Tidal disturbances of small cohesionless bodies: limits on planetary close approach distances

Abstract

The population of Near-Earth Objects contains small bodies that can make very close passages to the Earth and the other planets. Depending on the approach distance and the object's internal structure, some shape readjustment or disruption may occur as a result of tidal forces. A real example is the comet Shoemaker Levy 9 which disrupted into 21 fragments as a result of a close approach to Jupiter, before colliding with the planet during the next passage in July 1994. We have recently developed an exact analytical theory for the distortion and disruption limits of spinning ellipsoidal bodies subjected to tidal forces, using the Drucker-Prager strength model with zero cohesion. This model is the appropriate one for dry granular materials such as sands and rocks, for rubble-pile asteroids and comets, as well as for larger planetary satellites, asteroids and comets for which the cohesion can be ignored. Here, we recall the general concept of this theory for which details and major results are given in a recent publication. In particular, we focus on the definition of “material strength”: while it has great implications this concept is often misunderstood in the community of researchers working on small bodies. Then, we apply our theory to a few real objects, showing that it can provide some constraints on their unknown properties such as their bulk density. In particular it can be used to estimate the maximum bulk density that a particular object, such as 99942 Apophis, must have to undergo some tidal readjustments during a predicted planetary approach. The limits of this theory are also discussed. The cases where internal cohesion cannot be ignored will then be investigated in the near future.