After parachuting through the Martian atmosphere, the Mars Science Laboratory ex

Question

After parachuting through the Martian atmosphere, the Mars Science Laboratory executed a complex series of maneuvers that successfully placed the rover Curiosityon the surface of Mars in 2012. The final 22 s of the landing involved, in this order, firing rockets (1) to maintain a constant downward velocity of 32 m/s, (2) to achieve a constant deceleration that brought the downward speed to 0.75 m/s, and (3) to hold that constant velocity while the rover was lowered on cables from the rest of the spacecraft. The rover's touchdown was indicated by a sudden decrease in the rocket thrust needed to maintain constant velocity. (Figure 1) shows the rocket thrust (upward force) as a function of time during these final 22 s  of the flight and the first few seconds after touchdown. Remember that all this happened at Mars, so you'll need to consult Appendix E in the textbook.

a. Identify the two constant-velocity phases, the constant-deceleration phase, and the post-touchdown phase.

b. Find the magnitude of the spacecraft's acceleration during the constant-deceleration phase.

c. Determine the mass of the so-called powered descent vehicle (PDF), meaning the spacecraft with the rover attached.

d. Determine the mass of the rover alone.

Explanation / Answer

(c)

during constant velocity,

thrust = M*g =10 kN

mass of PDF is

M = 10000 / 3.71

M = 2695.4 kg

(b)

from the figure,

thrust F during the constant deceleration phase = 20 kN

(Mg = 10 kN is working down ward)

F - M*g = M*a

20000 - 10000 = 2695.4*a

a = 3.71 m/s^2

(d)

after rover lowered down,

from the figure,

F = 6 kN

mass of space craft alone is

m = 6000 / 3.71 = 1617.5 kg

mass of rover alone = 2695.4 - 1617.5

m' = 1078 kg

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