Question

A certain spherical asteroid has a mass of 3.5 × 10^16 kg and a radius of 8.8 km. What is the minimum speed needed to escape from the surface of this asteroid?A) 730 m/s B) 16 m/s C) 23 m/s D) 520 m/s

Answer 1

To solve this problem we will use the Newtonian theory that describes the escape velocity of a body of a planet as:

$v_e =  \sqrt{\frac{2GM}{r}}$

Where,

G = Gravitational Universal Constant

M = Mass of Asteroid

r = Radius

Our values are given as,

$M = 3.5*10^{16}kg$

$r = 8.8*10^3m$

Replacing we have,

$v_e = \sqrt{\frac{2(6.67*10^{-11})(3.5*10^{16})}{8.8*10^3}}$

$v_e = 23.03m/s$

Therefore the correct answer is C.