The shape of “the Spandex” and orbits upon its surface
2002; American Institute of Physics; Volume: 70; Issue: 1 Linguagem: Inglês
10.1119/1.1412645
ISSN1943-2909
AutoresGary White, Michael M. Walker,
Tópico(s)Advanced Mathematical Theories and Applications
ResumoWhat is the shape that results when a flat rubber sheet is warped by placing a heavy ball upon it? We show that, at distance R far from the center of a ball of mass M, the height h of the surface above the ball’s center is given by h(R)=AM1/3R2/3, where A is a constant determined by the stretchiness of the rubber and the earth’s gravitational constant. This happy result allows one to analyze the orbits of marbles and coins as they roll across the surface in some detail, providing very nice analogues for a wealth of topics in celestial mechanics, from Kepler’s laws to tides and the Roche limit.
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