Эффект Лензе-Тирринга - Wikipedia.

 

Увлечение инерциальных систем отсчёта, или эффект Лензе-Тирринга — явление в общей теории относительности (ОТО), наблюдаемое вблизи вращающихся массивных тел.

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Впервые в мире был измерен Иньяцио Чьюфолини (итал. Ignazio Ciufolini) из итальянского университета Лечче и Эррикосом Павлисом (Erricos Pavlis) из Мерилендского университета, Балтимор, США. Их результаты были опубликованы в октябре 2004 года. Чьюфолини и Павлис провели компьютерный анализ нескольких миллионов измерений дальности, полученных методом лазерной дальнометрии по уголковым отражателям на спутниках LAGEOS и LAGEOS II (LAser GEOdynamics Satellite), запущенных для изучения геодинамики и уточнения параметров гравитационного поля Земли. Обнаруженный средний поворот орбит спутников, вызванный эффектом Лензе-Тирринга, составляет 47,9 угловой микросекунды в год (mas/год), или 99% от значения, предсказанного теорией Эйнштейна (48,2 mas/год), с оцененной погрешностью ±10%. По мнению некоторых исследователей, реальная точность может быть порядка 20-30%.

 

 

Спутники LAGEOS и LAGEOS II (LAser GEOdynamics Satellite) - Wikipedia.

 

LAGEOS и LAGEOS II (LAser GEOdynamics Satellite) — спутники, разработанные и запущенные международной группой исследователей (NASA и др.) для изучения геодинамики и уточнения параметров гравитационного поля Земли.

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В результате анализа данных за 11 лет было вычислено, что орбита спутников смещалась на 2 метра в год в направлении вращения Земли. Это значение на 99% совпадает с предсказанным общей теорией относительности эффектом увлечения инерциальных систем отсчёта вращающимся телом (см. также "Gravity Probe B").

 

 

Спутник "Gravity Probe B" - Wikipedia.

 

Спутник "Gravity Probe B" был запущен с целью обнаружить два эффекта, предсказываемые общей теорией относительности (ОТО):

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1) геодезическую прецессию, возникающую вследствие искривления пространства-времени.

 

2) прецессию за счёт увлечения инерциальной системы координат вблизи вращающегося массивного тела (Земли) ‑ эффект Лензе-Тирринга.

 

Результаты программы "Gravity Probe B" подтвердили соответствие предсказываемых релятивистских эффектов реальным физическим.

 

 

Спутник LARES (Laser Relativity Satellite) - 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%.

 

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LARES — a satellite for studying General Relativity.

LARES — a completely passive satellite, 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. 

 

Launched today a 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 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). LAGEOS experiments.

 

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.

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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.

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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".