A Portable Demonstration of Orbits in Curved Space-Time

Abstract

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.