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 = 2.45 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

Explanation / Answer

the kinetic energy must be larger than the potential energy at the standpoint of the object: kinetic energy = 1/2 mv^2 potential energy = GMm/R where R is the distance to the center of the planet 1/2 mv^2 = GMm/R 1/2 v^2 = GM/R v^2 = 2GM/R v^2 = 2*6.67*10^-11*5.98*10^24/(6.37*10^8) vesc = 1119 m/s

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