Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

N.A. Lockerbie, X. Xu, A.V. Veryaskin

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Abstract

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinder's end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 104 times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies.
Original languageEnglish
Pages (from-to)1215-1229
Number of pages14
JournalGeneral Relativity and Gravitation
Volume27
Issue number11
DOIs
Publication statusPublished - Nov 1995

Keywords

  • spherical harmonic representation
  • gravitational coupling
  • hollow cylinder
  • gravitational source
  • STEP experiment

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