# The gravitational coupling between longitudinal segments of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

Lockerbie, N.A. and Xu, X. and Veryaskin, A.V.
(1996)
*The gravitational coupling between longitudinal segments of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment.*
Classical and Quantum Gravity, 13 (8).
pp. 2041-2059.
ISSN 0264-9381

## Abstract

The gravitational interaction is derived between a solid longitudinal segment cut from a cylinder of uniform density, and an external point mass. The derivation is expressed p(2p+m+1)(m)(cos theta), and the parametric form of the coupling coefficients K-2p,K-m,K-alpha(psi) is presented. This theory is applied to the gravitational interaction between a point mass and a finite hollow cylinder, where the cylinder bears a number of 'flats' cut into its outer surface. The 'flats' are imagined to be regularly spaced in azimuth around the cylinder, each flat being treated as the removal of a solid segment from the full cylinder. Such forms of test mass have been proposed for the satellite test of the equivalence principle (STEP) experiment, since the masses may then be prevented from rotating in azimuth-a factor which is considered to be essential for this experiment. The gravitational theory developed here is applied to such STEP test masses, and two 'low gravitational susceptibility' designs for test-mass pairs are considered, having four and six 'flats', respectively. An expression for the axial force on such masses is derived which is more than 10(5) times faster to compute than a Monte Carlo integration of similar accuracy, by virtue of which it is shown that a design with six or more 'flats' is to be preferred. This theory is shown to have much wider applicability to gravitational problems involving general segmented cylindrical bodies, including square- and hexagonal-section prisms of finite length (hollow or solid).

#### ORCID iDs

Lockerbie, N.A. ORCID: https://orcid.org/0000-0002-1678-3260, Xu, X. and Veryaskin, A.V.;Item type: Article ID code: 17619 Dates: DateEventAugust 1996PublishedKeywords: cosmology, gravitation, longitudinal segments, 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 SciencesDepositing user: Strathprints Administrator Date deposited: 30 Apr 2010 11:03 Last modified: 20 Jan 2021 18:22 URI: https://strathprints.strath.ac.uk/id/eprint/17619