Hubble’s Law

The earth is moving away from faraway galaxies. To put it another way, the cosmos is growing. In light of this, Georges Lemaitre developed Hubble’s Law, a significant physical cosmology conclusion that explains the relationship between galaxy distance and redshift. According to the law, the recessional velocity, also known as redshift, is proportional to the velocity’s distance. The rule of Hubble explains, in layman’s terms, that the distant galaxies are from the planet, the faster they move away from it. Hubble’s law is not just proof of the universe’s expansion, but also a key explanation for the big bang scenario.

Hubble’s Law Formula

The formula for Hubble’s Law is stated as:

v = H₀d

where,

• v = Recession velocity in km per second
• d = Distance in Mpc
• H₀ = Expansion Rate Today Hubble Parameter

Hubble Constant (H₀): The Hubble constant is a measuring unit that is used to describe the expansion of the cosmos. Hubble’s constant H per million-light-years is 160 km/s.

Limitations of Hubble’s Law

After calculating the recession velocity, one may use Hubble’s equation to calculate the distance of the galaxy from us by computing the shift in visible light into redshift in the spectrum. The following are some of Hubble’s law’s restrictions, which make measuring difficult:

• The observed velocity of galaxies is influenced by their intrinsic motion.
• Gravitational movements cause the galaxy to orbit.

Redshift

Redshift is the phenomenon in which an object’s wavelength increases due to electromagnetic radiation. Blueshift is opposite to redshift where the energy increases due to shorter wavelengths which are also known as negative redshift. The main reasons for redshift are as follows:

• Doppler effect ie; the movement of objects either closer or apart from each other in space.
• Strong gravitational force leads to gravitational redshift.
• Cosmological redshift is an expansion of space such that objects are separated without a change in their position.

Redshift Formula

The formula for Redshift is stated as:

z = Δλ/λ

where,

• z is the redshift
• Δλ is the shift in wavelength in the spectra
• λ is the wavelength

Sample Questions

Problem 1: For some cluster, velocity is measured as v = 10³ km/s. What is the distance? Assume H_ο = 60km/s/Mpc

Solution:

we know,

v = 10³ km/s,       H₀ = 60km/s/Mpc

The formula used is:

d = v/H_ο

=(10³ km/s)/(60km/s/Mpc)

=16.7 Mpc

Problem 2: The Hubble Constant value for galaxy NGC 123 is 70 km/s/Mpc, and its distance from us is of 1,320 km/s. According to Hubble’s Law, how far away is the galaxy?

Solution:

v = H_od

1320 = 70 d

Solve for d

d = v/h_o

d = 1,320/70

d = 18.9 Mpc

Problem 3: NGC 2342 is a galaxy with a velocity of 5,690 km/s and a distance of 74 Mpc away. Based on these numbers, what is the Hubble constant’s value?

Solution:

v = H_od

5690 = H_o 74

Solve for H_o

H_o = v/d

H_o = 5,690/74 = 77 km/s/Mpc

Problem 4: The wavelength of a calcium absorption characteristic is normally 3934  Å, however, it has been observed in a galaxy to be 4002 Å. What exactly is a redshift?

Solution:

 First you need to determine the value for Δλ , which is the change in wavelength

Δλ = 4002 – 3934 = 68 Å.

Since this is a positive value, the object is moving away from us. Now you can plug the values into the formula –

z = Δλ/λ

z = 68 / 3934

z = 0.017

Problem 5: An absorption feature of calcium usually has a wavelength of 3934 Å, but it is observed in a distant galaxy to have a wavelength of 8209 Å. What is the redshift?

Solution:

First you need to determine the value for Δλ, which is the change in wavelength

Δλ = 8209 – 3934 = 4275 Å.

Since this is a positive value, the object is moving away from us. Now you can plug the values into the formula –

z = Δλ/λ

z = 4275 / 3934

z = 1.09