# What is the radius of a round asteroid from which a person can develop the second cosmic speed, that is, jump into space and fly away?

**What is the radius of a round asteroid from which a person can develop the second cosmic speed, that is, jump into space and fly away? We assume that a person on Earth jumps to a height of h = 1 m, the density of the asteroid is ρ = 2 g / cm3**

we have a person who can put energy into a jump mgh = mV ^ 2/2, that is, develop a speed V = sqrt (2gh) = sqrt (2 * 10 * 1) = 4.5 m / s. This should be equal to the second space velocity for our asteroid.

The second cosmic = sqrt (2 * GM / R), where the mass of the asteroid is M = 4/3 * pi * R ^ 3 * ρ, we equate

2 * GM / R = 20

2 * G * 4/3 * pi * R ^ 2 * ρ = 20

R ^ 2 = 10 * 3 / (4 * 3.14 * ρ * G)

R = sqrt [10 * 3 / (4 * 3.14 * 2000 * 6.7 * 10 ^ -11)] = 10 ^ 5 * sqrt [3 / (4 * 3.14 * 20 * 6.7)] = 4200 meters