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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Top Related