The Roche limit is the radial distance from the center of a planet at which the tidal forces exerted by the planet on one of its moons will overcome the gravitational force holding the moon together. The result is that the moon will be torn apart (or never succeed in forming in the first place) and eventually form a ring around the planet from the material of the disintegrated moon. The Roche limit can be determined from 1/3 M. d = 1.26R moon M. where Rmoon is the radius of the moon and Mplanet and M moon planet moon are the masses of the planet and moon, respectively. (a) Titania, the largest moon of Uranus, has a radius of 7.88 x 105 m and mass of 3.53 x 1021 kg. At what distance from Uranus will Titania break up due to tidal forces exerted by the planet? (Give your answer in terms of Uranus's radius and measured from the planet's center.) RUranus (b) Near very dense bodies such as black holes, the tidal forces exerted by that body become enormous, so that matter is elongated in the radial direction in a process called spaghettification. A 66.3 kg astronaut wishes to approach a black hole eleven times more massive than the Sun, with a Schwarzschild radius of 32.4 km. If the human body can withstand a tension along its axis of 5.00 x 105 N, what is the distance of closest approach for the astronaut (in km) if he wishes to avoid spaghettification if he is 1.65 m tall? (Assume the astronaut intends to approach the black hole feet first.) km