-
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
Wang Hanxiao Shapiro Delay May 18 2015 2 / 14
-
Tests of general relativity
Bending of light in the gravitational field
Wang Hanxiao Shapiro Delay May 18 2015 3 / 14
-
Tests of general relativity
The perihelion shifts of Mercurys orbit due to general
relativity
Wang Hanxiao Shapiro Delay May 18 2015 4 / 14
-
Test of general relativity
Light originating in a gravitational field redshifted when
observed in a region of a weakergravitational field
Wang Hanxiao Shapiro Delay May 18 2015 5 / 14
-
Shapiro Delay
Irwin Shapiro1964-1971
Wang Hanxiao Shapiro Delay May 18 2015 6 / 14
-
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)
Wang Hanxiao Shapiro Delay May 18 2015 7 / 14
-
Shapiro Delay
Conjunction points
The most crucial configurations are those near superior
conjunction whenthe radar waves pass closest to the sun.
Wang Hanxiao Shapiro Delay May 18 2015 8 / 14
-
Shapiro Delay
Superior conjunction
tr {ln(4xexp
d2) (3xe + xp
2xe
)}d xe , xp
Wang Hanxiao Shapiro Delay May 18 2015 9 / 14
-
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)
Wang Hanxiao Shapiro Delay May 18 2015 10 / 14
-
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)
Wang Hanxiao Shapiro Delay May 18 2015 11 / 14
-
Application
Gravitational microlensing
Wang Hanxiao Shapiro Delay May 18 2015 12 / 14
-
Application
A Horseshoe Einstein Ring from Hubble
Wang Hanxiao Shapiro Delay May 18 2015 13 / 14
-
measuring A two-solar-mass neutron star
Wang Hanxiao Shapiro Delay May 18 2015 14 / 14
