Ignazio Ciufolini

A confirmation of the general relativistic prediction of the Lense–Thirring effect

An important early prediction of Einsteins general relativity was the advance of the perihelion of Mercurys orbit, whose measurement provided one of the classical tests of Einsteins theory. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system and to an Earth-orbiting satellite. General relativity also 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 per cent 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 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total ± 10 per cent uncertainty to include underestimated and unknown sources of error.

On a new method to measure the gravitomagnetic field using two orbiting satellites

SummaryWe describe a new method to obtain the first direct measurement of the Lense-Thirring effect, or dragging of inertial frames, and the first direct detection of the gravitomagnetic field. This method is based on the observations of the orbits of the laser-ranged satellites LAGEOS and LAGEOS II. By this new approach one achieves a measurement of the gravitomagnetic field with accuracy of about 25%, or less, of the Lense-Thirring effect in general relativity.

Dragging of inertial frames.

The origin of inertia has intrigued scientists and philosophers for centuries. Inertial frames of reference permeate our daily life. The inertial and centrifugal forces, such as the pull and push that we feel when our vehicle accelerates, brakes and turns, arise because of changes in velocity relative to uniformly moving inertial frames. A classical interpretation ascribed these forces to acceleration relative to some absolute frame independent of the cosmological matter, whereas an opposite view related them to acceleration relative to all the masses and ‘fixed stars’ in the Universe. An echo and partial realization of the latter idea can be found in Einstein’s general theory of relativity, which predicts that a spinning mass will ‘drag’ inertial frames along with it. Here I review the recent measurements of frame dragging using satellites orbiting Earth.

LISA: laser interferometer space antenna for gravitational wave measurements

LISA (laser interferometer space antenna) is designed to observe gravitational waves from violent events in the Universe in a frequency range from to which is totally inaccessible to ground-based experiments. It uses highly stabilized laser light (Nd:YAG, ) in a Michelson-type interferometer arrangement. A cluster of six spacecraft with two at each vertex of an equilateral triangle is placed in an Earth-like orbit at a distance of 1 AU from the Sun, and behind the Earth. Three subsets of four adjacent spacecraft each form an interferometer comprising a central station, consisting of two relatively adjacent spacecraft (200 km apart), and two spacecraft placed at a distance of from the centre to form arms which make an angle of with each other. Each spacecraft is equipped with a laser. A descoped LISA with only four spacecraft has undergone an ESA assessment study in the M3 cycle and the full six-spacecraft LISA mission has now been selected as a cornerstone mission in the ESA Horizon 2000-plus programme.

A COMPREHENSIVE INTRODUCTION TO THE LAGEOS GRAVITOMAGNETIC EXPERIMENT: FROM THE IMPORTANCE OF THE GRAVITOMAGNETIC FIELD IN PHYSICS TO PRELIMINARY ERROR ANALYSIS AND ERROR BUDGET

The existence of the gravitomagnetic field. generated by mass currents according to Einstein geometrodynamics, has never been proved. The author of this paper, after a discussion of the importance of the gravitomagnetic field in physics, describes the experiment that he proposed in 1984 to measure this field using LAGEOS (Laser geodynamics satellite) together with another non-polar, laser-ranged satellite with the same orbital parameters as LAGEOS but a supplementary inclination. The author then studies the main perturbations and measurement uncertainties that may affect the measurement of the Lense-Thirring drag. He concludes that, over the period of the node of ~3 years, the maximum error, using two nonpolar laser ranged satellites with supplementary inclinations, should not be larger than ~10% of the gravitomagnetic effect to be measured.

Testing General Relativity and gravitational physics using the LARES satellite

The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of “dark energy” constituting most of the Universe, has further revived the interest in testing Einstein’s theory of General Relativity. At the very foundation of Einstein’s theory is the geodesic motion of a small, structureless test-particle. Depending on the physical context, a star, planet or satellite can behave very nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet’s orbit, the dynamics of a binary pulsar system and of an Earth-orbiting satellite. Verifying geodesic motion is then a test of paramount importance to General Relativity and other theories of fundamental physics. On the basis of the first few months of observations of the recently launched satellite LARES, its orbit shows the best agreement of any satellite with the test-particle motion predicted by General Relativity. That is, after modelling its known non-gravitational perturbations, the LARES orbit shows the smallest deviations from geodesic motion of any artificial satellite: its residual mean acceleration away from geodesic motion is less than

Measurement of dragging of inertial frames and gravitomagnetic field using laser-ranged satellites

\ensuremath 0.5\times10^{-12}

Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models

m/s^2. LARES-type satellites can thus be used for accurate measurements and for tests of gravitational and fundamental physics. Already with only a few months of observation, LARES provides smaller scatter in the determination of several low-degree geopotential coefficients (Earth gravitational deviations from sphericity) than available from observations of any other satellite or combination of satellites.

The LARES mission revisited: an alternative scenario

SummaryBy analysing the observations of the orbits of the laser-ranged satellites LAGEOS and LAGEOS II, using the program GEODYN, we have obtained the first direct measurement of the Lense-Thirring effect, or dragging of inertial frames, and the first direct experimental evidence for the gravitomagnetic field. The accuracy of our measurement is of about 30%.

The 1995-99 measurements of the Lense-Thirring effect using laser-ranged satellites

Dragging of Inertial Frames and gravitomagnetism are predictions of Einstein’s theory of General Relativity. Here, after a brief introduction to these phenomena of Einstein’s gravitational theory, we describe the method we have used to measure the Earth’s gravitomagnetic field using the satellites LAGEOS (LAser GEOdynamics Satellite), LAGEOS 2 and the Earth’s gravity models obtained by the spacecraft GRACE. We then report the results of our analysis with LAGEOS and LAGEOS 2, and with a number of GRACE (Gravity Recovery and Climate Experiment) models, that have confirmed this prediction of Einstein General Relativity and measured the Earth’s gravitomagnetic field with an accuracy of approximately 10%. We finally discuss the error sources in our measurement of gravitomagnetism and, in particular, the error induced by the uncertainties in the GRACE Earth gravity models. Here we both analyze the errors due to the static and time-varying Earth gravity field, and in particular we discuss the accuracy of the GRACE-only gravity models used in our measurement. We also provide a detailed analysis of the errors due to atmospheric refraction mis-modelling and to the uncertainties in measuring the orbital inclination. In the appendix, we report the complete error analysis and the total error budget in the measurement of gravitomagnetism with the LAGEOS satellites.