Dietmar S. Theiss

On the Gravitational effects of rotating masses - The Thirring-Lense Papers

The purpose of this work is to provide a critical analysis of the classical papers of H. Thirring [Phys. Z.,19, 33 (1918);Phys. Z.,22, 29 (1921)] and J. Lense and H. Thirring [Phys. Z.,19, 156 (1918)] on rotating masses in the relativistic theory of gravitation and to render them accessible to a wider circle of scholars. An English translation of these papers is presented which follows the original German text as closely as possible. This is followed by a concise account of the significance of the results of these papers as well as the possibility of measuring the gravitational effects of rotating masses.

On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect

The difference in the proper azimuthal periods of revolution of two standard clocks in direct and retrograde orbits about a central rotating mass is proportional to J/M c 2 , where J and M are, respectively, the proper angular momentum and mass of the source. In connection with this gravitomagnetic clock effect, we explore the possibility of using spaceborne standard clocks for detecting the gravitomagnetic field of the Earth. It is shown that this approach to the measurement of the gravitomagnetic field is, in a certain sense, theoretically equivalent to the Gravity Probe-B concept.

A general relativistic effect of a rotating spherical mass and the possibility of measuring it in a space experiment

Abstract Tidal forces caused by a slowly rotating spherical mass are calculated using the relativistic theory of tides. The possibility of measuring the gravitational “magnetic” contribution of the earth to the tidal acceleration between test masses in a satellite is considered. It is shown that in such an experiment unexpectedly large secular “magnetic” contributions can occur. Already after ≈ 20 days of observation this new effect would reach a value which is larger than the total error of measurement by a factor of 102.

Relativistic Effects in the Motion of the Moon

The main general relativistic effects in the motion of the Moon are briefly reviewed. The possibility of detection of the solar gravitomagnetic contributions to the mean motions of the lunar node and perigee is discussed.

Gravitational influence of the rotation of the sun on the earth-moon system

Abstract A new approach to the relativistic theory of the motion of the moon is presented. In this framework, the contribution of the gravitational “magnetic” field of the sun to the tidal force acting on the earth-moon system is determined. Furthermore, the main relativistic perturbations in the lunar motion are estimated.

A gradiometer experiment to detect the gravitomagnetic field of the earth

We describe a space-borne experiment to detect the Lense-Thirring field produced by the proper rotation (mass-current) of the Earth. This gravitomagnetic field will generate an increasing signal in a gravity gradiometer orbiting the Earth in local inertial (gyroscope) orientation. For a polar orbit of 600 km altitude, the signal will grow with a (constant) rate of about 2 x 10−4E per month (1E = 1 Eotvos = 10−9sec−2). In view of instrumental accuracies achieved in the last years, this effect could, in principle, be detected at present by Paiks high-sensitive superconducting gravity gradiometer in combination with precise gyroscopes placed in a drag-free Earths satellite. A preliminary error analysis for the experiment indicates that the effect could already be measured after ≈ 1 month with sufficient accuracy (relative error of ≈ 1%). To achieve this, precise gyroscopes would be necessary, which, however, were allowed to be less precise than the present Stanford gyroscopes by a factor of - 20. In addition, we present a method for isolating the gravitomagnetic signal from the dominant Newtonian background.

A new gravitational effect of a deformed mass

Abstract A new relativistic tidal effect of a deformed axisymmetric mass is described and the possibility of measuring it in an earth satellite is considered. The calculations show that the quadrupole moment of the earth causes a large secular relativistic contribution to the relative acceleration between two test masses placed in a satellite around the earth. Already after ≈10 hours of observation this new relativistic effect would exceed the corresponding newtonian quadrupole effect by a factor of 10.