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The space probe Deep Space 1 was launched on October 24, 1998. Its mass was 474 kg. The goal of the mission was to test a new kind of engine called an ion propulsion drive. This engine generated only a weak thrust, but it could do so over long periods of time with the consumption of only small amounts of fuel. The mission was spectacularly successful. At a thrust of 56 mN how many days were required for the probe to attain a velocity of 790 m/s (1770 mi/h), assuming that the probe started from rest and that the mass remained nearly constant

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cjrodriguez89

Answer:

T = 77.5 days.

Explanation:

  • Assuming no other forces acting on the probe, according to Newton's 2nd law, we can find the acceleration attained by the probe due to the thrust (assumed constant) as follows:

       [tex]a = \frac{F}{m} = \frac{56e-3N}{474kg} = 1.18 e-4 N (1)[/tex]

  • Since the probe started from rest, we can express the final speed applying the definition of acceleration, as follows:

       [tex]v_{f} = a* t (2)[/tex]

  • We can solve for t (in seconds) as follows:

       [tex]t = \frac{v_{f}}{a} = \frac{790m/s}{1.18e-4m/s2} = 6694915 s (3)[/tex]

  • Since 1 day = 86400 s, we can find the time in days as follows:

       [tex]t_{days} = \frac{t_{sec} }{1 day} = \frac{6694915s}{86400s} = 77.5 days (4)[/tex]

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