Calculate Hubble constant from recession speed and distance
Define H₀ as recession speed divided by galaxy distance and use consistent SI units.
Section 6.2.3 · The Universe
Exam scope and assessment notes
Extended only (Supplement) · Physics 0972, 2026–2028. Use supplied distances, periods and stated orbital models. Drawings are not to scale. Written practice is self-checked. Human subject-teacher review, supervised practical competence and cumulative assessment remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
Before you begin
- Convert kilometres to metres.
- Divide quantities written in scientific notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which speed value is 6600 km/s in m/s?
What you will learn
- Define H₀ as recession speed divided by galaxy distance and use consistent SI units.
- Rearrange H₀ = v/d to find the ratio, speed or distance.
Define the measured ratio
The Hubble constant H₀ is the ratio of a galaxy’s recession speed v to its distance d: H₀ = v/d. In the simple far-galaxy relation, v = H₀d and d = v/H₀. Use the distance and speed that belong to the same galaxy and the stated model.
With v in m/s and d in metres, metres cancel and H₀ has unit s⁻¹, meaning per second. It is neither a speed in m/s nor a time in seconds. Mixing a speed number in km/s with a metre distance introduces a factor-of-1000 error.
Name the interpretation boundary
The relation describes a large-scale trend for far galaxies; local motions can contribute additional speed. A supplied pair yields a model ratio, not proof that one galaxy alone establishes the whole cosmic expansion history.
A larger distance at the same H₀ corresponds to a larger recession speed. This proportionality is not a claim that brightness directly equals speed or that physical star sizes grow by H₀ every second. Keep the measured quantities and their units distinct.
Pause and explain
What is the SI unit of v/d?
Worked example
Find H₀ for supplied v = 6600 km/s and d = 3.0 × 10²⁴ m.
Show the worked solution
- Convert v = 6.6 × 10⁶ m/s.
- Divide 6.6 × 10⁶ by 3.0 × 10²⁴.
- Cancel the metre units.
Answer 2.2 × 10⁻¹⁸ s⁻¹.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Use v = 4.4 × 10⁶ m/s and d = 2.0 × 10²⁴ m to calculate H₀.
Give me a hint
Divide coefficients and subtract exponents using SI units.
Compare my reasoning
- H₀ = v/d.
- 4.4/2.0 = 2.2 and 10⁶/10²⁴ = 10⁻¹⁸.
- Use the remaining s⁻¹ unit.
2.2 × 10⁻¹⁸ s⁻¹.
Look for these in your work
- Show v/d.
- Give per-second units.
Use H₀ = 2.2 × 10⁻¹⁸ s⁻¹ and d = 5.0 × 10²⁴ m to calculate v.
Give me a hint
Multiply the distance by the constant rather than dividing it.
Compare my reasoning
- Rearrange v = H₀d.
- Calculate 2.2 × 5.0 × 10⁶.
- Normalise the result.
1.1 × 10⁷ m/s.
Look for these in your work
- Use the correct rearrangement.
- Keep the speed unit.
Use H₀ = 2.2 × 10⁻¹⁸ s⁻¹ and v = 8800 km/s to find d.
Give me a hint
Convert speed before dividing by the per-second constant.
Compare my reasoning
- v = 8.8 × 10⁶ m/s.
- d = v/H₀.
- Calculate (8.8/2.2) × 10²⁴.
4.0 × 10²⁴ m.
Look for these in your work
- Convert km/s first.
- Return metres rather than seconds.
Common mistakes
- H₀ is per second, not a speed.
- Use a matching galaxy pair.
- Convert km/s before combining with metres.
What can you explain now?
What is the SI unit of v/d?
Compare with the explanation
s⁻¹
Dividing metres per second by metres leaves per second.
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Make it stick
Rearrange H₀ = v/d to find the ratio, speed or distance.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.