Roche limit result cannot be represented in an exact algebraic formula. Roche himself derived the following approximate solution for the Roche limit: However, a better approximation that takes into account the primary's oblateness and the satellite's mass is: where formula_59 is the oblateness of the primary. The numerical factor is calculated with the aid of a computer. The fluid solution is appropriate for bodies that are only loosely held together, such as a comet. For instance, comet Shoemaker–Levy 9's decaying orbit around Jupiter passed within its Roche limit in July 1992, causing it to fragment into a number of smaller pieces. On
Comet Shoemaker–Levy 9 thus a serendipitous discovery, but one that quickly overshadowed the results from their main observing program. Comet Shoemaker–Levy 9 was the ninth periodic comet (a comet whose orbital period is 200 years or less) discovered by the Shoemakers and Levy, hence its name. It was their eleventh comet discovery overall including their discovery of two non-periodic comets, which use a different nomenclature. The discovery was announced in IAU Circular 5725 on March 27, 1993. The discovery image gave the first hint that comet Shoemaker–Levy 9 was an unusual comet, as it appeared to show multiple nuclei in an elongated region