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 carbon disulfide persisted in the atmosphere for at least fourteen months after the collisions, with a considerable amount of ammonia being present in the stratosphere as opposed to its normal location in the troposphere. Counterintuitively, the atmospheric temperature dropped to normal levels much more quickly at the larger impact sites than at the smaller sites: at the larger impact sites, temperatures were elevated over a region wide, but dropped back to normal levels within a week of the impact. At smaller sites, temperatures higher than the surroundings persisted for almost two weeks. Global stratospheric temperatures rose immediately after the impacts,