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A Portable Demonstration of Orbits in Curved Space-Time

Published online by Cambridge University Press:  12 April 2016

David B. Friend
Affiliation:
Department of Astronomy and Department of Physics, Williams College, Williamstown, Massachusetts 01267, U.S.A.
Kevin Forkey
Affiliation:
Department of Astronomy and Department of Physics, Williams College, Williamstown, Massachusetts 01267, U.S.A.

Extract

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Many introductory astronomy students, when confronted with the idea of curved space-time in discussions of relativity and cosmology, don’t have a very good grasp of what this really means. They are told that the presence of mass “curves” space-time, but it is often not clear to them what is meant by that statement. We have developed a simple portable demonstration of what is meant by curved space-time, by using a two-dimensional analog. We have stretched a thin rubber sheet over a circular metal frame which is supported a few inches above a table top. By placing a heavy weight (about a kilogram) in the center of the sheet, we can mimic the effect of the curvature of space-time around a massive object on an orbiting body (such as a planet orbiting a star). We roll a small ball around the sheet, and the ball describes approximately elliptical orbits around the weight (see the photograph). The orbits aren’t exactly elliptical for two reasons: energy is dissipated by friction between the ball and the sheet, and the sheet doesn’t quite have the correct shape (it is shaped roughly like In r instead of 1/r: see this by solving Laplace’s equation in two dimensions with circular symmetry). We like to project this demonstration with a video camera placed directly above the sheet, so that the students can see the “orbit” without actually seeing the curvature of the sheet.

Type
7. Teaching Aids and Resources
Copyright
Copyright © Cambridge University Press 1990