Question

Please help w/ astronomy hw

Wolf 359 is the fifth closest star system to the Sun at a distance of 7.78 light years. Calculate how many miles away it is. Use 186,000 mi/s for the speed of light.

Answer 1

Since they gave you miles/second, I assume they want you to convert all the way from seconds to years. If that's the case, this is the conversion path you'll need to follow:

seconds -> minute -> hour -> day -> year

Answer 2

It would look something like this:

\[\large \frac{186,000~mi}{1~sec}*\frac{60 ~sec}{1~min}*\frac{60 mins}{1~hr}\frac{24~hr}{1~day}*\frac{365~day}{1 yr} \]\
and that'll give you the \(\large \frac{miles}{year}\) light travels.

Just multiply that value by the 7.78 light years you are given:
\[\large (\frac{186,000~mi}{1~sec}*\frac{60 ~sec}{1~min}*\frac{60 mins}{1~hr}\frac{24~hr}{1~day}*\frac{365~day}{1 yr}) * \color{red}{7.78 ly} \]\