Question

How long does it take light to travel $500$ light-years?

Answer 1

Step 1: Given data

Distance $d=500ly$

Step 2: Assumptions

This is dependent on the type of travel; obviously, if it is light travel, then $500$ years. $500$ light-years is the distance traveled by light in $500$ years in a vacuum.

Speed, $s=\frac{d}{t}$

Here $d$ is the distance, $t$ is the time taken.

Speed of light = $3\times {10}^{5}Km/s$

Step 3: Calculate the distance traveled.

Distance traveled by light in a year

$d=s\times t=3\times {10}^{5}km/s\times 3600secs\times 24hrs\times 365days$

$=9.4608\times {10}^{12}Km$

The distance traveled in 500 years is $=9.4608\times {10}^{12}Km\mathit{\times }\mathit{500}\mathit{=}$$4.7304\times {10}^{15}Km$

Step 4: Calculate the time required.

So the time required to travel this distance is,

$$\begin{gathered} t=\frac{d}{s} \\ =\frac{4.7304\times {10}^{15}}{3\times {10}^5} \\ =1.5768\times {10}^{10}s \end{gathered}$$

In years the time required would be

$$\begin{gathered} \frac{1.5768\times {10}^{10}}{3600\times 24\times 365} \\ =500years \end{gathered}$$

Therefore, it would take $500$ years to travel $500$ light-years.