A NASA mission to update the electronics on a circular orbiting space station ha

Question

A NASA mission to update the electronics on a circular orbiting space station has required the work of four astronauts. The astronauts have been docked to the space station which is orbiting the Earth with a speed V=1.64 km/s, for 8 days. The next mission is to travel away from Earth to Mars. In order to do this, the astronauts' shuttle must escape the gravity of Earth by firing it's thrusters. What speed, Vesc, must the astronauts' shuttle attain to escape the Earth? The radius of the Earth is Re=6.37*10^6 m., the mass of the Earth Me=5.98*10^24 kg, the acceleration due to gravity on the surface of the Earth g=9.81 m/s^2 and the gravitational constant G=6.67*10^-11 N m^2/kg^2.

Explanation / Answer

Vesc = sqrt 2 times of Vo

= 1.414 * 1.64 KM/s

= 2.31 km/s

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