What Is Hubble’s Law? / Statement of Hubble’s Law / Hubble’s Law Formula / What Is the Hubble Constant? / What Is Redshift? / Redshift Formula

Hubble’s Law is one of the most important ideas in astronomy. It explains that the universe is expanding.

In simple words:

  The farther a galaxy is from Earth, the faster it is moving away from us.

This discovery was made by Edwin Hubble and later refined by Georges Lemaître, which is why it is also called the Hubble–Lemaître Law. It is a key topic in physical cosmology and provides strong evidence for the Big Bang theory and the cosmological principle, which states that the universe is uniform in all directions on large scales.

Statement of Hubble’s Law

The recessional velocity (redshift) of a galaxy is directly proportional to its distance from the observer.

This means:

• Nearby galaxies move away slowly

• Distant galaxies move away much faster

Hubble’s Law Formula

The mathematical form of Hubble’s Law is:

$$v = H_0 d$$

Where:

• v = velocity of the galaxy (km/s)

• H₀ = Hubble constant (km/s/Mpc)

• d = distance of the galaxy (megaparsecs, Mpc)

Important Unit:

• 1 megaparsec (Mpc) = 3.26 million light-years

What Is the Hubble Constant?

The Hubble constant (H₀) measures the rate at which the universe is expanding.

It tells us how fast galaxies move away per unit distance.

A commonly used value is approximately:

$$H_0 \approx 67–74 \ \text{km/s/Mpc}$$

This means that for every extra megaparsec of distance, a galaxy’s speed increases by about 70 km/s.

What Is Redshift?

Redshift occurs when light from a distant galaxy is stretched to longer wavelengths as the universe expands.

Types of Redshift:

1. Doppler redshift – due to motion of objects

2. Gravitational redshift – caused by strong gravity

3. Cosmological redshift – caused by expansion of space (most important for Hubble’s Law)

Redshift Formula

$$z = \frac{\Delta \lambda}{\lambda}$$

Where:

• z = redshift

• Δλ = change in wavelength

• λ = original wavelength

A higher redshift means the galaxy is farther away and the universe has expanded more since the light was emitted.

Relationship Between Redshift and Distance

Hubble found a linear relationship between redshift and distance:

• Small redshift → nearby galaxy

• Large redshift → distant galaxy

This relationship allows astronomers to estimate galactic distances using spectral data.

Example of Hubble’s Law

Question:
A galaxy has a velocity of 1000 km/s.
If H₀ = 60 km/s/Mpc, find its distance.

Solution:

$$d = \frac{v}{H_0}$$ $$d = \frac{1000}{60} = 16.7 \ \text{Mpc}$$

Answer:
The galaxy is 16.7 megaparsecs away.

Limitations of Hubble’s Law

Hubble’s Law works best for very distant galaxies. It has limitations for nearby objects because:

• Galaxies have their own random motions

• Gravitational interactions affect velocity

Therefore, it is not applicable to:

• Stars in the Milky Way

• Objects in the Solar System

Units Derived from the Hubble Constant

1. Hubble Time

The Hubble time estimates the age of the universe assuming steady expansion:

$$t_H = \frac{1}{H_0}$$

Approximate value:

• 14.4 billion years

2. Hubble Length (Hubble Distance)

The Hubble length is the distance light travels in one Hubble time:

$$\frac{c}{H_0} \approx 14.4 \ \text{billion light-years}$$

3. Hubble Volume

The Hubble volume is the volume of the observable universe, modeled as a sphere with radius equal to the Hubble length.

Frequently Asked Questions (FAQs)

What is Hubble’s Law used for?

Hubble’s Law is used to study the expansion of the universe and provides evidence for the Big Bang theory.

Where does Hubble’s Law not apply?

It does not apply to stars within galaxies or to Solar System objects. It applies only to distant galaxies.

Why is Hubble’s Law important?

It helps scientists:

• Estimate the age and size of the universe

• Study dark energy and cosmic expansion

What is the value of the Hubble constant?

Modern measurements place it between:

• 67–74 km/s/Mpc

Why is the Hubble constant uncertain?

Different measurement methods give slightly different values. However, the expansion rate is uniform at a given time and location, which is why it is still called a “constant.”

Final Tip for Students

If you remember just one thing, remember this:

Distance increases → Speed increases → Universe expands

Solved Numericals on Hubble’s Law

Numerical 1: Finding Distance of a Galaxy

Problem:

A distant galaxy is observed to be moving away from Earth with a velocity of 1400 km/s.

If the Hubble constant is 70 km/s/Mpc, calculate the distance of the galaxy.

Solution:
Using Hubble’s Law:

$$v = H_0 d$$
$$d = \frac{v}{H_0}$$ $$d = \frac{1400}{70}$$ $$d = 20 \ \text{Mpc}$$

Answer:
The galaxy is 20 megaparsecs away.

Numerical 2: Finding Recessional Velocity

Problem:

A galaxy is located at a distance of 50 Mpc from Earth.

If the Hubble constant is 72 km/s/Mpc, find its recessional velocity.

Solution:

$$v = H_0 d$$
$$v = 72 \times 50$$
$$v = 3600 \ \text{km/s}$$

Answer:
The galaxy is moving away at 3600 km/s.

Numerical 3: Calculating the Hubble Constant

Problem:
A galaxy at a distance of 25 Mpc is observed to recede at 1750 km/s.
Calculate the value of the Hubble constant.

Solution:

$$H_0 = \frac{v}{d}$$ $$H_0 = \frac{1750}{25}$$ $$H_0 = 70 \ \text{km/s/Mpc}$$

Answer:
The Hubble constant is 70 km/s/Mpc.

Numerical 4: Estimating the Age of the Universe (Hubble Time)

Problem:
Assuming the Hubble constant is 70 km/s/Mpc, estimate the age of the universe.

Solution:
The Hubble time is given by:

$$t_H = \frac{1}{H_0}$$

Convert units:

$$t_H \approx 14 \ \text{billion years}$$

Answer:

The estimated age of the universe is approximately 14 billion years.

Numerical 5: Distance Using Redshift (Low Redshift Approximation)

Problem:
A galaxy has a redshift value of z = 0.02.
Assume the speed of light c = 3 × 10⁵ km/s and H₀ = 75 km/s/Mpc.
Calculate the distance of the galaxy.

Solution:
For small redshift values:

$$v = cz$$
$$v = (3 \times 10^5)(0.02)$$
$$v = 6000 \ \text{km/s}$$

Now apply Hubble’s Law:

$$d = \frac{v}{H_0}$$ $$d = \frac{6000}{75}$$ $$d = 80 \ \text{Mpc}$$

Answer:
The galaxy is 80 megaparsecs away.

Numerical 6: Comparing Two Galaxies

Problem:

Galaxy A is 10 Mpc away, and Galaxy B is 40 Mpc away.

If H₀ = 70 km/s/Mpc, compare their recessional velocities.

Solution:

For Galaxy A:

$$v_A = 70 \times 10 = 700 \ \text{km/s}$$

For Galaxy B:

$$v_B = 70 \times 40 = 2800 \ \text{km/s}$$

Answer:
Galaxy B is moving away four times faster than Galaxy A.

Exam Tip for Students

Remember the core formula:

$$\boxed{v = H_0 d}$$

If distance increases, velocity increases proportionally — this is the key idea behind Hubble’s Law.