FYKOS Year 39 Series 4 Problem 3 — The Little Prince · FYKOS 39 #39.4.3

Physics · mechanics · modern-physics

Problem

What is the minimum initial velocity required for the Little Prince to jump from the asteroid B-612, of density

\rho_1=3~000\,\mathrm{kg\cdot m^{-3}}

and radius

R=5\,\mathrm{km}

, in order to land on the surface of the King's asteroid, which has the density of

\rho_2=2~500\,\mathrm{kg\cdot m^{-3}}

and radius

r=3\,\mathrm{km}

? The distance between the centers of the asteroids is fixed at

d = 50\,\mathrm{km}

. The asteroids do not move toward each other. Atmospheric effects, orbital motion, and rotation of both homogeneous asteroids may be neglected.