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 730 m/s (1630 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

Thrust x Time = change im momentum

= 474 kg* 730m/s

Solve for the time, which will be in seconds, and convert thzt to days.

They expect you to ignore the gravity of distant planets and the sun.

This doesn't look very stressful.

346020

To find out the number of days it took for the probe to attain a velocity of 730 m/s, we can use the concept of acceleration and the equations of motion.

Acceleration is defined as the rate of change of velocity with respect to time. In this case, the acceleration is the thrust (F) divided by the mass (m) of the probe:

a = F/m

Given that the thrust is 56 mN (millinewtons) and the mass is 474 kg, we can calculate the acceleration:

a = (56 mN) / (474 kg)

Now we need to find the time taken to reach a velocity of 730 m/s. The equation we can use is:

v = u + at

Where:
v = final velocity (730 m/s)
u = initial velocity (0 m/s, as the probe starts from rest)
a = acceleration (calculated previously)
t = time taken

Rearranging the equation to solve for time (t), we get:

t = (v - u) / a

Plugging in the values, we have:

t = (730 m/s - 0 m/s) / ((56 mN) / (474 kg))

Converting millinewtons to newtons (1 mN = 0.001 N), we have:

t = (730 m/s - 0 m/s) / ((56 * 0.001 N) / (474 kg))

Simplifying further:

t = (730 m/s) / (0.056 N / 474 kg)

Finally, calculating the value:

t = 730 m/s / 0.000118 N/kg

t ≈ 6,186,440 seconds

To convert this time into days, we divide by the number of seconds in a day:

t ≈ 6,186,440 seconds / 86,400 seconds/day

t ≈ 71.6 days

Therefore, it took approximately 71.6 days for the probe to attain a velocity of 730 m/s.