| 74 | Saturn and its System |
sequence directly from his investigations on the minimum distance a small fluid satellite may safely approach a fluid primary; for within a certain distance the differential or tidal pull of the planet must disrupt the satellite. This distance is called Roche's limit.
For equal densities of planet and satellite, Roche's limit is 2.44 times the planet's radius ;
for unequal densities, as , where is the density of the primary; of the satellite.
![{\displaystyle \textstyle {\sqrt[{3}]{\frac {d}{d'}}}\times {2.44}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81034730da86da7fcaaa0027acc7c35328839027)
Saturn's system offers the only instance where matter circulates within the limit, and Roche stated distinctly that the rings, therefore, must be mere meteoric stones.
Even Laplace had shown that the rings must be broken up for stability's sake into several narrow ones, each revolving at its own rate. Pierce proved that they could in no case be solid. Maxwell then demonstrated that they could not be so much as liquid, as disrupting waves would be set up, but must consist of a swarm of small bodies,—brickbats he likened them to,—each pursuing its own path. What the spectroscope in Keeler's ingenious hands made visible to the eye had thus been known to mechanics from the time of Laplace.
