How old is the Visible Universe?

Let's assume that the recessional velocities of the galaxies have remained constant in time


How long has it taken for a given galaxy to reach its present distance from us?

time = distance / velocity

We know from Hubble's Law that velocity is proportional to distance in the above equation

Hubble's Law:


v = H₀ d

so, time = distance / velocity = distance /H₀ d

time = 1 / H₀

Now suppose Hubble's constant (H₀) is 70 km/s / Mpc

This is 70 km/s / 3.26 Mly = 21.5 km/s / Mly

But 1 Mly = 9.5 x 10¹⁸ km

(10⁶ x 300,000 km/sec x 3.16 x 10⁷ sec)

so

H₀ = 21.5 km/s / Mly
= 21.5 km/s / 9.5 x 10¹⁸ km = 2.3 x 10^-18 / sec = 1 / 4.4 x 10¹⁷ sec

and

1/H₀ = = 4.4 x 10¹⁷ seconds = 14 x 10⁹ years
(since there are 3.16 x 10⁷ seconds in one year)

so, . . . time = 1 / H0 = 14 x 109 years

Notice this time is independent of the distance to the galaxy, since galaxies farther away are moving faster.



Also, notice the assumption that the velocities have remained constant.


(We have evidence that this assumption is not quite correct, but it is close)