Question

It would take almost 2 years for the fastest human-made spacecraft to travel from earth to europa. about how long would it take such a spacecraft to travel to wolf 359? study island

Answer 1

First, we need the distance of Europe and Wolf-359 from Earth.
- The distance of Europe from Earth is: $d_E = 6.28 \cdot 10^8 km$
- The distance of Wolf-359 from Earth is instead 7.795 light years. However, we need to convert this number into km. 1 light year is the distance covered by the light in 1 year. Keeping in mind that the speed of light is $c=3 \cdot 10^8 m/s$, and that in 1 year there are 
365 days x 24 hours x 60 minutes x 60 seconds = $3.154 \cdot 10^7 s/y$, the distance between Wolf-359 and Earth is
$d_W = 7.995 ly\cdot3\cdot 10^8 m/s \cdot 3.154 \cdot 10^7 s=7.38 \cdot 10^{16}m=7.38 \cdot 10^{13}km$

Now we can calculate the time the spaceship needs to go to Wolf-359, by writing a simple proportion. In fact, we know that the spaceship takes 2 years to cover $d_E$, so
$2 y:d_E = x:d_W$
from which we find $x$, the time needed to reach Wolf-359:
$x= \frac{2 y\cdot d_W}{d_E}=2.35 \cdot 10^5 years$