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 Despite published predictions, astronomers had not expected to see the fireballs from the impacts and did not have any idea in advance how visible the other atmospheric effects of the impacts would be from Earth. Observers soon saw a huge dark spot after the first impact. The spot was visible even in very small telescopes, and was about (one Earth radius) across. This and subsequent dark spots were thought to have been caused by debris from the impacts, and were markedly asymmetric, forming crescent shapes in front of the direction of impact. Over the next six days, 21 distinct impacts