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1.We assume a spherical orbit for the star and a spherical distribution of mass within the galaxy.
2.Vera Rubin, “Seeing dark matter in the Andromeda galaxy,” Phys. Today 59 (12), 8 (2006).
3.V. C. Rubin, W. K. Ford Jr., and N. Thonnard, “Rotational properties of 21 Sc galaxies with a large range of luminosities and radii, from NGC 4605 (R=4 kpc) to UGC 2885 (R=122 kpc),” Astrophys. J. 238, 471487 (1980).
4.James B. Hartle, Gravity: An Introduction to Einstein's General Relativity (Addison-Wesley, 2003).
5.In the universe, changing the distances between observer, lens, and source (which are determined from cosmological redshifts) will also affect the size of the Einstein ring, and the accuracy with which these distances are measured will impact the uncertainty in the final mass estimate. In the gravity simulator, these distances are relatively fixed, as massive lenses naturally sink to the center. The effect of distances on θE can be explored using the wine glass demonstration discussed at the end of this article.
6.Gary D. White and Michael Walker, “The shape of ‘the Spandex’ and orbits upon its surface,” Am. J. Phys. 70, 48 (Jan. 2002).
7.Chad A. Middleton and Michael Langston, “Circular orbits on a warped spandex fabric,” Am. J. Phys. 82, 287 (April 2014).
9.Melissa Hoffman and Meredith Woy, “Fabric of the Cosmos,” 2012 Science Outreach Catalyst Kit,
10.We used plywood to create the circular frame because we found that PVC pipes were too rigid to bend into a circle of our designated diameter. This is in contrast to experience discussed in Ref. 8.
11.Here we used a localized central mass to investigate orbital rotation speeds. A more accurate model of dark matter would be to use an extended object—perhaps a flexible sheet of lead—attached to the underside of the spandex, since the dark matter is known to extend far beyond the visible matter of a galaxy (see Fig. 1). However, our students do not appear to suffer misconceptions about dark matter detection because of this model limitation.
12.In this respect, we started similarly to the activity “Introduction to Spandex as a Model for Spacetime,” described in the 2012 Science Outreach Catalyst Kit in Ref. 9.
13.In order to compare the Einstein radius of different lenses, it is important to have a way to standardize the initial speed of the photons.
14.The facilitator may need to remove the optional foam pipe insulation around the edge of the simulator in order to allow marbles to roll off the device and into the telescope bucket.
15.A similar activity, titled “Formation of the Solar System,” is described in Ref. 9.
16.Paul Huwe and Scott Field, “Modern gravitational lens cosmology for introductory physics and astronomy students,” Phys. Teach. 53, 266270 (May 2015).
17.Maria Falbo-Kenkel, and Joe Lohre, “Simple gravitational lens demonstrations,” Phys. Teach. 34, 555557 (Dec. 1996).
18.Don Lincoln, “Dark matter,” Phys. Teach. 51, 134138 (March 2013).
20.For elementary school students it could be a model of the solar system, while for more advanced students it could be a visualization of Einstein's curved spacetime.

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Dark matter makes up most of the matter in the universe but very little of a standard introductory physics curriculum. Here we present our construction and use of a spandex sheet-style gravity simulator to qualitatively demonstrate two aspects of modern physics related to dark matter. First, we describe an activity in which students explore the dependence of orbital velocities on the central mass of a system, in a demonstration of how scientists first discovered dark matter. Second, we discuss the use of the gravity simulator as a visualization of gravitational lensing, a current astronomical technique for mapping dark matter in the sky. After providing the necessary background for the phenomena of interest, we describe our construction of the gravity simulator and detail our facilitation of these two activities. Together, these activities provide a conceptual visualization of gravitational phenomena related to indirect detection techniques for studying dark matter.


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