Question

What is the distance of the star (in km) from which light takes $3\times {10}^9\mathrm{years}$ to reach the earth? The speed of light, is $\mathrm{C}=3\times {10}^8\mathrm{m}/\mathrm{s}$.

Answer 1

Step 1: Given information

Time is taken by light to reach earth,

$\mathrm{Time}=3\times {10}^9$

By converting it into seconds we get,

$\mathrm{Time}=3\times {10}^9\times 365\times 24\times 60\times 60=9.46\times {10}^{16}\mathrm{s}$

The speed of light,

$\mathrm{C}=3\times {10}^8\mathrm{m}/\mathrm{s}$

Step 2: Finding the distance of the star

$\mathrm{Distance}=\mathrm{speed}\times \mathrm{time}$

By substituting the given values we get

$\mathrm{Distance}=\mathrm{speed}\times \mathrm{time}=3\times {10}^8\mathrm{m}/\mathrm{s}\times 9.46\times {10}^{16}\mathrm{s}=2.838\times {10}^{22}\mathrm{km}$

Therefore, the star's distance (in km) from which light takes $3\times {10}^9\mathrm{years}$ to reach the earth will be $2.838\times {10}^{22}\mathrm{km}$.