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Interaction of weak gravitational waves with a small gyroscope universal-mounted in a macroscopic shell

  • Hans-Joachim SchornEmail author
Research Article
  • 60 Downloads

Abstract

The interaction of a weak plane gravitational wave with a small gyroscope universal-mounted in a macroscopic gimbal is calculated. The microscopic gyroscope can be exemplified by a small hollow sphere with a massive spherical rotor inside. The macroscopic gimbal may be realized by a massless sphere with a rigidly coupled bar-bell of two masses. The gravitational wave causes a torque on the bar-bell, which is transferred to the gyroscope by the gimbal. For the proposed configuration the calculation results in a precession angle of the gyroscope proportional to \(\varGamma \times \omega _r / \omega _G\) where \(\varGamma \) is the amplitude of the gravitational wave, \(\omega _r\) is the angular velocity of the rotor and \(\omega _G\) is the frequency of the gravitational wave. The precession angle can be measured, in principle, by angular laser interferometry and leads for our configuration to a length difference of \(\varDelta L \approx 10^{-18}\text { m}\) which is comparable with the formal arm length difference of LIGO for the assumed gravitational wave amplitude \(\varGamma = 10^{-21} \text { with }\omega _G = 1 \text { Hz}\).

Keywords

Gravitational waves Gyroscope Precession 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.SpitConsultConstanceGermany

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