Physics 11–12 · Year 12

Modelling the expanding Universe with elastic and markers, and Hubble's law from galaxy data

Module 8: From the Universe to the Atom (Origins of the Elements)

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The idea

If space expands uniformly, every galaxy recedes from every other at a speed proportional to its distance, and 1 over the constant of proportionality, the Hubble time, is how long the expansion would have taken at today's rate.

What you need

3 m of wide dressmaker's elastic with paper galaxy markers pinned at unequal spacings, metre rules (the NSW Department of Education Module 8 guide, Appendix 1)
Spreadsheet; Hubble's law page from the CSIRO Cosmic Engine resource

How to do it

Assign two learners to hold the ends of the elastic and others to measure each gap.
At each time step both end-holders take one pace back; the measurers record every gap and the cumulative distance of each galaxy from galaxy 1.
Plot distance from galaxy 1 against time step for each galaxy; the gradient is its recession velocity.
Plot recession velocity against initial distance; fit a straight line through the origin.
Compute 1 over the gradient (in appropriate units), the Hubble time, and compare it with 1/H0 for measured values of the Hubble constant and with the measured age of the Universe.

What you should see

Larger gaps grow faster and the velocity-distance plot is a straight line through the origin, as in Hubble's 1929 diagram. With the modern value H0 = 70 km/s per Mpc a galaxy at 100 Mpc recedes at 7000 km/s and the Hubble time 1/H0 is 13.97 billion years. Planck 2018's H0 of 67.4 km/s per Mpc gives a Hubble time of 14.5 billion years and SH0ES's 73.04 gives 13.4; the disagreement between those two measurements of H0 is the current Hubble tension. The Hubble time is not the age of the Universe, because the expansion rate has changed over time: Planck 2018's own fit gives the age as 13.8 billion years (13.797 plus or minus 0.023).

What changes

What you change: initial distance of a galaxy marker
What you measure: recession velocity
What you keep the same: uniform stretch (equal paces)
same time step

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Galaxies are flying apart through space from a central point; space itself expands and no point is the centre.
Our galaxy is expanding too; gravity holds galaxies together and only the space between them stretches.

Safety card

Low riskLearners carry it out

Hazards

elastic snapping back

Controls

release the elastic slowly

Note

Record the activity in RiskAssess (https://www.riskassess.com.au/) and follow the Science ASSIST risk management information sheet (https://asta.edu.au/resource/ais-risk-management-and-risk-assessment/).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Physics Stage 6 Syllabus (2017), current: Year 11 until the end of 2026, Year 12 until Term 3 2027PH12-15 PH11/12-5 PH11/12-6
Physics 11-12 Syllabus (2025), not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027, first HSC examination 2028PY-12-04 PY-12WS-05
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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