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After launch from Earth orbit, a robot spacecraft of mass 5400 kg is coasting at constant speed halfway through its six- month flight to Mars when a NASA engineer discovers that, instead of heading for a 100-km-high orbit above the Martian surface, it is headed on a collision course directly toward the center of the planet. To correct the course, the engineer orders a short burst from the spacecraft's thrusters transverse to the direction of its motion. The thrust engines provide a constant force of 1200 N. For how long a time must the thrusters fire to achieve the correct course? Take needed data from Appendix C, and assume the distance between Earth and Mars to re- main constant at its smallest possible value.

After launch from Earth orbit, a robot spacecraft of mass 5400 kg is coasting at constant speed halfway through its six- month flight to Mars when a NASA engineer discovers that, instead of heading for a 100-km-high orbit above the Martian surface, it is headed on a collision course directly toward the center of the planet. To correct the course, the engineer orders a short burst from the spacecraft's thrusters transverse to the direction of its motion. The thrust engines provide a constant force of 1200 N. For how long a time must the thrusters fire to achieve the correct course? Take needed data from Appendix C, and assume the distance between Earth and Mars to re- main constant at its smallest possible value.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
The radius of Mars is 3396 km. Rounding off to two significant figures, the radius of the Mars will be 3400 km.
A transverse direction signifies the angle is the right angle. So the distance that the thrusters have imparted a momentum sufficient to direct the space craft to the side of the original path would be,
d = 100 km+3400 km
= 3500 km
As the space craft is half way through the six month journey, thus it has 3 months to move the 3500 km to the side.
So, time, t = 3 months
To obtain the corresponding transverse speed v, substitute 3500 km for d and 3 months for t in the equation v = d/t,
v = d/t
=(3500 km/3 months)
=(3500 km/3 months) (103 m/1 km) (1 month/30 days) (1 day/24 h) (1 h /3600 s)
= 0.45 m/s.
To find the time Δt for the rocket to fire, substitute 5400 kg for the mass of spacecraft m, 0.45 m/s for speed v and 1200 N for F in the equation Δt = mv/F,
Δt = mv/F
= (5400 kg) (0.45 m/s)/(1200 N)
= (5400 kg) (0.45 m/s)/(1200 N) )(1 kg.m/s2/1 N)
= 2.0s
From the above observation we conclude that, the required time for the rocket to fire would be 2.0s.

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