Episode 704: The expanding universe

Lesson for 16-19 IOP TAP

Activity time 120 minutes
Level Advanced

The universe is expanding; don’t confuse this with the big bang (see episode 705: Cosmology).

Lesson Summary

Student activity: Looking at a galaxy (20 minutes)
Discussion: The scale of the universe (10 minutes)
Discussion: Hubble’s observations (10 minutes)
Demonstrations: Expanding universe (20 minutes)
Student activity: Modelling Hubble’s law (20 minutes)
Discussion: Cosmological red shift (10 minutes)
Student questions: Red shift of quasars (30 minutes)

Student activity: Looking at a galaxy

In 1925 Hubble showed that the Andromeda nebula was a collection of stars (i.e. a galaxy) outside and quite distinct from our own Milky Way galaxy. Students can look for Andromeda using binoculars.

Episode 704-1: Two million-year-old light: Seeing the Andromeda nebula (Word, 60 KB)

Discussion: The scale of the universe

Discuss the different ways in which astronomers determine distances in space, and the units used.

Episode 704-8: The ladder of astronomical distances (Word, 106 KB)

1 light-year (1 ly) = 9.46 × 10¹⁵ m

1 parsec (1 pc) = 3.09 × 10¹⁶ m

1 Mpc = 3.09 × 10²² m

Episode 704-2: Distances in light travel time (Word, 42 KB)

Discussion: Hubble’s observations

Hubble measured 24 galaxies. 22 had red shifted light. He plotted recession speed v against distance d.

Speed was much easier to measure (from the Doppler shift) than distance. There are real problems in setting a length scale. Different methods are used at the ever increasing distances, each overlapping to allow a (hopefully) consistent calibration.

Hubble found v ∝ d; for each increase in distance of 1 Mpc the recessional speed of galaxies increases by 70 km s^-1. This is the H₀ . The bigger H₀ the faster the universe expands (and thus the younger it is) and vice versa.

This gives us an idea of the age of the universe:

H₀ in km s^-1 per km = 70 km s^-13.09 × 10¹⁹ km

H₀ = 2.26 × 10^-18 s^-1;

Age of universe = 12.26 × 10^-18 s^-1

Age of universe = 4.4 × 10¹⁷ s

So 15 My, more or less.

Episode 704-3: Hubble’s law and the age of the universe (Word, 200 KB)

Demonstration: Expanding universe

It is useful to show that, although the whole of the universe is expanding, this does not imply that there is a single centre of expansion.

Inflate a balloon with sticky paper dots attached to it, representing galaxies. Note that the galaxies move apart, but they do not themselves get bigger (because gravity holds them together).

Episode 704-4: Relativity and the expanding universe (Word, 140 KB)

Draw up two OHP sheets, each with a matrix of dots. They have the same pattern, but one has a greater spacing. Overlay second OHP sheet – whichever dot on the bottom sheet you use as the origin to match to a dot on the second sheet, all the other dots move away from the chosen dot. There is no centre from which all dots move away from.

Student activity: Modelling Hubble’s law

Students could use a length cut from a wide rubber band. Mark dots to represent galaxies. Identify a home galaxy. Stretch the rubber. A dot twice as far from the home galaxy moves twice the distance; this is the Hubble Law.

The Hubble law thus implies that the universe is expanding.

What’s it expanding into? Nothing! Space (or rather space-time) is being created as the universe expands.

If universe is expanding, why don’t we see it locally – e.g. in the solar system? Is it too small an effect? Yes; the expansion is overcome by gravity.

Discussion: Cosmological red shift

The so called cosmological red shift is not due to relative speeds as such – it’s due to the expansion of space itself, stretching the wavelength of light because space(time) is expanding but the resulting formula for red shift is the same.

A red shift of 1 corresponds to 7 × 10⁹ years ago, i.e. the light was emitted when the universe was half as old as it is now. Red shifts > 5 have been observed.

Episode 704-5: Red shift (Word, 199 KB)

Episode 704-6: Red shifts of galactic spectra (Word, 156 KB)