First calculated theoretically in 1850 by French mathematician Eduardo Roche, the Roche limit is the approximate distance from a Jovian planet beyond which moons are found. Within this distance, tidal forces (differential gravitational forces) are stronger than the gravitational binding forces between particles so moons cannot form and instead rings are found. Tidal forces are the differences in gravitation force exerted on different parts of an object due to being different distances from the source. This paper presents a simulation of a scientific experiment. First, a simple expression for the Roche limit, the boundary between the distances from a Jovian planet that the ring systems and moons are found, is derived. A computer simulation of an observation is then used to test the expression “experimentally.”

Topics
Celestial mechanics, Gravitational force, Computer simulation, Educational assessment, Mathematician
1.
See http://www.asterism.org/tutorials/tut25-1.htm or http://burro.cwru.edu/Academics/Astr221/Gravity/roche.html, as well as Astronomy Encyclopedia, edited by Sir P. Moore (Oxford University Press, 2002), p. 345.
2.
B.W. Caroll and D.A. Ostlie, An Introduction to Modern Astrophysics (Addison Wesley, New York, 1996), pp. 766–767, mentions that it is incorrect only to consider tidal and binding forces and that more careful analysis would result in a numerical factor of 2.456.
3.
M. Zeilik and S.A. Gregory, Introductory Astronomy and Astrophysics, 4th ed. (Brooks/Cole, USA, 2005), pp. 48–50, used only tidal and binding forces, integrating to obtain a numerical factor of 2.5, and comments that the cohesive strength of the materials in the satellite should also be considered.
4.
E. Weisstein's World of Physics, http://scienceworld.wolfram.com/physics/RocheLimit.html, had the most rigorous derivation that included the rotation of a satellite and obtained a numerical factor of 2.423.
5.
See also http://pegasus.phast.umass.edu/a100/handouts/roche.html or http://www.astro.lsa.umich.edu/users/cowley/lecture32.
6.
Voyager SkyGazer, college edition, version 3.4, Carina Software, http://www.carinasoft.com, comes with this simulation, Saturn and 28 Sgr, in the “Basics” folder, but a similar simulation should be able to be set up and carried out with other comparable planetarium software packages such as Starry Night, Redshift, or The Sky.
7.
Planetary data, including the densities of planets and their moons, are generally available in any introductory astronomy text, i.e., J. Bennett, M. Donahue, N. Scheider, and M. Voit, The Cosmic Perspective (Pearson Inc. Addison-Wesley, San Francisco, 2004), pp. A-16–17.
8.
This and many other useful images of Saturn can be found at NASA's Solar System exploration webpage at http://solarsystem.nasa.gov/planets/profile.cfm?Object=Saturn&Display=Gallery.
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© 2006 American Association of Physics Teachers.
2006
American Association of Physics Teachers
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