6.2.3 The Universe

The Milky Way itself contains many billions of stars and has an approximate diameter of 100 000 light-years.

Light therefore takes about 100 000 years to travel a distance equal to the Milky Way's diameter. This is a galactic scale, far larger than the Solar System.

Astronomers compare identifiable spectral lines in received starlight with the wavelengths of the same lines measured in a laboratory. A shift to longer wavelengths is a redshift.

For a receding source, successive wavefronts arrive more spread out, so the observed wavelength is longer than the emitted or laboratory wavelength.

If a hydrogen line has wavelength 656 nm in a laboratory but is observed at 667 nm from a galaxy, the observed wavelength has increased: 667 − 656 = 11 nm. The galaxy's light is redshifted.

The known laboratory spectrum acts as the reference. Matching the pattern of lines identifies the element; their displacement to longer wavelength identifies redshift.

When light from galaxies in all directions is generally redshifted, the large-scale separations between galaxies are increasing. This is evidence that the Universe is expanding.

Running the expansion model backwards implies that matter was closer together in the past. Redshift therefore supports the Big Bang Theory.

More distant galaxies generally show greater redshift and recession speed, strengthening the expansion interpretation.

Detectors receive this faint microwave background from every direction rather than from one local star, planet or galaxy.

Its all-sky presence is why it is described as a cosmic background: it is a property observed throughout the surrounding Universe.

As the Universe expanded, the wavelength of this radiation was stretched to longer wavelengths.

That expansion shifted the radiation into the microwave region of the electromagnetic spectrum, where it is observed today from all directions.

The CMBR's ancient origin, stretched wavelength and all-sky distribution support the model of a hot early Universe that has expanded.

A larger wavelength increase means a larger redshift and, under the syllabus model, a greater speed away from Earth.

A supernova of known intrinsic brightness appears dimmer when it is farther away. Comparing its observed brightness with the expected intrinsic brightness provides the distance.

Astronomers can therefore obtain the two quantities needed for Hubble analysis in different ways: supernova brightness gives distance, while redshift gives recession speed.

If H₀ is treated as constant, v = H₀d, so recession speed is directly proportional to distance. A graph of v against d has gradient H₀ when units are consistent.

If v is in m/s and d is in m, the metres cancel and H₀ has unit s⁻¹. Convert kilometres and light-years before substitution when required.

The s⁻¹ unit follows from H₀ = v/d: (m/s)/m = 1/s.

The very small value is expected because cosmic expansion is measured over extremely large distances and timescales.

Using H₀ = 2.2 × 10⁻¹⁸ s⁻¹ gives age ≈ 1/H₀ ≈ 4.5 × 10¹⁷ s. Dividing by about 3.2 × 10⁷ s/year gives approximately 1.4 × 10¹⁰ years.

Galaxies are now receding, and more distant galaxies generally recede faster. Extrapolating their separations backwards implies that matter was closer together and supports the idea that all matter was once concentrated at a single point.

This is an estimate based on using the current expansion relation over cosmic history; it is not a direct stopwatch measurement.