Most asteroids are oblong in shape. Approximate an asteroid as being made up of two identical spheres of mass M and radius R that are just touching each other, in a figure eight. In terms of G, M, and R, what is the escape velocity for a spaceship taking off from the top of the figure eight? A) (2GM/R)^1/2 B) (4GM/3R)^1/2 C) (8GM/3R)^1/2 D) (3GM/R)^1/2 E) (7GM/5R)^1/2

Question

Quizplus · Accepted Answer

The escape velocity is derived from the gravitational potential energy and kinetic energy. For two spheres touching, the potential energy is the sum of the potential energies due to each sphere. The escape velocity is calculated as v = sqrt(2 * (G * M / R + G * M / (2R))) = sqrt(8GM/3R).

Most Asteroids Are Oblong in Shape