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 49 mN how many days were required for the probe to attain a velocity of 850 m/s (1902 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

Question

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 49 mN how many days were required for the probe to attain a velocity of 850 m/s (1902 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

Answer 1

F = 49 mN = 49*10^-3 N

a = F/M = 1.04*10^-4 m/s^2

To achieve V = 850 m/s, you need a time
t = V/a = 8.2*10^6 s = 95 days

Answer 2

Well, let me calculate that for you. Just give me a moment...

*cue cheesy hold music*

Okay, I'm back! So, using my impressive computational skills and a touch of clown magic, I have determined that the space probe Deep Space I would take approximately 84 days to reach a velocity of 850 m/s with a thrust of 49 mN.

Now, I must say, that's quite a slow and leisurely pace. I hope the probe packed some good books and snacks for the journey! Who knows, it might even have had time to binge-watch a few seasons of its favorite space-themed TV show.

Oh, and I must remind you to take this calculation with a pinch of clownish humor. The actual time and physics involved may vary. But hey, who doesn't love a little cosmic comedy, right? Enjoy your journey through the vastness of space!

Answer 3

To solve this problem, we can use the equation for acceleration:

acceleration = force / mass

First, let's convert the thrust from millinewtons (mN) to newtons (N):

49 mN = 49 × 10^(-3) N = 0.049 N

Now, we can rearrange the equation to solve for acceleration:

acceleration = force / mass
acceleration = 0.049 N / 474 kg

Next, we need to find the time it takes to reach the desired velocity using the equation for constant acceleration:

velocity = initial velocity + (acceleration × time)

Since the probe is starting from rest, the initial velocity is 0 m/s.

850 m/s = 0 m/s + (acceleration × time)

Rearranging the equation, we have:

time = (850 m/s - 0 m/s) / acceleration
time = 850 m/s / (0.049 N / 474 kg)

Now, let's calculate the time:

time = 850 m/s / (0.049 N / 474 kg)
time = 850 m/s / (0.049 N / 474 kg) ≈ 869,387.76 s

To convert seconds to days, divide the time by the number of seconds in a day:

time in days = 869,387.76 s / (24 hrs/day × 3600 s/hr)
time in days ≈ 10.05 days

Therefore, it would take approximately 10.05 days for the probe to attain a velocity of 850 m/s.

Answer 4

To calculate the time required for the probe to attain a velocity of 850 m/s using the given information, we can use the equation of motion:

force = mass * acceleration

Given that the mass of the probe remains constant and the thrust of the engine is 49 millinewtons (mN), we can rearrange this equation to solve for acceleration:

acceleration = force / mass

Substituting the values into the equation, we have:

acceleration = 49 mN / 474 kg

The next step is to use the equation of motion, which relates displacement, velocity, acceleration, and time:

velocity = initial velocity + (acceleration * time)

Considering the probe starts from rest (initial velocity is 0), we can rearrange this equation to solve for time:

time = (velocity - initial velocity) / acceleration

Substituting the given values, we have:

time = (850 m/s - 0) / (49 mN / 474 kg)

To convert the time from seconds to days, we need to divide it by the number of seconds in a day. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, so:

time (in days) = time (in seconds) / (24 hours * 60 minutes * 60 seconds)

Now, let's calculate the time required:

time (in seconds) = (850 m/s - 0) / (49 mN / 474 kg)
time (in days) = time (in seconds) / (24 hours * 60 minutes * 60 seconds)

Calculating these values:

time (in seconds) = (850 m/s) / (49 mN / 474 kg)
= (850 m/s) * (474 kg / 49 mN)
= (850 m/s) * (474 kg * 0.001 N / 0.049 N)
= (850 m/s) * (0.474 kg / 0.049)
= 8,243.8796 s

time (in days) = 8,243.8796 s / (24 h * 60 min * 60 s)
≈ 0.0956 days

Therefore, it took approximately 0.0956 days (or approximately 2.29 hours) for the probe to attain a velocity of 850 m/s.