To study the Hubble’s law we have to study the Red Shift first.
Red Shift: From the studies it was found that the spectrum automatically bends towards the red end of the spectrum with the passage of time. This is called Red Shift. Red color has maximum wavelength. Similarly, the Red side is having the maximum wavelength. So, the spectrum will bend towards the region having higher wavelength. The equation of red shift is shown below:
represents the wavelength of spectral line when the galaxy is at rest i.e. stationary.
represents the wavelength of spectral lines when the galaxy is in motion.
If the value of will be greater than that of . Then the values of z will be greater than zero. If z will be greater than zero then Red Shift can be seen in galaxies. Doppler’s Effect is used to study the Red Shift properly. Suppose that the galaxy is moving at a farther place from us, having speed V. By using the Doppler’s formula the equation formed will be:
= v / c —– (2)
In the above equation c represents the velocity of light. From the above result it is clear that the recession velocity can be found easily by calculating the red shift of a galaxy.
As we have noticed that galaxies are going far from us at extremely higher speeds. This shows that instead of being stationary, our universe is expanding.
Hubble’s Law: From the study of the red shift by various galaxies by the scientists Milton and Hubble, it was found that the distance r of a galaxy with respect to us is directly proportional to red shift.
Z r or V / C r
Therefore Z= V / C
V= Hr —— (3)
H in the above equation is the Hubble’s constant.
Hubble’s law states that the recession velocity of a galaxy is directly proportional to its distance with respect to us. Using equation 3 we get:
H= V/ r
So, the dimensions of H = L T-1 / L = T-1
The above result shows that the Hubble’s constant has the dimensions same as that of time. By using this result we can get some help in finding the evolution of Universe.
A graph is plotted below between recession velocity and distance.
The experimental value of Hubble’s constant is found to be 16Kms-1 per million light years. It states that a galaxy present at any point in Universe, one million light years away with respect to us, then it is receding at a constant rate of 16Kms-1.