# 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

Lockerbie, N.A. and Xu, X. and Veryaskin, A.V.
(1995)
*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.*
General Relativity and Gravitation, 27 (11).
pp. 1215-1229.
ISSN 0001-7701

## 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.

Item type: | Article |
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ID code: | 17645 |

Keywords: | spherical harmonic representation, gravitational coupling, hollow cylinder, gravitational source, STEP experiment, Physics, Physics and Astronomy (miscellaneous) |

Subjects: | Science > Physics |

Department: | Faculty of Science > Physics Faculty of Science > Strathclyde Institute of Pharmacy and Biomedical Sciences > Pharmaceutical Sciences |

Depositing user: | Strathprints Administrator |

Date Deposited: | 05 May 2010 10:50 |

Last modified: | 04 May 2016 13:59 |

URI: | http://strathprints.strath.ac.uk/id/eprint/17645 |