Petit Prince

01 May 2024

Please estimate (i) the mass and density of the planet of the Petit Prince, assuming that there is the same surface gravity as on Earth, (ii) the tidal field between head and feet of the Petit Prince, (iii) the gravitational time dilation between head and feet, (iv) the pressure inside the planet from the height of the volcanic plume.

bonus question: Would the Petit Prince remain on the surface of the Planet despite the centrifugal force if there are 43 sunsets each day?

bonus question 2: Could the Petit Prince jump into space by accelerating to the escape velocity?

bonus question 3: What would the planet of the Petit Prince consist of?

bonus question 4: Where would be the planetostationary orbit for the planet of the Petit Prince?

bonus question 5: At what height above the surface can you hold a glass of water upside down without spilling it?

bonus question 6: Antoine de Saint-Exupery blows a spherical cloud of smoke with his pipe, which orbits the planet: how would the shape of the cloud change in time?

bonus question 7: How long would you need to wait until the cloud of smoke forms a ring around the planet?

bonus question 8: The Petit Prince makes a soap bubble and lets it orbit the planet. Would the soap bubble burst under the action of tidal forces?

bonus question 9: What would be the relationship between height and atmospheric pressure? Would the total mass of the atmosphere be finite?