1190.12 – Light Year

A light year is the distance that light travels in a year. How far is this, if light travels 186,000 miles per second?

Solution

60 sec min⋅60 min hr⋅24 hr day⋅365.25 days year=31,557,600 sec year186,000 mi sec⋅31,557,600 sec year=5,869,714,000,000 mi year\begin{aligned}\dfrac{60 \text{ sec}}{\text{ min}}\cdot\dfrac{60 \text{ min}}{\text{ hr}}\cdot\dfrac{24 \text{ hr}}{\text{ day}}\cdot\dfrac{365.25 \text{ days}}{\text{ year}} = \dfrac{31,557,600 \text{ sec}}{\text{ year}}\\\\\dfrac{186,000 \text{ mi}}{\text{ sec}}\cdot\dfrac{31,557,600 \text{ sec}}{\text{ year}}= \dfrac{5,869,714,000,000 \text{ mi}}{\text{ year}}\end{aligned}

So one light year is almost 6 trillion miles.

The average distance from the earth to the sun is 93,000,000 miles, or 0.00001584 light years, or 8.333 light minutes. If the sun suddenly went out, we wouldn't know it for 8.333 minutes. The nearest star to earth (after the sun), Alpha Centauri, is 4.367 light years away.