects =gt new parameters +

Precession of the perihelion Orbit fitting of asteroids

PPN parameter [amount of non-linearity in the superposition law of gravitational fields]

new tests to be set from the relativistic modelling

March 31 2006 Birmingham

The physical linkThe physical link

75 10101 γ

a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle lack of universality of the constants of microphysics etc)

The exact amount of the violations depends on the particular scalar-tensor theory adopted=gtquantization of gravity

bull for GR =1 alternative theories called scalar-tensor predict small deviations from GR values

Current best estimateCurrent best estimate 510)3212(1γ

bull GPB expected precision 5-1031γ

Cassini-Earth Sun conjunction (B Bertotti LIess amp PTortora Nature 425 2003)

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

SummarySummary

1 PPN 1 PPN γγ measurement through measurement through global astrometry global astrometry

2 PPN 2 PPN γγ and detection of the and detection of the quadrupole effect due to a planet quadrupole effect due to a planet with differential astrometric with differential astrometric measurementsmeasurements

3 Conclusions amp perspectives3 Conclusions amp perspectives

March 31 2006 Birmingham

Why

-arcsecond accuracy

Relativistic models ofLight propagation

Tests of General Relativity(and alternative theories)

Relativistic AstrometryRelativistic Astrometry

March 31 2006 Birmingham

Gaia relativity tests within the Gaia relativity tests within the Solar SystemSolar System

Light deflection

Global astrometry PPN parameter amount of curvature by unit rest mass]

Small field astrometry Eddington-like experiments

Local relativistic effects =gt new parameters +

Precession of the perihelion Orbit fitting of asteroids

PPN parameter [amount of non-linearity in the superposition law of gravitational fields]

new tests to be set from the relativistic modelling

March 31 2006 Birmingham

The physical linkThe physical link

75 10101 γ

a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle lack of universality of the constants of microphysics etc)

The exact amount of the violations depends on the particular scalar-tensor theory adopted=gtquantization of gravity

bull for GR =1 alternative theories called scalar-tensor predict small deviations from GR values

Current best estimateCurrent best estimate 510)3212(1γ

bull GPB expected precision 5-1031γ

Cassini-Earth Sun conjunction (B Bertotti LIess amp PTortora Nature 425 2003)

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Why

-arcsecond accuracy

Relativistic models ofLight propagation

Tests of General Relativity(and alternative theories)

Relativistic AstrometryRelativistic Astrometry

March 31 2006 Birmingham

Gaia relativity tests within the Gaia relativity tests within the Solar SystemSolar System

Light deflection

Global astrometry PPN parameter amount of curvature by unit rest mass]

Small field astrometry Eddington-like experiments

Local relativistic effects =gt new parameters +

Precession of the perihelion Orbit fitting of asteroids

PPN parameter [amount of non-linearity in the superposition law of gravitational fields]

new tests to be set from the relativistic modelling

March 31 2006 Birmingham

The physical linkThe physical link

75 10101 γ

a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle lack of universality of the constants of microphysics etc)

The exact amount of the violations depends on the particular scalar-tensor theory adopted=gtquantization of gravity

bull for GR =1 alternative theories called scalar-tensor predict small deviations from GR values

Current best estimateCurrent best estimate 510)3212(1γ

bull GPB expected precision 5-1031γ

Cassini-Earth Sun conjunction (B Bertotti LIess amp PTortora Nature 425 2003)

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Gaia relativity tests within the Gaia relativity tests within the Solar SystemSolar System

Light deflection

Global astrometry PPN parameter amount of curvature by unit rest mass]

Small field astrometry Eddington-like experiments

Local relativistic effects =gt new parameters +

Precession of the perihelion Orbit fitting of asteroids

PPN parameter [amount of non-linearity in the superposition law of gravitational fields]

new tests to be set from the relativistic modelling

March 31 2006 Birmingham

The physical linkThe physical link

75 10101 γ

a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle lack of universality of the constants of microphysics etc)

The exact amount of the violations depends on the particular scalar-tensor theory adopted=gtquantization of gravity

bull for GR =1 alternative theories called scalar-tensor predict small deviations from GR values

Current best estimateCurrent best estimate 510)3212(1γ

bull GPB expected precision 5-1031γ

Cassini-Earth Sun conjunction (B Bertotti LIess amp PTortora Nature 425 2003)

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

The physical linkThe physical link

75 10101 γ

a remnant of a long range scalar field would violate GR (the assumptions in the equivalence principle lack of universality of the constants of microphysics etc)

