Speed of light, c = 3 x 10$^8$ m s$^{-1}$
Time taken by light to reach the earth from the galaxy is
$\displaystyle t = \frac {10^{25}m}{3\times 10^8m\,s^{-1}}\,=\,3\times 10^{16}s$

Wavelength of $H _\alpha$ line, 
$\lambda=6563A^o$
$=6563\times10^{-10}$

Milky way is about 100,000 light years or 30kpc.

Average distance from the centre of the Earth to the centre of the Sun forms the astronomical unit (AU). It equals to around 149.6 million kilometres.

Parallax is used by astronomers to measure the distance between the stars. Parallax is also known as trigonometric parallax.

Parsec is a unit of length used in astronomy to measure distances outside our solar system. One parsec equals to around 3.26156 light years.

The brightness of the stars changes over time. The difference in the brightness over time allows calculating the distance to the star. This is the cepheid variable stars method that is used to measure the distance to stars beyond 100 light years.

Units used in astronomy by astronomers are an astronomical unit, light year and parsec.

The brightness of the stars changes over time. The difference in the brightness over time allows calculating the distance to the star. This is the cepheid variable stars method that is used to measure the distance to stars beyond 100 light years.

Proxima Centauri, a part of a triple star system named Alpha Centauri, is the closest star to our solar system. It is about 4.24 light years away from the Earth.

Andromeda galaxy is the nearest galaxy to our Milky Way. It is about 2.537 million light-years away.

The velocity of the light is precisely 299792458 metres per second or 3 x 10$^8$ m/s.

Heavenly bodies are very far away from each other. It is impossible to measure their distances by using conventional units like miles and kilometres. Hence light year is used to measure the distance of heavenly bodies from each other.

Our Sun is the nearest star to the Earth. After the Sun, the next nearest star is 4.3 light years away. A light year is the distance light travels in one year. One light year is 10 trillion kilometers. Hence, all the stars are not the same distance from our Earth. They are at different distances. Hence, given statement is false.

$\dfrac{\triangle v}{v}=\dfrac{V _{radiant}}{C}$
$v=\dfrac{C}{\lambda}$
$d.v=\dfrac{C}{\lambda^2}.dv=\dfrac{\dfrac{x}{\lambda^2}}{\dfrac{C}{\lambda}}=\dfrac{d\lambda}{\lambda}$
$\dfrac{d\lambda}{\lambda }=\dfrac{V _{radial }}{C}$
$\dfrac{5 \times 10^{-10}}{6563 \times 10^{-10}}=\dfrac{C _{radial}}{3\times 10^8}$
Calculate $V _radial=\dfrac{5}{6563}\times 3\times 10^8$
$=\dfrac{15}{6563}\times 10^8$
$\dfrac{15}{6.56}\times 10^5$
$2.29\times 10^5m/s$

One light year is the distance travelled by the light in one year. So,

The diameter of milky way is about ${ 10 }^{ 5 }$ light years

Out of these four units kilometer is the smallest unit.

Alpha century is a star system closest to earth other than sun. Its distance from the earth is about $4.367$ light years.

1 light year = $\dfrac { 1 }{ 3.26 } $ parsec

Ans : $3\times { 10 }^{ 5 }km/s$

Distance between Earth and Sun$=1.496\times {10}^{8}\ km=1.496\times {10}^{11}\ m$
Speed of light $=3\times {10}^{8}\ m/s$
By using the formula:
$speed=\cfrac{Distance}{Time}$
or $3\times {10}^{8}\ m/s=\cfrac{1.496\times {10}^{11}m}{Time}$
So,  $Time=\cfrac{1.496\times {10}^{11}\ m}{3\times {10}^{8}\ m/s}$ = $\cfrac{1496}{3}s$ $=498.66\ s$ 

Speed of light $=3\times {10}^{8}\ m/s$
Time taken $=25\ min\ 30\ sec = 1530\ sec$
By using the formula, 
$Speed=\cfrac{Distance}{Time}$
or 

Given $t=15$min
Speed of light $=3\times {10}^{8}m/s$
$\therefore$ $t=15min=15\times 60=900 sec$
By using the formula
$Speed=\cfrac{Distance}{Time}$
$Distance=Speed \times time$ $=3\times {10}^{8}m/s\times 900 sec$ $=2700\times {10}^{8}m$ $=2.7\times {10}^{8}km$

The brightness of the stars changes over time. The difference in the brightness (difference in the apparent brightness to the true brightness) over the time allows calculating the distance to the star. This is the cepheid variable stars method that is used to measure the distance to stars beyond 100 light years.