### Theory:

In astronomy, the most commonly used measures of distance are the light year, and astronomical unit.

By now we know well how to measure distance from one place to another place in earth.

Earth is one of the planet in the solar family. Is it possible to measure the distance between sun and earth?

Yes, we can.

Earth is one of the planet in the solar family. Is it possible to measure the distance between sun and earth?

Yes, we can.

It is measured that the average distance between the earth and the sun is about 149.6 million kilometre.

This average distance is taken as one astronomical unit.

Astronomical units are usually used to measure distances within our solar system.

**Astronomical unit and light years:**

$\begin{array}{l}1\phantom{\rule{0.147em}{0ex}}\mathit{AU}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}149.6\phantom{\rule{0.147em}{0ex}}\mathit{million}\phantom{\rule{0.147em}{0ex}}\mathit{km}\\ \\ \phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}149.6\phantom{\rule{0.147em}{0ex}}\times \phantom{\rule{0.147em}{0ex}}{10}^{6}\mathit{km}\phantom{\rule{0.147em}{0ex}}\\ \\ =\phantom{\rule{0.147em}{0ex}}1.496\phantom{\rule{0.147em}{0ex}}\times \phantom{\rule{0.147em}{0ex}}{10}^{11}\phantom{\rule{0.147em}{0ex}}m.\end{array}$

Where astronomical unit are denoted as AU.

Most objects in space are far away to be measured in kilometres or even astronomical units.

For instance measuring the distance between galaxies even astronomical units are not sufficient.

So, astronomers measure distances to objects which are outside our solar system in light-years.

A light-year (ly) is unit of distance. It is the distance that light can travel in one light year.

When light moves at a velocity of about $3\times {10}^{8}$ m/s. each second. So in one year (there are 365 days, and each day has 24 hours; each hour has 60 minutes; each minute has 60 seconds). Thus, the total number of seconds in one year is $3.153\phantom{\rule{0.147em}{0ex}}\times \phantom{\rule{0.147em}{0ex}}{10}^{7}$second.

Where light year is denoted as ly.

**The total number of second in one year:**

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

One light year is defined as the distance travelled by light in vacuum during the period of one year.

$\begin{array}{l}\mathit{One}\phantom{\rule{0.147em}{0ex}}\mathit{light}\phantom{\rule{0.147em}{0ex}}\mathit{year}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{Light}\phantom{\rule{0.147em}{0ex}}\mathit{year}\phantom{\rule{0.147em}{0ex}}\times \mathit{total}\phantom{\rule{0.147em}{0ex}}\mathit{number}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{second}\phantom{\rule{0.147em}{0ex}}\mathit{in}\phantom{\rule{0.147em}{0ex}}\mathit{one}\phantom{\rule{0.147em}{0ex}}\mathit{year}\\ \\ =3\times 1{0}^{8}\times \phantom{\rule{0.147em}{0ex}}3.153\phantom{\rule{0.147em}{0ex}}\times \phantom{\rule{0.147em}{0ex}}{10}^{7}\\ \\ \mathit{One}\phantom{\rule{0.147em}{0ex}}\mathit{light}\phantom{\rule{0.147em}{0ex}}\mathit{year}\phantom{\rule{0.147em}{0ex}}=9.46\times {10}^{15}\phantom{\rule{0.147em}{0ex}}m\end{array}$

Thus, the one light year is $9.46\times {10}^{15}\phantom{\rule{0.147em}{0ex}}m$.