2. The Little Prince In the novel The Little Prince by Antoine de Saint-Exupéry, the Prince lives on a planet which is about a size of a house. Let's assume that the planet is a sphere of radius R = 10.0 m and that its density, p = M/v, is similar to that of the Earth (5520 kg/m³). Little Prince —10.0 m- (a) Calculate the mass of the planet in kilograms. (b) What is the gravitational acceleration, ag, on the surface of the planet? Use Newton's universal gravitation to find it. Is this a realistic number or is the novel a fiction after all? (c) Find the escape velocity from the surface of the planet. (d) There are days and nights on the Little Planet as it rotates about its axis. However, the planet cannot be rotating too fast, otherwise the Little Prince will be thrown off. The fastest possible angular velocity, w, is that for which the gravitational acceleration, ag, on the Little Prince just barely provides the centripetal acceleration, ac Rw2, needed to keep him in a uniform circular motion around the equator. Calculate the greatest possible angular velocity for the Planet, and then determine the shortest possible length of one day on the Planet. Express your answer in hours. =

2. The Little Prince In the novel The Little Prince by Antoine de Saint-Exupéry, the Prince lives on a planet which is about a size of a house. Let's assume that the planet is a sphere of radius R = 10.0 m and that its density, p = M/v, is similar to that of the Earth (5520 kg/m³). Little Prince —10.0 m- (a) Calculate the mass of the planet in kilograms. (b) What is the gravitational acceleration, ag, on the surface of the planet? Use Newton's universal gravitation to find it. Is this a realistic number or is the novel a fiction after all? (c) Find the escape velocity from the surface of the planet. (d) There are days and nights on the Little Planet as it rotates about its axis. However, the planet cannot be rotating too fast, otherwise the Little Prince will be thrown off. The fastest possible angular velocity, w, is that for which the gravitational acceleration, ag, on the Little Prince just barely provides the centripetal acceleration, ac Rw2, needed to keep him in a uniform circular motion around the equator. Calculate the greatest possible angular velocity for the Planet, and then determine the shortest possible length of one day on the Planet. Express your answer in hours. =