Consider two small identical spheres of uniform density pm and radius r. the spheres are just touching each other and are at a distance d from a large planet with density pm and radius r (see figure 4). by equating the gravitational force of attraction between the touching spheres and the tidal force of the planet on the spheres, show that the spheres will be pulled apart by the planet's tidal forces if they venture closer than: pm r d~2.5(a) you may assume d 》 r 》 r. this is a good estimate of the planet's roche limit. the coefficient will change with the properties of the masses, but this is generally good enough b) estimate the roche limit for saturn and compare with the positions of saturn's rings use reasonable estimates for the densities of saturn and the particles composing its rings