Question

How many light-years away is Mars from earth?

Answer 1

Step 1: Express light-years in $km$

A light-year is defined as the distance traveled by light in one year.

The speed of light in vacuum is $3\times {10}^{8}m/s$.

$1yr=365d\times 24h\times 60min\times 60s$

$=3.1\times {10}^{7}s$

We know that,

In $1s$ light travels $3\times {10}^{8}m$.

Therefore, in $3.1\times {10}^{7}s$ light will travel

$3\times {10}^8\times 3.1\times {10}^{7}m$$=9.5\times {10}^{15}m$

$=9.5\times {10}^{12}km$

Step 2: Calculate distance in light-years

The distance between Earth and Mars $2.5\times {10}^{8}km$

Therefore this distance in light year is,

$d=\frac{2.5\times {10}^8}{9.5\times {10}^{12}}$

$=2.63\times {10}^{-5}ly$

Hence, there is $2.63\times {10}^{-5}$ light years of distance between Mars and Earth.