You own a spaceship that can travel up to 25 m/s. Are you able to use it to escape from a spherical astroid that has a mass of 3.5 x 10^16 kg, and a radius of 8.8 km?

Question

You own a spaceship that can travel up to 25 m/s. Are you able to use it to escape from a spherical astroid that has a mass of 3.5 x 10^16 kg, and a radius of 8.8 km?

How do I solve this, and what equations do I use?

Answer 1

The escape velocity is found using the equation

v = √2GM/R

For this problem, M = 3.5*10¹⁶, R = 8.8 * 10³ (in meters), and G is the gravitational constant. So the escape velocity would be:

v = √2 (6.67*10^-11)(3.5*10¹⁶)/8.8*10³

v = 23.03 ^m/_s

So yes, you can escape because you can travel faster than the escape velocity