of the internal gravity, produced by the same operation. By such action as this the icy globe should be quickly torn into pieces and distributed around its primary in the form of a ring of fragments.
Prof. Daniel Vaughan has shown that such is the origin of the rings of Saturn, and ascribed the close approach of the two satellites which formed them to the action of a resisting medium.
If this were a globe of water instead of ice, it is very evident that much less disruptive energy would be required to tear it to pieces, on account of the greater mobility of its parts; most probably not more than one-seventh of the above-named force would be required to accomplish this result.
If this force be sufficient, and the globe of water be made to revolve around any large planet in fifteen hours or less, the tidal energy will tear it into atoms by virtue of the following law:
It can be demonstrated—1. That the tidal energy generated on a spherical satellite of small but constant mass, when revolving around a large primary, varies directly as its diameter; 2. That it varies, also, inversely as the square of its periodic time; and 3. That the ability of the same satellite to resist the disruptive tendency of this tidal energy varies inversely as the square of its diameter; provided there be no cohesive force to aid in resisting this tendency, and in a nebulous satellite there would be none to do so.
As the first and third propositions relate to the diameter, they may be included in one, and then the law may be stated as follows:
The disruptive ability of the tidal energy of a primary planet on a nebulous satellite of small but unvarying mass varies directly as the cube of the diameter and inversely as the square of the periodic time. Let us apply this law to the case in hand. To do this it may be very safe to estimate that a ten-mile globe of water, while yet in the state of a nebulous satellite, would occupy the globular space of at least one hundred miles in diameter. This would give it a density of only 1000 of that of water, which, however, would still be millions of times greater than that of the original nebula out of which the entire system was made.
According to the above law, the disruptive ability of the tidal energy on the nebulous satellite must be 103, or 1,000 times as effective as on the ten-mile liquid one, if revolving in the same time. Now, to find the shortest time by the above law in which this nebulous globe could revolve around its primary without disruption, we must multiply the fore-named fifteen hours by the square root of 103; the product of this multiplication amounts to about 194 days. As this is the shortest time in which any small nebulous satellite of this density can revolve around any large primary without disruption, it becomes very evident that nearly all the solid ones in our system must have been
- "Popular Physical Astronomy," by Prof. Daniel Vaughan. Cincinnati: Freeman & Spofford. 1858.