You are a visitor aboard the New International Space Station, which is in a circ

Question

You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of v_o = 1.10 km/s. The station is equipped with a High Velocity Projectile Launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or else eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth. With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to 'escape" in this way? For reference, recall that the radius of the Earth is R_E = 6.37 times 10^8 m, the mass of the Earth is M_E = 5.98 times 10^24 kg, the acceleration due to gravity on the surface of the Earth is g = 9.81 m/s^2 and the universal gravitational constant is G = 6.67 times 10^-11 N middot m^2/kg^2.

Explanation / Answer

The minimum escape velocity will be:

v(esc) = sqrt (2GMe/R)

v(esc) = sqrt (2 x 6.67 x 10^-11 x 5.98 x 10^24/6.37 x 10^8 )

v(esc) = 1.12 x 10^3 m/s

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