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The experiments to test STR and GTR using space satellites


Lense–Thirring precession — Wikipedia.


In general relativity, Lense–Thirring precession or the Lense–Thirring effect (named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect. According to a recent historical analysis by Pfister, the effect should be renamed as Einstein–Thirring–Lense effect. It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum{\displaystyle S}.


The difference between de Sitter precession and the Lense–Thirring effect is that the de Sitter effect is due simply to the presence of a central mass, whereas the Lense–Thirring effect is due to the rotation of the central mass. The total precession is calculated by combining the de Sitter precession with the Lense–Thirring precession.

Italian scientist Ignazio Ciufolini (Lecche) and Erricos Pavlis (Maryland University, Baltimore) made first measurements, published in October 2004. They conducted computer analysis of millions of distance measurements (laser) on LAGEOS and LAGEOS II (LAser GEOdynamics Satellite, studying geodynamics and the parameters of Earth’s gravitational field). They have discovered an average orbit angle deviation, in line with the Lense-Thirring effect, of 47,9 mas / year, which 99 % of the value predicted by Einstein (48,2 mas / year), with an error margin estimated at ± 10%. Some experts believe that the real error margin is about 20-30 %.



LAGEOS (LAser GEOdynamics Satellite) — Wikipedia.


LAGEOS, Laser Geodynamics Satellite or Laser Geometric Environmental Observation Survey, are a series of two scientific research satellites designed to provide an orbiting laser ranging benchmark for geodynamical studies of the Earth.


11 years of data analysis show that the orbit of these satellites was 2 meters in advance, in the direction of Earth’s rotation. This value corresponds at 99 % to the predictions of the GTR, through the impact of a rotating body on inertial systems (see also “Gravity Probe B”).



"Gravity Probe B" — Wikipedia.


"Gravity Probe B" (GP-B) was a satellite-based mission which launched on 20 April 2004. Its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor (which is related to the distribution and the motion of matter in space) in and near Earth. This provided a test of general relativity, gravitomagnetism and related models.


​This satellite should measure two effects, predicted by the GTR :

1) geodesic precession, in result of the curve of space-time.

2) precession due to the impact of a rotating massive body on the inertial system of coordinates (effect Lense-Thirring).


The results of the "Gravity Probe B" program confirmed these predictions.


Laser Relativity Satellite (LARES) — Wikipedia.


The main scientific target of the LARES mission is the measurement of the Lense-Thirring effect, also known as frame-dragging, with an accuracy of about 1%.


LARES — a satellite for studying General Relativity.


LARES is a satellite for studying General Relativity. It is a completely passive satellite, and has been designed to minimize the effects of non-gravitational perturbations on its orbit.

This is a small space mission that will achieve important measurements in gravitational physics, General Relativity, space geodesy and geodynamics. In particular, together with the LAGEOS and LAGEOS 2 satellites and with the GRACE models, it will provide a very accurate determination of the Earth gravitomagnetic field and of the Lense-Thirring effect.



European "Disco Ball" Probe to Test Einstein's Relativity.


The low-cost space probe LARES (Laser Relativity Satellite) will test Albert Einstein's general theory of relativity.



International Laser Ranging Service (ILRS).


LAser GEOdynamics Satellite-1 (LAGEOS) was designed by NASA and launched in 1976. It was the first spacecraft dedicated exclusively to high-precision laser ranging and provided the first opportunity to acquire laser-ranging data that were not degraded by errors originating in the satellite orbit or satellite array. LAGEOS-2, based on the LAGEOS-1 design, was built by the Italian Space Agency and was launched in 1992.

​There are plans for the launch of a LAGEOS-3, which is a joint multinational program with collaboration from France, Germany, Great Britain, Italy, Spain and the United States.


As World Turns it Drags Time and Space.


The research, reported in the journal Nature, is the most accurate direct measurement to date of the Lense-Thirring Effect — a bizarre effect of general relativity, which predicts a rotating mass will drag space around it.

The researchers observed the orbits of the Laser Geodynamics Satellite I (LAGEOS I), a NASA spacecraft, and LAGEOS II, a joint NASA/Italian Space Agency (ASI) spacecraft.

This measurements agrees 99% with what is predicted by general relativity, which is within our margin of error of ±5%.



A confirmation of the general relativistic prediction of the Lense-Thirring effect. (I.Ciufolini, E.C.Pavlis) (2004). (pdf)


General relativity predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it, which will affect the orbit of a satellite.


This Lense-Thirring effect has hitherto not been detected with high accuracy, but its detection with an error of about 1% is the main goal of "Gravity Probe B" — an ongoing space mission using orbiting gyroscopes. Here we report a measurement of the Lense-Thirring effect on two Earth satellites: it is 99 ±5% of the value predicted by general relativity.



A critical analysis of a recent test of the Lense-Thirring effect with the LAGEOS satellites. (Lorenzo Iorio) (2006)


We discuss the impact of the present-day uncertainties in the recently released CHAMP and/or GRACE Earth gravity models on the measurement of the Lense-Thirring effect with the nodes of the LAGEOS satellites. Also the role of the secular variations Jdots of the even zonal harmonics is quantitatively assessed via numerical simulations and tests. While the systematic error due to the static part of the geopotential ranges from 4% (EIGEN-GRACE02S) to 9% (GGM02S), the impact of the Jdots amounts to 13% over 11 years. This yields a 19% 1-sigma total error in the test recently performed with EIGEN-GRACE02S.


A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model. (2016)


Ignazio Ciufolini, Antonio Paolozzi, Erricos C. Pavlis, Rolf Koenig, John Ries, Vahe Gurzadyan, Richard Matzner, Roger Penrose, Giampiero Sindoni, Claudio Paris, Harutyun Khachatryan, Sergey Mirzoyan.

We present a test of General Relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS and LAGEOS-2 laser-ranged satellites together with the Earth's gravity field model GGM05S produced by the space geodesy mission GRACE. We measure μ=(0.994±0.002)±0.05, where μ is the Earth's dragging of inertial frames normalized to its General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the estimated systematic error mainly due to the uncertainties in the Earth's gravity model GGM05S. Our result is in agreement with the prediction of General Relativity for Lense-Thirring effect.



Testing Einstein's Theories With Satellites Stuck in Eccentric Orbits. (Alexander Hellemans) (2015)


Gravitational redshift, or time dilation, necessary for correcting timing signals transmitted from navigation satellites because their clocks operate slightly slower than those on the Earth's surface is a matter of routine. The relationship between the slowing of time and the distance from Earth was tested in 1976 with the one-shot experiment, the "Gravity Probe A".

Measurement of anomalous angle of deviation of light during Satellite Laser Ranging. (I.Ignatenko, Yu. Ignatenko, A.Makeyev, V.Tryapitsyn) (2008) (pdf)



Measurement of anomalous angle of deviation of light during Satellite Laser Ranging. (Presentation)

(I.Ignatenko, Yu. Ignatenko, A.Makeyev, V.Tryapitsyn) (2008) (pdf)



Deviation of light in space, near Earth. (Игнатенко Ю.В., Тряпицын В.Н., Игнатенко И.Ю.) (2009)  

(pdf, in Russian)

See also : Измерение отклонения лазерного луча вблизи поверхности Земли. (Игнатенко Ю.В., Тряпицын В.Н., Игнатенко И.Ю.) (2009)



Direction of the Light Deviation Vector during Satellite Laser Ranging. (Presentation)

(Yuriy V. Ignatenko, Vladimir M. Tryapitsyn, Andriy A. Makeyev, Igor Yu. Ignatenko) (2011)


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