Question

How long does it take to travel 500 light years?

Answer 1

Hint: Light years tells us about how much light travels in a year. Using the speed of light we can calculate the distance travelled by light in one year and hence in 500 years and use the speed, distance, time relation to calculate the time taken to travel the total distance.

Complete step-by-step solution:
The light travels at the speed of 1 light year. Therefore, if we assume light to be travelling, then it will travel 500 light years in 500 years.
The light travels at a speed of $c=3\times {{10}^{8}}m{{s}^{-1}}$.
The distance travelled by light in 1 day is $3\times {{10}^{8}}\times 24hrs\times 3600\sec =2.6\times {{10}^{13}}m$
Therefore, the distance travelled in one day will be $2.6\times {{10}^{13}}m$.
The distance travelled in one year is $2.6\times {{10}^{13}}m\times 365=9.5\times {{10}^{15}}m$
Therefore, the distance travelled in one year is $9.5\times {{10}^{15}}m$.
In 5 years, light travels a distance of $9.5\times {{10}^{15}}m\times 500=4.73\times {{10}^{16}}m$
We know that,
$\begin{align}
  & s=\dfrac{d}{t} \\
 & \Rightarrow t=\dfrac{d}{s} \\
\end{align}$
Here,
$s$ is the speed
$d$ is the distance travelled
$t$ is the time taken
If we assume that this distance is travelled by a rocket, then a rocket needs a minimum speed of$618km\,{{s}^{-1}}=618\times {{10}^{3}}m{{s}^{-1}}$ to escape the gravitational force of the sun.
We substitute values in the above equation to get,
$\begin{align}
  & t=\dfrac{d}{s} \\
 & \Rightarrow t=\dfrac{4.73\times {{10}^{16}}}{618\times {{10}^{3}}} \\
 & \Rightarrow t=7.65\times {{10}^{10}}s \\
\end{align}$
Therefore, the time taken to travel 500 light years will be $7.65\times {{10}^{10}}s$
Time taken in years to travel 500 light years is $\dfrac{7.65\times {{10}^{10}}s}{3600\times 24\times 365}=2.42\times {{10}^{3}}years$

Therefore, it will take us $2.42\times {{10}^{3}}years$ to travel 500 light years.


Note:
Light year is an astronomical distance unit. It is the measure of distance travelled by light in one year. As light is an electromagnetic wave, it does not require a medium to travel. All the planets are revolving around the sun due to the gravitational force of the sun binding the planets to it. In order to escape beyond the Milky Way we will have to overcome the force of gravity of the sun.