The Roche limit. Some ???bodies??? in the solar system are a collection of rocks held together solely or mainly by their gravitational attraction. When such an object comes close to a planet, so-called tidal forces will break the object apart. Consider an asteroid composed of two pieces, each of mass m = 1 ?? 10¹⁶kg, and each spherical with diameter d = 2 ?? 10⁴m. Suppose this object approaches the Earth as shown in Figure P6.102. The two pieces of the asteroid are at slightly different distances from the Earth, so the Earth???s gravitational force on the two pieces will be slightly different. At what distance R from the Earth will the Earth???s gravitational force pull this asteroid apart? This distance is called the Roche limit, and it determines when asteroids or moons near planets such as Saturn break apart to form rings around the planet.

Figure P6.102

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R Asteroid Earth