### Theory:

Proxima Centauri is found to be the nearest star to our solar system. However, it is at a distance of $$2,68,770\ AU$$ in terms of astronomical units, which would be difficult to calculate. Also, for measuring the distance between any two galaxies, astronomical units are not sufficient.

So, astronomers use a specific measurement unit known as a 'light year' to measure distances in deep space.

The speed of light in the absence of air (vacuum) is about $$300,000$$ $$km\ per\ second$$. This means that the distance covered by the light is $$3 \times{10^8}$$ $$m$$ in one second.

Consider the non-leap year for calculation since it has $$365\ days$$ with $$24\ hours$$ in a day. Each hour has $$60\ minutes$$ and $$60\ seconds$$ in each minute. Thus, the total number of seconds in one year is calculated as,

$\begin{array}{l}\mathit{Time}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}365\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}24\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}60\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}60\\ =\phantom{\rule{0.147em}{0ex}}3.153\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}{10}^{7}\mathit{second}\end{array}$

The distance covered by the light travelling at a speed of $$3 \times{10^8}$$ $$m$$ in one second for a year gives one light year.
A light-year is defined as the total distance travelled by light in one year.
Calculation of light year
The value of one light-year can be calculated by multiplying the speed of light and the total time taken by the light in one year.

$\begin{array}{l}\mathit{One}\phantom{\rule{0.147em}{0ex}}\mathit{light}\phantom{\rule{0.147em}{0ex}}\mathit{year}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{Speed}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{light}\phantom{\rule{0.147em}{0ex}}×\mathit{Time}\\ \\ =3×1{0}^{8}×\phantom{\rule{0.147em}{0ex}}3.153\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}{10}^{7}\\ \\ =9.46×{10}^{15}\phantom{\rule{0.147em}{0ex}}m\end{array}$

Distance of stars

Proxima Centauri is the nearest star at a distance of $$40,000,000,000,000$$ $$km$$ from the Earth. To find the distance of Proxima Centauri in terms of light-years, divide the distance given in $$kilometres$$ by the value of one light year.

$\mathit{Light}\phantom{\rule{0.147em}{0ex}}\mathit{year}=\frac{\left(40×{10}^{12}\right)}{\left(9.4607305×{10}^{12}\right)}=4.228$

In terms of light-years, the distance is approximately $$4.23\ light\ years$$ from the Earth. Likewise, the distance of another star, Alpha Centauri, the second-closest star, is at $$4.3\ light\ years$$.
Reference:
https://c.pxhere.com/photos/1f/69/planet_earth_globe_space_world_continents_blue_light-632989.jpg!d