The space probe Deep Space I 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 spetacularly successful. At a thrust of 59 mN how many days were required for the probe to attain a velocity of 710 m/s (1588 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?
force*timeinseconds= mass*changeinvelocity
compute time in seconds, then convert it to days.
The space probe Deep Space I was launched on October 24, 1998. It's 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 49 mN how many days were required for the probe to attain a velocity of 830 m/s (1857 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?
72
To calculate the number of days required for the probe to attain a velocity of 710 m/s, we need to use the equation of motion:
F = ma
Where:
F = Force (thrust of the engine)
m = Mass of the probe
a = Acceleration
First, let's convert the thrust from millinewtons (mN) to newtons (N). 1 mN = 0.001 N, so the thrust is 59 * 0.001 N = 0.059 N.
Now, we can rearrange the equation to solve for acceleration:
a = F/m
a = 0.059 N / 474 kg
a ≈ 0.000124479 N/kg
Next, we'll use the kinematic equation to determine the time it takes to reach a certain velocity:
v = u + at
Where:
v = Final velocity (710 m/s)
u = Initial velocity (0 m/s)
a = Acceleration (0.000124479 N/kg)
t = Time taken
We can rearrange the equation to solve for time (t):
t = (v - u) / a
t = (710 m/s - 0 m/s) / 0.000124479 N/kg
t ≈ 5,702,385 seconds
To convert seconds to days, we'll divide by the number of seconds in a day:
t ≈ 5,702,385 seconds / (24 hours * 60 minutes * 60 seconds)
t ≈ 66.12 days
Therefore, it would take approximately 66.12 days for the probe to attain a velocity of 710 m/s.