Question

How long does it take to travel to the nearest star at the speed of light?

Answer 1

Hint: Though Sun is the nearest star to our planet at about 150 million kilometers, to answer our question, we should consider the nearest star outside our solar system. And the nearest star outside our solar system is the Proxima centauri. The distance from Earth is roughly about $(4\times {{10}^{13}})$kilometers. Now, to calculate the time taken to travel this distance at the speed of light that is $(3\times {{10}^{5}})$ kilometer per second, we use the distance formula. That is, distance can be written as a product of speed and time.

Complete answer:
To begin with our solution, let us first assign the known and unknown terms some variables. It will make our calculations easier as we move ahead.
Let the distance between the Earth and Proxima Centauri be denoted by $(D)km$ .
Let the speed at which light travels be $(u)km/s$
Now, we know:
$\begin{align}
  & \Rightarrow D=4\times {{10}^{13}}km \\
 & \Rightarrow u=3\times {{10}^{5}}km/s \\
\end{align}$
Therefore, time taken by light to travel this distance can be given by:
$\Rightarrow t=\dfrac{D}{u}$
Putting the values of (D) and (u) in the above equation, we get:
$\begin{align}
  & \Rightarrow t=\dfrac{4\times {{10}^{13}}}{3\times {{10}^{5}}}\sec \\
 & \Rightarrow t=1.34\times {{10}^{8}}\sec \\
\end{align}$
Since, we know there are 86,400 seconds in a day.
Therefore, total seconds in a year is equal to:
$\begin{align}
  & =86400\times 365 \\
 & =31536000\sec \\
\end{align}$
Thus, the time taken by light in years to reach Proxima Centauri can be given by:
$\begin{align}
  & \Rightarrow t=\dfrac{1.34\times {{10}^{8}}}{31536000}yrs \\
 & \Rightarrow t=4.24yrs \\
\end{align}$
Hence, the time taken by us to travel to the nearest star at the speed of light is 4.24yrs.

Note:
The fact that Proxima centauri is the nearest star outside our solar system is a question of General Knowledge. These key facts should be known to us all. Also, if the question would have been to find the time taken to travel to the most distant planet in our solar system, the planet from which the distance should be calculated should have been Neptune and not Pluto as it is no longer a planet. So these basic facts should always be clear to us.