What is Hubble's law and how does it relate to the expansion of the universe?

Hubble's law is a fundamental principle in astronomy that states that the velocity at which a galaxy is receding from us is directly proportional to its distance from us. This relationship is expressed as v = H₀d, where v is the velocity, H₀ is the Hubble constant, and d is the distance. This law provides evidence for the expansion of the universe, suggesting that galaxies are moving away from each other as the universe itself expands.

How does the Big Bang theory explain the origin of the universe?

The Big Bang theory posits that the universe began as an extremely hot and dense point approximately 13.8 billion years ago and has been expanding ever since. This theory is supported by several key observations, including the cosmic microwave background radiation and the abundance of light elements. It provides a comprehensive explanation for the observed expansion of the universe, as described by Hubble's law.

What evidence supports Hubble's law and the Big Bang theory?

Several lines of evidence support Hubble's law and the Big Bang theory. The redshift of light from distant galaxies indicates they are moving away from us, consistent with Hubble's law. The cosmic microwave background radiation is a remnant from the early universe, supporting the Big Bang theory. Additionally, the observed abundance of light elements like hydrogen and helium aligns with predictions from the Big Bang nucleosynthesis.

What is the significance of the Hubble constant in cosmology?

The Hubble constant (H₀) is a crucial parameter in cosmology that quantifies the rate of expansion of the universe. It allows astronomers to estimate the age and size of the universe. Determining the precise value of the Hubble constant is essential for understanding the dynamics of the cosmos and for making accurate cosmological models. However, there is ongoing research to resolve discrepancies in its measured value using different methods.

How do Hubble's law and the Big Bang theory fit into the Cambridge International A Levels Physics curriculum?

In the Cambridge International A Levels Physics curriculum, Hubble's law and the Big Bang theory are integral to the study of Astronomy and Cosmology. Students learn about the observational evidence supporting these concepts, such as redshift and cosmic microwave background radiation. Understanding these theories helps students grasp the large-scale structure and evolution of the universe, which are key topics in advanced physics education.

Why is "Wrong sign of $\Delta\lambda$" a common mistake in Hubble’s law and the Big Bang theory ?

Why it happens: Confuse observed and rest wavelength. How to avoid it: Redshift: \lambda_observed > \lambda_rest, so POSITIVE. Source: 9702 Examiner Reports 2022-2024

Why is "Inconsistent units for $H_0$" a common mistake in Hubble’s law and the Big Bang theory ?

Why it happens: Mixing km/s/Mpc with SI. How to avoid it: The 2025-2027 syllabus is explicit: candidates will only be required to use SI units. So convert H_0 to s^-1 and keep distances in metres and speeds in m/s throughout. Source: 9702 syllabus 2025-2027, statement 25.3.4 note

Cambridge International A Levels Physics (9702)

Hubble’s law and the Big Bang theory

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Short Notes - Hubble’s law and the Big Bang theory

Detailed Study Notes

Detailed notes on Astronomy and Cosmology for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Hubble's Law & the Big Bang Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Expanding universe — Hubble, redshift, age estimate.

At a glance

Redshift: $\Delta\lambda/\lambda \approx v/c$ .
Hubble: $v = H_0 d$ .
Age: $t \approx 1/H_0$ .
Galaxies recede in every direction.
Evidence for Big Bang.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

25.3.1 — Use the Doppler formula for redshift.
25.3.2 — Apply Hubble's law.
25.3.3 — Estimate the age of the universe.

Cosmological redshift

$\Delta\lambda/\lambda \approx v/c$ .

Observation. Spectral lines from distant galaxies appear shifted to LONGER wavelengths (redshifted).

Cause. Recession of source. For $v \ll c$ , non-relativistic Doppler: $\frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}$

where $\Delta\lambda = \lambda_{\text{observed}} - \lambda_{\text{rest}}$ .

Figure 1 — Redshift: the same lines, moved to longer wavelength

The pattern of lines is unchanged, so the element is identifiable; only the whole set has moved to longer wavelength. The further the galaxy, the bigger the shift.

Interpretation. Not actual motion through space — space itself is EXPANDING, stretching light en route.

Figure 2 — Expanding space, seen from any galaxy

Pick any galaxy as home and the picture looks the same: neighbours recede slowly, distant ones recede fast. That is exactly v = H₀d.

Cambridge tip. Use rest wavelength on the denominator.

$\Delta\lambda/\lambda \approx v/c$ .
Universal recession.
Space itself expands.

See the full worked example for hubble’s law and the big bang theory →

Hubble's law and age of universe

$v = H_0 d$ .

Hubble's law. Recession speed proportional to distance: $v = H_0 d$

Plot $v$ vs $d$ for many galaxies → straight line through origin with gradient $H_0$ .

Figure 3 — Hubble's law: a straight line through the origin

Plotting v against d for many galaxies gives a line through the origin whose gradient is H₀. Take the gradient over most of the line, not over two adjacent points.

Age estimate. If expansion were constant, time since Big Bang is when all galaxies were at $d = 0$ : $t \approx 1/H_0$

For $H_0 \approx 2.3 \times 10^{-18}$ s $^{-1}$ , $t \approx 1.4 \times 10^{10}$ years.

Figure 4 — Why 1/H₀ is only an upper bound on the age

Running the expansion backwards at today's rate gives 1/H₀. Gravity made the early expansion faster than that, so the true age is somewhat less.

