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The spacecraft is designed to leave the surface of Mars with the first stage of its...

The spacecraft is designed to leave the surface of Mars with the first stage of its propulsion system and be put into Martian orbit. Then, the second stage is used to boost the spacecraft from Martian orbit into an interplanetary trajectory and return to Earth. If the spacecraft is in Martian orbit at an altitude of 224 km, what is the velocity required to escape the gravitational attraction of Mars. Give your answer in km/s. Note that the velocity direction and magnitude required to actually return to Earth may be different.

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Answer #1

Given: Altitude at which spacecraft is in the Martian Orbit = 224 km

Escape Velocity is calculated using the formula

where G is the Universal Gravitational Constant, G=6.67*10-11 m3/kg s2

M is the Mass of Planet from which the spacecraft should escape i.e., Mass of Mars in this case

M=6.39*1023 kg

R0 is the Distance between the centers of the two bodies i.e., distance between center of Mars and the spacecraft.  

R0=Radius of Mars+Altitude

Radius of Mars, R= 3390 km

R0=3390+224=3614 km= 3614000 m

Substitute the values in the above formula

v= 4856.62 m/s= 4.85662 km/s

The spacecraft should travel with a velocity of 4.86 km/s to escape the gravitational attraction of Mars.

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