State the relation used to estimate the age of the universe from the Hubble constant, defining each symbol.

t ≈ 1/H₀, where t is the estimated age of the universe in seconds and H₀ is the Hubble constant in s⁻¹.

Show how the age relation follows from Hubble's law.

If a galaxy has been receding at a constant speed v ever since the expansion began, then d = vt, so t = d/v, and substituting v = H₀d gives t = d/(H₀d) = 1/H₀.

Calculate the age of the universe in seconds, taking the Hubble constant as 2.4 × 10⁻¹⁸ s⁻¹.

t = 1/H₀ = 1/2.4 × 10⁻¹⁸ = 4.2 × 10¹⁷ s, and 1 ÷ 4.17 × 10¹⁷ s returns 2.4 × 10⁻¹⁸ s⁻¹ as given.

Convert an age of 4.2 × 10¹⁷ s into years, taking one year as 3.15 × 10⁷ s.

t = 4.17 × 10¹⁷ / 3.15 × 10⁷ = 1.3 × 10¹⁰ years, that is about 13 billion years, and 1.32 × 10¹⁰ × 3.15 × 10⁷ returns 4.2 × 10¹⁷ s.

What assumption about the expansion is made when the age of the universe is estimated as 1/H₀?

It assumes every galaxy has been receding at the same constant speed since the expansion began, so that the rate of expansion has never changed.

Why is the assumption behind the 1/H₀ estimate not exactly correct?

Gravity between all the matter in the universe has acted to slow the expansion, and observations indicate the expansion rate has also changed in other ways, so the rate now is not the rate it has always had.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Astronomy

The age of the universe

3 things to know
Unit AS 2

Overview

Recall questions on the estimate t ≈ 1/H₀ and how it follows from Hubble's law, worked calculations in seconds and in years, the assumption of a constant expansion rate and why it is not exactly right, the effect of a larger Hubble constant, why the oldest stars must be younger than the estimate, and the observable limit a finite age imposes.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Why is the assumption behind the 1/H₀ estimate of the age of the universe not exactly correct?

Key term

How does the finite age of the universe limit how much of it can be observed?

Key term

How would evidence that the expansion of the universe is speeding up affect the estimate of its age?

Questions from this subtopic

Each one with the model answer underneath.

1
State the relation used to estimate the age of the universe from the Hubble constant, defining each symbol.
Model answer
t ≈ 1/H₀, where t is the estimated age of the universe in seconds and H₀ is the Hubble constant in s⁻¹.
2
Show how the age relation follows from Hubble's law.
Model answer
If a galaxy has been receding at a constant speed v ever since the expansion began, then d = vt, so t = d/v, and substituting v = H₀d gives t = d/(H₀d) = 1/H₀.
3
Calculate the age of the universe in seconds, taking the Hubble constant as 2.4 × 10⁻¹⁸ s⁻¹.
Model answer
t = 1/H₀ = 1/2.4 × 10⁻¹⁸ = 4.2 × 10¹⁷ s, and 1 ÷ 4.17 × 10¹⁷ s returns 2.4 × 10⁻¹⁸ s⁻¹ as given.
4
Convert an age of 4.2 × 10¹⁷ s into years, taking one year as 3.15 × 10⁷ s.
Model answer
t = 4.17 × 10¹⁷ / 3.15 × 10⁷ = 1.3 × 10¹⁰ years, that is about 13 billion years, and 1.32 × 10¹⁰ × 3.15 × 10⁷ returns 4.2 × 10¹⁷ s.
5
What assumption about the expansion is made when the age of the universe is estimated as 1/H₀?
Model answer
It assumes every galaxy has been receding at the same constant speed since the expansion began, so that the rate of expansion has never changed.
6
Why is the assumption behind the 1/H₀ estimate not exactly correct?
Model answer
Gravity between all the matter in the universe has acted to slow the expansion, and observations indicate the expansion rate has also changed in other ways, so the rate now is not the rate it has always had.

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