The exact amount of the violations depends on the particular scalar-tensor theory adopted=gtquantization of gravity

bull for GR =1 alternative theories called scalar-tensor predict small deviations from GR values

Current best estimateCurrent best estimate 510)3212(1γ

bull GPB expected precision 5-1031γ

Cassini-Earth Sun conjunction (B Bertotti LIess amp PTortora Nature 425 2003)

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

The adopted metric is the PPN expression for the Schwarzschild metric in isotropic coordinate (in geometrized units)

11Light deflection the PPN Light deflection the PPN global global experiment with Gaiaexperiment with Gaia

)sin(2

122

1( 22222222

2 ddrdrr

Mdtc

r

M

r

Mds SunSunSun

bullGeodesics for light rays kv kmicro = 0

Relativistic astrometry models the RAMOD project

Bucciarelli B Crosta MT de Felice F Lattanzi MG and Vecchiato A (ESA SP 576 - p 259 )

)(cos iiiiif

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

Known

part

part

part

part

part

part

part

partsin )1()1( ffff

ii

ii

ii

ii

BUTBUT hellip hellip

part

part

part

part

part

part

part

partsin )()( ffff

ii

ii

ii

ni

ni

part

part

part

part

part

part

part

partsin )2()2( ffff

ii

ii

ii

ii

Unknown Unknown UnknownUnknown Unknown Unknown Unknown

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

The mathematical The mathematical problemproblem

1 1 observationobservation 1 1 condition equationcondition equation

bb=A=AxxOver-Over-

determined determined system of system of equations to be equations to be solved with solved with least-squares least-squares methodmethodAATTbb=A=ATTAA

xx

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

GaiaGaia expected expected precisionprecision

Vecchiato A et al

AampA 399 2003

71051

No other foreseen measurements of can challenge Gaia in the

next decade

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

First experiment quadrupolar light deflectionFirst experiment quadrupolar light deflection Simulation of light deflection experiments of the stars behind Simulation of light deflection experiments of the stars behind

JupiterJupiter tthe observable is the relative displacement due to Jupiterrsquos he observable is the relative displacement due to Jupiterrsquos presence with respect to the zero-deflection position without Jupiterpresence with respect to the zero-deflection position without Jupiter

New estimate ofNew estimate of by comparison of small fieldsby comparison of small fields Detection Detection of the Quadrupole Efficiency Factorof the Quadrupole Efficiency Factor due to the planetdue to the planet

= 0 no multipole light effect =1 validation of GR prediction= 0 no multipole light effect =1 validation of GR prediction

2 The GAREX projectGAia Relativistic Experiments

Investigation of observational strategies to test General Relativity with Gaia

astro-ph0512359

JJals ΦΦΦ

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Light deflection produced by an oblate body PPN formalism locally perturbed

minkowskian geometry

Observer view The position of the star is displaced both in the radial (-n) and orthoradial (m) directions The spin axis of the planet lies somewhere out of plane

the deflection angle is a vector

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Light deflection diplacements Light deflection diplacements around Jupiter from the observerrsquos around Jupiter from the observerrsquos

point of view mid2013point of view mid2013monopole quadrupole

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Cumulative effect (mid2012 -Cumulative effect (mid2012 -

mid2018)mid2018) monopole quadrupole

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Results of the Montecarlo runsResults of the Montecarlo runs

331011

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Strategy for the actual Strategy for the actual experimentsexperiments

I Evolution of the errors on and with the magnitude

for various impact parameters amp for various epochs

bull = Full Gaia field

o=2013 =gtcrossing of the galactic plane

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

II Open cluster against the galactic plane crossed

by JupiterM18 Sagittarius

V=12 V=13hellipbut in 2019

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17

March 31 2006 Birmingham

Our simulationsOur simulations

prove that the expected accuracy of Gaia in the prove that the expected accuracy of Gaia in the determination of the PPdetermination of the PPN N parameter is 10parameter is 10-7-7

give a prerequisite for a first evidence of the quadrupole light deflection due a Jupiter

In a close futureIn a close future

Realistic simulations with the final error budget and initial Realistic simulations with the final error budget and initial condition of scanning law (real fieldcondition of scanning law (real field background noise background noise + + straylight profile straylight profile etc) etc)

Test models of the light deflection with a moving body =gt Test models of the light deflection with a moving body =gt speed of gravity speed of gravity

Extension of the simulation to the case of SaturnExtension of the simulation to the case of Saturn

Investigation on the indirect determination of the center of Investigation on the indirect determination of the center of gravitymass of the planet throughout the light displacement gravitymass of the planet throughout the light displacement vector field around itvector field around it

3 Conclusion amp Perspectives

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