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 largest impacts. The waves were thought to be travelling within a stable layer acting as a waveguide, and some scientists thought the stable layer must lie within the hypothesised tropospheric water cloud. However, other evidence seemed to indicate that the cometary fragments had not reached the water layer, and the waves were instead propagating within the stratosphere. Radio observations revealed a sharp increase in continuum emission at a wavelength of after the largest impacts, which peaked at 120% of the normal emission from the planet. This was thought to be due to synchrotron radiation, caused by the injection of relativistic