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 Vess 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 p = 4.10 x 10 g/m' and volume V = 2.86 x 102m'. Recall that the universal gravitational constant is G = 6.67 x 10-" N.m/kg?. m/s Vesc

Answer 1

The Escape velocity of the obeject is given by the formula

$v_{esc}= {\sqrt \frac{2GM}{R} }$

G- Gravitational Constant

M - Mass of the Asteroid

R- Radius of the Asteroid

Given 1- 4.10 x 100 8 1 m3 VE 2.86 x 102 m3 GE 6.67 x 101 Nm²/ kg 2 P. <3 M 8 ху # 10 x 10° nog mo. 2.86 x10" m3 11.726 15 X 10 Volume of sphere & 4 TR3 R3 3 V R. 3/34 2.8661012 4x3.14 R = 8.807, 09 m Escape Vel Ve locity Veec 26M R. 2 X6.67 xD x 11. 126 x 1015 8807.09 √ 177.613 desc 13.33 mis

Therefore, the Escape Velocity = 13.33 m/s

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