A team of astronauts is on a mission to land on and explore a large asteroid. In

Question

A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density = 3.19 × 106 g/m3 and volume V = 1.25 × 1012 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 N·m2/kg2.

Explanation / Answer

Given that,

density = 3.19 x 106 g/m3 = 3190 kg/m3

Volume = 1.25 x 1012 m3

G = 6.67 x 10-11

We know that, mass = density x volume = 3190 x  1.25 x 1012 = 3.988 x 1015 kg

4/3 pi r3 = 1.25 x 1012  m3 which gives us r = 6683.65 m

Escape velocity is given by

v = sqrt(2Gm)/r = sqrt [(2 x 6.67 x 10-11 x 3.988 x 1015 )/ 6683.65] = 8.92 m/s

Hence, v = 8.92 m/s

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