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
Lexell's Comet The comet was also noted by several other astronomers. The comet was observed in Japan. Surviving records identify it as an astronomical and historical phenomenon. It was observed in the Hejaz in Safar 1184 AH (June 1770), where some believed it to be the comet predicted by the poet al-Fasi, portending future events. On July 1, 1770, the comet passed 0.015 astronomical units from Earth, or approximately 6 times the radius of the Moon's orbit. Charles Messier measured the coma as 2° 23' across, around four times the apparent angular size of the Moon. An English astronomer at the time