**P. 4059.** The Little Prince (the main character of the novel written by Antoine de Saint-Exupéry) lives on the spherical planet named B-612, the density of which is 5200 kg/m^{3}. The Little Prince noticed that if he quickens his pace, he feels himself lighter. When he reached the speed of 2 m/s he became weightless, and began to orbit about the planet as a satellite.

*a*) Suppose that the asteroid does not rotate. What is the radius of the planet?

*b*) What is the escape speed on this planet?

*c*) Suppose that the asteroid rotates about its axis, and one day is twelve hours. What is the least speed of the little Prince at which he should run in order to orbit about the asteroid?

(4 points)

**Deadline expired on 11 April 2008.**