Deflection of light induced by the sun gravity field and measured with geodetic vlbi
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Deflection of light induced by the Sun gravity field and measured with geodetic VLBI. Oleg Titov (Geoscience Australia) Anastasiia Girdiuk (Institute of Applied Astronomy, RAS). Outline. 1. Introduction – General Relativity in geodetic VLBI 2. Gravitational delay vs light deflection angle

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Deflection of light induced by the sun gravity field and measured with geodetic vlbi

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI

Oleg Titov (Geoscience Australia)

AnastasiiaGirdiuk (Institute of Applied Astronomy, RAS)


Outline
Outline measured with geodetic VLBI

  • 1. Introduction – General Relativity in geodetic VLBI

  • 2. Gravitational delay vs light deflection angle

  • 3. Observational results

  • 4. Extra deflection with VLBI

  • 5. Conclusion

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Introduction
Introduction measured with geodetic VLBI

  • Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps;

  • General relativity is presented by the gravitational delay and a coordinate term in the geometric delay;

  • Gravitational delay caused by the Sun gravitational field is about 40 ns near the Sun and about 400 ps in opposite direction;

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Introduction1
Introduction measured with geodetic VLBI

  • Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay with accuracy up to 30 ps;

  • General relativity is presented by the gravitational delay and a coordinate term in the geometric delay;

  • Gravitational delay caused by the Sun gravitational field is about 40 ns near the Sun and about 400 ps in opposite direction;

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Introduction2
Introduction measured with geodetic VLBI

  • Effect of general relativity is split into two separate terms;

  • Gravitational delay is expressed as a function of the barycentric distances and . Geometric delay is a function of baseline length

  • Light deflection angle is not presented – no link to the optical astrometry.

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Introduction3
Introduction measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs gravitational delay
Light deflection angle vs gravitational delay measured with geodetic VLBI

  • Q – quasar, B – deflecting body (Sun)

b

Q

s

B

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs gravitational delay1
Light deflection angle vs gravitational delay measured with geodetic VLBI

  • Q – quasar, B – deflecting body (Sun)

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Difference between two models measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs gravitational delay measured with geodetic VLBI

Deflection angle for arbitrary …

…now explicitly presented in the equation

for the VLBI group delay

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs gravitational delay measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Observational results
Observational results measured with geodetic VLBI

  • 1. Geodetic VLBI data from 1991-2001

  • 2. Gravitational delay and coordinate term in geometric delay were switched off for a set of selected radio sources

  • 3. Equatorial coordinates of the selected radio sources were estimated as daily parameters for each 24-hour VLBI sessions

  • 4. The estimated coordinates are converted to the deflection angle  and PPN parameter .

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle 1803 784
Light deflection angle 1803+784 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle 1606 106
Light deflection angle 1606+106 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle 1334 127
Light deflection angle 1334-127 measured with geodetic VLBI

  • Minimum elongation 2.6

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs elongation 1606 106
Light deflection angle vs elongation 1606+106 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs elongation 1606 1061
Light deflection angle vs elongation 1606+106 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs elongation 1606 1062
Light deflection angle vs elongation 1606+106 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs elongation 0229 131
Light deflection angle vs elongation 0229+131 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Light deflection angle vs elongation 0229 1311
Light deflection angle vs elongation 0229+131 measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


New formula b enefits
New formula: measured with geodetic VLBIbenefits

  • 1. Simple;

  • 2. Consistent with the geometric part of group delay model;

  • 3. Linked to the deflection angle directly;

  • 4. Free off coordinate terms;

  • 5. Partial derivate for  is optimal;

  • 6. Allows more flexibility;

  • 7. Looking good as an alternative option for IERS Conventions

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Outreach when gr works
Outreach – “When GR works?” measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Observations
Observations measured with geodetic VLBI

If all the general relativity effects are switched off the VLBI group delay model,

the light deflection angle will be observed at any moment and at any elongation of a radio sources to the Sun (the closer, the better).

The old good time (before 2002) when the radio sources were observed close to the Sun (as close as 1.5). The PPN parameter  was estimated very accurately (0.001) from a standard 24-hour session, if the number of delays is  100.

The accuracy would be about 0.0001, were a dedicated session for observation of a strong radio source within 3 arranged.

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


The minor terms 1
The “minor” terms ( measured with geodetic VLBI = 1)

The minor terms are not negligible in the small angle approximation (  0)

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


The minor terms
The “minor” terms measured with geodetic VLBI

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


The minor terms for the sun
The “minor” terms for the Sun measured with geodetic VLBI

The additional deflection angle is individual for all baselines

For geodetic VLBI observation of the radio sources near the Solar limb

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


The minor terms for jupiter
The “minor” terms for Jupiter measured with geodetic VLBI

Angular size

Mass g

=70.000 km

For grazing light

For geodetic VLBI observation of the radio sources near Jupiter

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


The minor terms1
The “minor” terms measured with geodetic VLBI

The additional deflection angle is individual for all baselines and could

be detected with observations within 2 from the Sun and 2’ from Jupiter

Total magnitude

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Additional angle and its geometric interpretation
Additional angle and its geometric interpretation measured with geodetic VLBI

  • Q – apparent position;

  • Q’ – true position;

  • B – deflecting body,

Q



Q’

b

B

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Additional angle may be observed
Additional angle may be observed measured with geodetic VLBI

  • Q – apparent position;

  • Q’ – true position;

  • B – deflecting body,

Q

B

Q’

b

B

  • Traditional deflection angle (unobservable)

  • Additional deflection angle (observable), if b/R ~ 0.1

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Close alignment of star and radio source 0758 737
Close alignment of star and radio source 0758-737 measured with geodetic VLBI

  • Separation is less than 2”

0758-737

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Conclusion
Conclusion measured with geodetic VLBI

  • 1. General relativity effects in VLBI could be expressed in term of the light deflection angle ;

  • 2. The light deflection angle could be estimated for an arbitrary elongation from the Sun with high precision;

  • 3. The equation for light deflection at arbitrary elongation was tested using a set of VLBI data;

  • 4. The PPN parameter  was estimated for several 24-hour sessions with accuracy 0.001.

  • 5. Additional deflection angle could be observed for a close approach to the Sun or Jupiter;

  • 6. A dedicated observational programs for detection of the additional angle are required.

Deflection of light induced by the Sun gravity field and measured with geodetic VLBI


Any questions
Any Questions? measured with geodetic VLBI

  • Thank you for your attention

Phone: +61 2 6249 9111

Web: www.ga.gov.au

Email: [email protected]

Address:Cnr Jerrabomberra Avenue and Hindmarsh Drive, Symonston ACT 2609

Postal Address: GPO Box 378, Canberra ACT 2601


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