If the universe has expanded at a constant rate since the Big Bang, Hubble's law can be used to estimate its age.Imagine a galaxy now at a distance d, moving away at speed v. If its speed has always been the same, the time t it has taken to reach its current position from the start of the expansion is:t = d/v Hubble's law gives v = H0d, so d/v = 1/H0. The distance cancels, so the result is the same for every galaxy:t ≈ H0−1 To get an age in seconds, H0 must be in s−1. If it is given in km s−1 Mpc−1, convert first: km to m (× 103) and Mpc to m (× 3.1 × 1022).Worked example: H0 = 70 km s−1 Mpc−1. Estimate the age of the universe.
H0 = (70 × 103) / (3.1 × 1022) = 2.26 × 10−18 s−1
t = 1/H0 = 1 / 2.26 × 10−18 = 4.4 × 1017 s
t = 4.4 × 1017 / 3.16 × 107 = 1.4 × 1010 years (about 14 billion years)This is only an estimate. The rate of expansion has not been constant: gravity slowed it in the past, and dark energy is now accelerating it. The value of H0 is also uncertain, because the distances to galaxies are hard to measure. The best current estimate of the age of the universe is about 13.8 billion years.
H0 = (70 × 103) / (3.1 × 1022) = 2.26 × 10−18 s−1
t = 1/H0 = 1 / 2.26 × 10−18 = 4.4 × 1017 s
t = 4.4 × 1017 / 3.16 × 107 = 1.4 × 1010 years (about 14 billion years)This is only an estimate. The rate of expansion has not been constant: gravity slowed it in the past, and dark energy is now accelerating it. The value of H0 is also uncertain, because the distances to galaxies are hard to measure. The best current estimate of the age of the universe is about 13.8 billion years.