EG 31 Fundamentals of Engineering Profs. Munden & Berdanier Problem Set #2 rA Qu

Question

EG 31 Fundamentals of Engineering Profs. Munden & Berdanier Problem Set #2 rA Quicker Way to Mars 1. The VASIMR plasma thruster is designed to efficiently power a spaceship to Mars, or even beyond. It ejects a hydrogen plasma to generate continuous thrust throughout the whole trip to Mars. This means you can accelerate at a constant rate during the first half of the trip (to Mars), then turn the ship around and decelerate for the second half of the trip (to stop at Mars). How long will a round-trip to Mars take if the thruster generates only 5N of force for the whole trip, and the spaceship has a mass of 100,000 kg? What is the top speed the ship will reach?

Explanation / Answer

given thrust generated by the engine, T = 5 N
mass of the spaceship, m = 100,000 kg
so acceleration a = T/m = 5*10^-5 m/s/s

now distance to mars, form earth, d = 54.6*10^9 m
so half of this distance will be spent accelewrating
time taken to accelerate = t
so starting from rest
d/2 = 0.5*a*t^2
t = sqroot(d/a) = 3.3045*10^7 seconds
so toatal time of round trip = 4t ( as the trip can be divided into 4 parts of equal time interval, accelerating to mars, decelerating to mars and same steps while coming back)
so total time pf journey = 13.2181*10^7 s = 4.191 years

maximum speed in the journey = v
v = a*3.3045*10^7 = 1652.25 m/s

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