Age of universe on stargazing live

[paler31]

I was watching Stargazing live last night and they were talking about the expansion of the universe and quoted the Hubble constant which describes the expansion of the universe as 70km/s/Mparsec. Apparently from this figure you can determine the age of the universe. Here is what I did to determine the age of the universe from this figure.

Firstly I converted Mparsec into km. Now the speed of light in a vacuum is quoted as 299792458 m/s now the number of seconds in 1 year is 60x60x24x365.25 = 31557600s therefore light will travel a distance of 299792458 x 31557600 = 9.46 x 10¹⁵ m = 9.46 x 10 ¹²km in 1 year.

Now 1 parsec is a distance of 3.26 light years therefore 1 parsec is a distance of:-

3.26 x 9.46 x10¹²= 3.08 x10 ¹³ km so a Mega Parsec is 3.08x10¹³ x 1x10⁶= 3.08 x 10¹⁹km

We can now wright Hubbles constant as 70 km/s/3.08x10 ¹⁹km now the km cancel out and you are left with 70/3.08x10¹⁹s = 2.27x10^-18/s Putting this figure into 1 should give the age of the universe so we have the universes age as 1 / 2.27x10^-18 = 4.41 x10¹⁷s and we already know there are 31557600s in 1 year therefore the age of the universe is 4.41 x10¹⁷ / 31557600 = 1.40 x 10 ¹⁰ years or 14 billion years. Now they said that this calculation should yield a figure of 15 billion years so where have I lost my billion years from can anybody spot it? I can not see an error in my logic but i am sure I must be doing something wrong. Can anyone help?

John

[Kai]

You have already posted the same question

Im going to lock this one to keep the replies in the same place.