Shapiro Delay

Wang Hanxiao

May 18 2015

Wang Hanxiao Shapiro Delay May 18 2015 1 / 14

Tests of general relativity

gravitational lensing

the perihelion precession of Mercury

the gravitational redshift of light

Shapiro delay

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Tests of general relativity

Bending of light in the gravitational field

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Tests of general relativity

The perihelion shifts of Mercurys orbit due to general relativity

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Test of general relativity

Light originating in a gravitational field redshifted when observed in a region of a weakergravitational field

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Shapiro Delay

Irwin Shapiro1964-1971

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Shapiro Delay

Schwarzschild metric

c2d2 =(1 rs

r

)c2dt2 (1 rs

r

)1dr2 r2(d2 + sin2d2)

where rs =2GMc2

The difference tr between the proper-time delay predicted in generalrelativity and the corresponding flat-space value

tr 4r0c

{ln[ xp + (x2p + d2)1/2xe + (x2e + d2)1/2

] 1

2

[ xp(x2p + d

2)1/2+

2xe + xp(x2e + d

2)1/2]}

+ O( r20c2)

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Shapiro Delay

Conjunction points

The most crucial configurations are those near superior conjunction whenthe radar waves pass closest to the sun.

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Shapiro Delay

Superior conjunction

tr {ln(4xexp

d2) (3xe + xp

2xe

)}d xe , xp

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Experiment and measurements

Lincoln Laboratory Haystack radar and Millstone radarMercury - 18 Jan, 11 May, 24 Aug 1967

Fourth Test of General Relativity: Preliminary Results. Shapiro, Irwin I. et al. , Phys. Rev.Letters 20.1265 (1968)

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Experiment and measurements

Haystack Observatory and Arecibo ObservatoryVenus - 25 Jan 1970

Fourth Test of General Relativity: New Radar Results. Shapiro, Irwin I. et al. , Phys. Rev.Letters 26.1132 (1971)

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Application

Gravitational microlensing

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Application

A Horseshoe Einstein Ring from Hubble

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measuring A two-solar-mass neutron star

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