MYP Physics · topic MYP-16.05
Redshift and an expanding universe
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
A Hubble estimate with a local-motion warning
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A known spectral line has laboratory wavelength 500.0 nm. In one galaxy it appears at 510.0 nm. Independent distance measurements for other galaxies and their low-redshift recession speeds are supplied. Use c = 3.0×10⁵ km s⁻¹, v≈cz and 1 Mpc = 3.09×10¹⁹ km. Ignore curvature and detailed cosmological evolution in this local estimate. Supplied model: Use z = (λobserved−λrest)/λrest and v = H₀d in the stated low-redshift approximation. Supplied data (Distance / Mpc; Recession speed / km s⁻¹): (20, 1400), (40, 2800), (60, 4200), (80, 5600). (a) Find the redshift, approximate recession speed, Hubble parameter and inferred galaxy distance. [3 marks] (b) Estimate 1/H₀ in years using 1 yr = 3.16×10⁷ s, and explain two limits of treating it as an exact cosmic age. [3 marks]
Local distance–recession evidence
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Recession speed / km s⁻¹
Horizontal axis (x): Distance / Mpc
Read the exact data as a table
| Distance / Mpc | Recession speed / km s⁻¹ |
|---|---|
| 20 | 1400 |
| 40 | 2800 |
| 60 | 4200 |
| 80 | 5600 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Show a hint
Begin with part (a): Find the redshift, approximate recession speed, Hubble parameter and inferred galaxy distance.
Reveal the worked solution
- z = (λobserved−λrest)/λrest = (510−500)/500 = 0.0200.
- The low-z approximation gives v≈cz = 6000 km s⁻¹. The graph gradient gives H₀ = 1400/20 = 70 km s⁻¹ Mpc⁻¹.
- Distance estimated from v = H₀d is 6000/70≈85.7 Mpc. This inference assumes recession dominates the observed line shift.
- Convert H₀ to s⁻¹: 70/(3.09×10¹⁹)≈2.27×10⁻¹⁸ s⁻¹. Its reciprocal is 4.41×10¹⁷ s≈1.40×10¹⁰ yr.
- The cosmic expansion rate evolves, so a current rate extrapolated backward as constant need not give the true age.
- Galaxies also have peculiar motions. A nearby galaxy may be blueshifted despite the large-scale expansion, so one local observation does not overturn the population trend.
Answer (a) z = 0.0200; v≈6000 km s⁻¹; H₀≈70 km s⁻¹ Mpc⁻¹; distance≈85.7 Mpc. (b) Hubble time≈1.40×10¹⁰ years; it is an indicative timescale rather than an exact age.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.