The three relations, and the units trap.

Relation	What it gives	Units to use
$\dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$	Recession speed from the shift of a spectral line	Any consistent pair for $\Delta\lambda$ and $\lambda$ ; $v$ and $c$ in m s $^{-1}$
$v = H_0 d$	Distance from speed, or speed from distance	$v$ in m s $^{-1}$ , $d$ in m, $H_0$ in s $^{-1}$
$t \approx 1/H_0$	An upper bound on the age of the universe	$H_0$ in s $^{-1}$ gives $t$ in s — convert to years at the end

Syllabus 25.3.4 is explicit: convert everything to SI first. Mpc and km s $^{-1}$ Mpc $^{-1}$ are where most marks are lost.

Big Bang. Hubble redshifts + cosmic microwave background (~2.7 K blackbody) + light-element abundances support a hot dense origin.

Cambridge tip. $1/H_0$ is an UPPER bound (true expansion was slower in past due to gravity).

$v = H_0 d$ .
$t \approx 1/H_0$ ≈ 14 Gyr.
Big Bang model.

See the full worked example for hubble’s law and the big bang theory →

Quick recap

Redshift $\Delta\lambda/\lambda \approx v/c$ .
$v = H_0 d$ .
$t \approx 1/H_0 \approx 14$ billion years.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$\Delta\lambda/\lambda \approx v/c$ .
$v = H_0 d$ .
$t \approx 1/H_0$ .
SI units only — convert $H_0$ to s $^{-1}$ , $d$ in metres, $v$ in m/s (syllabus 25.3.4).

How it’s examined

Hubble's law on Paper 4 typically 10-12 marks. Most-tested: redshift → v calc (5 marks), $1/H_0$ age estimate (6 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Hubble’s law and the Big Bang theory

Step-by-step solutions to past-paper-style questions on hubble’s law and the big bang theory , written exactly the way a tutor would explain them at the board.

1Recession speed from redshift (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• redshift
Question
Galaxy spectrum line shifted from 656 nm to 660 nm. Find recession speed v. (5 marks)
Step-by-step solution
1. Step 1
  $\Delta\lambda/\lambda \approx v/c$ .
  $v = c \times \Delta\lambda/\lambda = 3 \times 10^{8} \times 4/656 \approx 1.83 \times 10^{6} \text{ m/s}$
Answer
$v \approx 1.8 \times 10^{6}$ m/s.
2Distance from Hubble's law (4 marks)
Extended• Hubble
Question
$v = 1.8 \times 10^{6}$ m/s, $H_0 = 2.3 \times 10^{-18}$ s $^{-1}$ . Find d. (4 marks)
Step-by-step solution
1. Step 1
  $d = v / H_0$ .
  $d \approx 1.8 \times 10^{6} / 2.3 \times 10^{-18} \approx 7.8 \times 10^{23} \text{ m}$
Answer
$d \approx 7.8 \times 10^{23}$ m ( $\approx$ 26 Mpc).
3Age of universe estimate (5 marks)
Extended• cosmology
Question
Estimate age of universe from $H_0 = 2.3 \times 10^{-18}$ s $^{-1}$ . (5 marks)
Step-by-step solution
1. Step 1
  $t \approx 1/H_0$ .
  $t \approx 1 / 2.3 \times 10^{-18} \approx 4.3 \times 10^{17} \text{ s} \approx 1.4 \times 10^{10} \text{ years}$
Answer
$\approx 1.4 \times 10^{10}$ years (~14 billion years).

Key Formulae — Hubble’s law and the Big Bang theory

The formulae you need to memorise for hubble’s law and the big bang theory on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Cosmological redshift
$\dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$
When to use
Non-relativistic Doppler. $\Delta\lambda$ = observed minus rest wavelength.
Hubble's law
$v = H_0 d$
When to use
Recession speed proportional to distance.
Age of universe (rough)
$t \approx 1/H_0$
When to use
Lower-bound estimate assuming constant expansion.

Key Definitions and Keywords — Hubble’s law and the Big Bang theory

Definitions to memorise and the exact keywords mark schemes credit for hubble’s law and the big bang theory answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Cosmological redshift
Examiner keyword
Observed increase in wavelength of light from distant galaxies caused by expansion of space.
Hubble constant
Examiner keyword
Proportionality constant relating recession speed and distance. Units: s $^{-1}$ (or km/s/Mpc).
Big Bang
Examiner keyword
Model: universe began in hot dense state and has been expanding ever since. Supported by Hubble redshifts and CMB.

Common Mistakes and Misconceptions — Hubble’s law and the Big Bang theory

The traps other students keep falling into on hubble’s law and the big bang theory questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Wrong sign of $\Delta\lambda$
9702 Examiner Reports 2022-2024
Why it happens
Confuse observed and rest wavelength.
How to avoid it
Redshift: $\lambda_{\text{observed}} > \lambda_{\text{rest}}$ , so $\Delta\lambda$ POSITIVE.
✕Inconsistent units for $H_0$
9702 syllabus 2025-2027, statement 25.3.4 note
Why it happens
Mixing km/s/Mpc with SI.
How to avoid it
The 2025-2027 syllabus is explicit: candidates will only be required to use SI units. So convert $H_0$ to s $^{-1}$ and keep distances in metres and speeds in m/s throughout.