In an experiment carried out at the University of Wuppertal, two pendulums are positioned between two heavy "field masses." Since the gravitational force on a pendulum depends on its distance to the field masses, moving the latter with spindles also increases or decreases the distance of the pendulums from each other.
The constant G can be determined from this movement of the pendulums relative to each other. This process involves computing sixtuple integrals of the form
where the integration is over the volumina of one field mass and (a part of) one pendulum with densities ρ, and d denotes the directed distance between the respective points. Due to the complicated geometry of the pendulums they are subdivided into segments S( i, k ).
In this project we have developed adaptive techniques that yield the value of a multi-dimensional integral with a guaranteed prescribed maximum error. Using these methods we were able to show that
|||Bruno Lang. Derivative-based subdivision in multi-dimensional verified Gaussian quadrature. In Götz Alefeld, Jiři Rohn, Siegfried Rump, and Tetsuro Yamamoto, editors, Symbolic Algebraic Methods and Verification Methods, pages 145--152, Wien, 2001. Springer-Verlag. [ Abstract ]|
|||Bruno Lang. A comparison of subdivision strategies for verified multi-dimensional Gaussian quadrature. In Tibor Csendes, editor, Developments in Reliable Computing --- SCAN-98 Proceedings, pages 67--75, Dordrecht, The Netherlands, 1999. Kluwer Academic Publishers. [ Abstract ]|
|||Bruno Lang. Verified quadrature in determining Newton's constant of gravitation. J. Univers. Comput. Sci., 4(1):16--24, 1998. [ Abstract ]|
|||Oliver Holzmann, Bruno Lang, and Holger Schütt. Newton's constant of gravitation and verified numerical quadrature. Reliab. Comput., 2(3):229--239, November 1996. [ Abstract ]|
|||Oliver Holzmann. Untersuchungen zur Integration bei der Messung der Newtonschen Gravitationskonstanten. Diploma thesis, Bergische Universität Gesamthochschule Wuppertal, Germany, May 1996.|