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

Question

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 400 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.

Explanation / Answer

We know that

The diamter of mars is (d) =6794km

Then the radius of the mars is (r) =d/2 =3397km =3397*103m

Mass (M) =6.42*1023kg

The universal gravitational constant (G) =6.67*10-11N.m2/kg2

If the spacecraft is in Martian orbit at an altitude of (h) = 400 km =400*103m

Now the total radius (R) =r+h =3397*103m+400*103m =3797*103m

The velocity required to escape the gravitational attraction of Mars is

v = Sqt(2GM/R) =Sqrt(2*6.42*1023kg*6.67*10-11N.m2/kg2/3797*103m)=Sqrt (0.02255*109) =0.4748*104 =4748m/s =4.748km/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.