Table of Contents
Section 4
Every body is held together by two forces, its self-gravitation and its internal strength due to molecular bonding. With no external forces on it (and no initial rotation), a liquid body would form a perfect sphere just from self-gravitation (and from very weak molecular forces -- surface tension). Approaching another body, the sphere would begin to elongate toward that body. Finally, when the difference in gravitational force on the near side and far side of the former sphere exceeded the self-gravitation, the body would be torn apart. The distance from the larger body at which this disruption occurs is the so-called Roche limit, named for the man who first studied the problem. The differential gravitational effects of the Moon and the Sun are what raise the tides in Earth's oceans, and such forces are often referred to as tidal forces.
Solid bodies have intrinsic strength due to their molecular bonds. Aluminum wire may have a tensile strength of 2.4 x 10^9 dynes/cm^2 (5 million lb./ft.^2) and good steel wire a tensile strength 10 times larger still, which far exceeds the tidal force of anything short of a black hole. As stated in Section 1, comets have very low tensile strength, near 1 x 10^3 dynes/cm^2 (2 lb./ft.^2). They can be pulled apart very easily by tidal force (or any other substantial force, for that matter). Some 25 comets have been observed to split over the past two centuries. In other cases, two or more comets have been discovered in nearly the same orbit, and calculations have indicated that they were once a single comet. A few of these cases have been obviously attributable to the tidal forces of Jupiter (Comet Brooks 2 and Comet Shoemaker-Levy 9) or the Sun (the Kreutz comet family), while other splittings have to be attributed to less obvious causes. For example, the loss of material from an active comet, which tends to occur from a few localized areas, is bound to weaken it. It may be that a rapidly rotating comet can be weakened to the point where the centrifugal force is sufficient to cause large pieces to break off.
The Kreutz family is the name given to many comets which closely approach the Sun from one direction in space. They always approach the Sun to within 3 million kilometers (1.9 million miles) or less, and some have actually hit the Sun. The family was named for Heinrich Kreutz, who published extensive monographs on three of these comets and supported the idea that they had a common origin, perhaps in a giant comet observed in 372 B.C. Today the Kreutz family has eight definite, well-studied members; 16 probable members (that are listed as probable only because they didn't survive passage within 800,000 kilometers or 500,000 miles of the Sun to permit further study); and three more possible members. Extensive work by Brian Marsden suggests that all of these may have resulted from the splitting of two comets around 1100 A.D., which in turn may have been the parts of the great comet of 372 B.C. Those Kreutz fragments which survive their encounters with the Sun are often found to have split yet again!
The classic Roche limit for a (fluid) body of density 1 g/cm^3 approaching Jupiter is about 119,000 kilometers (74,000 miles) above the cloud tops of the planet. It is about 169,000 kilometers (105,000 miles) for a body having a density of 0.5 g/cm^3. More complete modern theories making different assumptions result in a somewhat smaller limit. In 1886, Comet Brooks 2 came within 72,000 kilometers (44,740 miles) of Jupiter's clouds and split into two pieces. In July 1992, Comet Shoemaker-Levy 9 came within about 25,000 kilometers (15,500 miles) of Jupiter's clouds and fragmented into 21 or more large pieces and an enormous amount of smaller debris down to micron or submicron size. Details of this last event follow.