Use the syllabus Hubble reference and proportional graph
Use the syllabus reference H₀ = 2.2 × 10⁻¹⁸ s⁻¹ and interpret a correctly labelled speed-distance graph.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Use v = H₀d.
- Calculate a straight-line graph gradient.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the gradient of speed versus distance?
What you will learn
- Use the syllabus reference H₀ = 2.2 × 10⁻¹⁸ s⁻¹ and interpret a correctly labelled speed-distance graph.
- Distinguish a reference estimate, axis scaling and an exact empirical constant claim.
Use the specified examination reference
The selected 2026–2028 syllabus gives H₀ = 2.2 × 10⁻¹⁸ per second. Use that reference when no different value is supplied in these tasks. It is a syllabus estimate, not a claim that all present research measurements agree exactly or that H₀ is a speed.
In a model graph of recession speed v against distance d, the gradient is H₀. Axis scaling matters: if distance numbers denote 10²⁴ m and speed numbers denote 10⁶ m/s, a plotted gradient of 2.2 corresponds to 2.2 × 10⁻¹⁸ s⁻¹ after restoring units.
Read points and compare ratios
Using the reference, distances 1, 2 and 3 × 10²⁴ m give speeds 2.2, 4.4 and 6.6 × 10⁶ m/s. These supplied points lie on a proportional model through the origin. They are not a telescope dataset or a guarantee that every measured galaxy falls exactly on one line.
A different supplied positive estimate changes model predictions and the reciprocal age estimate. Compare quantities under the same assumptions and units. Do not rank constants by exponent alone; compare their full normalised numerical values.
Sources for this lesson
Pause and explain
What does 2.2 × 10⁻¹⁸ s⁻¹ represent here?
Worked example
A v-axis is in 10⁶ m/s and d-axis in 10²⁴ m. A line rises 4.4 axis units over 2 distance units. Find H₀.
Show the worked solution
- Restore Δv = 4.4 × 10⁶ m/s.
- Restore Δd = 2 × 10²⁴ m.
- Divide Δv by Δd.
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.
Recall H₀ and calculate v for d = 1.5 × 10²⁴ m.
Give me a hint
Use the selected reference with v = H₀d.
Compare my reasoning
- H₀ = 2.2 × 10⁻¹⁸ s⁻¹.
- v = 2.2 × 1.5 × 10⁶.
- Keep m/s for speed.
H₀ = 2.2 × 10⁻¹⁸ s⁻¹; v = 3.3 × 10⁶ m/s.
Look for these in your work
- State the reference unit.
- Apply proportionality.
The plotted v-axis rise is 6.6 in 10⁶ m/s over a d-axis run of 3 in 10²⁴ m. Calculate the physical slope.
Give me a hint
Restore both axis multipliers before dividing.
Compare my reasoning
- Δv = 6.6 × 10⁶ m/s.
- Δd = 3 × 10²⁴ m.
- H₀ = Δv/Δd.
2.2 × 10⁻¹⁸ s⁻¹, not simply 2.2 s⁻¹.
Look for these in your work
- Include axis powers.
- Give the physical unit.
Compare reference 2.2 × 10⁻¹⁸ with supplied alternative 2.5 × 10⁻¹⁸ s⁻¹ at distance 2.0 × 10²⁴ m.
Give me a hint
Calculate both predictions for the same distance and model.
Compare my reasoning
- First speed is 4.4 × 10⁶ m/s.
- Second speed is 5.0 × 10⁶ m/s.
- Difference is 0.6 × 10⁶ m/s.
4.4 × 10⁶ versus 5.0 × 10⁶ m/s; difference 6.0 × 10⁵ m/s.
Look for these in your work
- Hold distance fixed.
- Do not call either an exact universal measured speed.
Common mistakes
- Axis multipliers affect physical slope.
- H₀ is a reference estimate.
- Model points are not real observations.
What can you explain now?
What does 2.2 × 10⁻¹⁸ s⁻¹ represent here?
Compare with the explanation
The selected syllabus Hubble estimate
It is the examination reference for the simple far-galaxy model.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Distinguish a reference estimate, axis scaling and an exact empirical constant claim.
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.