Question

The farthest objects that are discovered in our universe by modern astronomers are so distant that light emitted by them takes billions of years to reach the earth. These objects known as quasars have many puzzling features, which have not yet been satisfactorily explained. What is the distance in Km of a quasar from which light takes around 3.0 billion years to reach us?

Answer 1

The speed of light is known that is 3 $\times$ 10$^8$ m/s the distance from the quasars can be determined as the product of the speed of light and the time taken to reach earth. The long distances are calculated in light-years.

Formula Used:
The formula for calculating the distance is:
$d = s \times t$

Complete step by step answer:
Convert the time given in years to seconds.
$t = \,3\,billion\,years$
$= 3 \times {10^9}\,Yrs$
$= 3 \times {10^9} \times 365 \times 24 \times 60 \times 60$
$= 9.46 \times {10^{16}}\,{\rm{s}}$
The formula for calculating the distance is:
$d = s \times t$
Here $d$ is the distance, $s$ is the speed and $t$ is the time.
Put the value of time taken and speed of light in the above equation.
$d = \left( {3 \times {{10}^8}{\rm{m/s}}} \right)\, \times \left( {9.46 \times {{10}^{16}}\,{\rm{s}}} \right)$
$= 2.8 \times {10^{22}}\,{\rm{km}}$

Therefore, the distance is $2.8 \times {10^{22}}\,{\rm{km}}$.

Additional Information:
If we talk about the sun then the light from the sun merely takes 8 min to reach the surface of the earth. The light is generally made of photons and it is basically the speed of the photons which are contributing to the speed of light.

Note:
The units of the quantities should be converted into SI units so that the result can be easily converted into the required unit. The distance that we got is very large and the distance of the celestial bodies is generally calculated in light-years.