Hubble's law, the age of the universe and its fate

Overview

Recall questions on v = H₀d, the value and unit of the Hubble constant, the estimate t ≈ 1/H₀ and the assumption behind it, worked ages in seconds and years, the critical density and the conditions for an open, closed or flat universe.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State Hubble's law as an equation, defining every symbol and its unit.

   Model answer

   The law is v = H₀D, where v is a galaxy's radial velocity of recession in m s⁻¹, D is its distance in metres and H₀ is the Hubble constant in s⁻¹.

2. 2

   What does Hubble's law tell us about the universe?

   Model answer

   It tells us that galaxies are receding from us at speeds proportional to their distances. That is exactly how an expanding universe appears from any point within it.

3. 3

   Convert a Hubble constant of 2.2 × 10⁻¹⁸ s⁻¹ into km s⁻¹ Mpc⁻¹, taking 1 Mpc as 3.09 × 10²² m.

   Model answer

   Multiplying gives 2.2 × 10⁻¹⁸ × 3.09 × 10²² = 6.8 × 10⁴ m s⁻¹ per Mpc, that is about 68 km s⁻¹ Mpc⁻¹. Dividing 6.8 × 10⁴ m s⁻¹ by 3.09 × 10²² m returns 2.2 × 10⁻¹⁸ s⁻¹.

4. 4

   Why does an observer in any galaxy see all the others receding, without being at a special place?

   Model answer

   Space itself is expanding, so every separation grows in proportion to its size, and that gives a recession speed proportional to distance from whichever galaxy the observation is made.

5. 5

   What is cosmological red shift?

   Model answer

   Cosmological red shift is the increase in the wavelength of light from a distant galaxy caused by the expansion of space stretching the wave while it travels, rather than by motion through space.

6. 6

   A galaxy's spectral lines show a fractional shift of 0.050 towards longer wavelengths. Calculate its distance, taking H₀ as 2.2 × 10⁻¹⁸ s⁻¹.

   Model answer

   The recession speed is v = c × Δλ/λ = 3.00 × 10⁸ × 0.050 = 1.5 × 10⁷ m s⁻¹, so D = v/H₀ = 1.5 × 10⁷ ÷ 2.2 × 10⁻¹⁸ = 6.8 × 10²⁴ m. Multiplying 6.82 × 10²⁴ m by 2.2 × 10⁻¹⁸ s⁻¹ returns 1.5 × 10⁷ m s⁻¹.

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