The Age of the Universe

Hubble's law can be used to estimate the age of the universe.If galaxies are all moving apart, then in the past they were closer together. Run time backwards and all the matter was together at one point, the Big Bang. Assume a galaxy now at distance d has always moved at its present speed v. The time taken to reach d ist = d ÷ vBut Hubble's law says v = H₀d, so d/v = 1/H₀, the same for every galaxy:t ≈ 1 ÷ H₀Worked example: take H₀ = 70 km s⁻¹ Mpc⁻¹. First convert to s⁻¹ (1 Mpc = 3.09 × 10²² m):H₀ = 7.0 × 10⁴ ÷ 3.09 × 10²² = 2.27 × 10⁻¹⁸ s⁻¹t = 1 ÷ 2.27 × 10⁻¹⁸ = 4.4 × 10¹⁷ st = 4.4 × 10¹⁷ ÷ 3.15 × 10⁷ = 1.4 × 10¹⁰ yearsSo the universe is roughly 14 billion years old.This is only an estimate. It assumes the rate of expansion has been constant, but gravity would have slowed the expansion and there is evidence it is now accelerating. The value of H₀ itself is also uncertain, because distances to far galaxies are hard to measure, so different values of H₀ give different ages. This is one source of controversy about the age of the universe.