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\subsection{Age of the Universe}  Now you've measured Hubble's constant, With some trivial dimensional analysis,  you can estimate calculate  the age of the Universe. We see everything rushing away from us, with a velocity   proportional to its distance Universe  from us. This means everything was closer   together in the past. Let's say a galaxy is 100 Mpc away Hubble's law.  Do this using your value of $H_0$  from us  today, Hydra I  and that $H_0 = 100\ {\rm km}s^{-1}{\rm Mpc}^{-1}$. 100 Mpc compare your result to the best   current estimate of the age of the Universe, which  is $1.38 \times 10^{10}$ years.  \[    100 \times 10^6 \times 3.1 \times 10^{16} {\rm m} = 3.1 \times 10^{21} {\rm km}   \]  Because the galaxy is 100 Mpc away, Hubble's law tells us it is moving  away from us with a velocity  \[    v = H_0 \times d = 100 \times 100 = 10^{4} {\rm km}s^{-1}   \]  Now extrapolate backwards (assume that the galaxy has always moved with the   same speed). How long ago was the galaxy right here? The answer $t$ is  \[    \frac{3.1 \times 10^{21}}{10^4} = 3.1 \times 10^{17} s = 10^{10} {\rm years}   \]  Try the calculation for galaxies at different distances \ -- \ they were  always here the same time ago (why?). So what was this time in the past  where all the universe was piled on top of us? The Big Bang! We've found out  how long ago the Big Bang was. Do the calculation for Hydra I, using your  value of its distance and Hubble's constant. How old do you make the  universe? This measurement of the age of the universe is very a little  crude, because it assumes that the universe has been expanding at exactly the same rate  ever since the Big Bang. If Bang (try putting in the Planck value of $H_0$ and see what age  you do a detailed calculation, solving  Einstein's equations for get,  it's still wrong!).  To get  the Universe, right answer,  you find that need to take into account how  the universe  was expanding faster earlier. This means that Hubble `constant' changes  between  the age you calculated Big Bang and now.   There  is too  big (why?). The correct answer turns out no neat analytic expression for this age, but it is a relatively straightforward   calculation  to be 2/3 of the age you calculated.  Multiply your answer by 2/3 do on a computer, here is a link  to get your best estimate of a program that calculate this and  other cosmological parameters made by students in  the age of Astro group here at  the universe. University of Melbourne:  http://ph.unimelb.edu.au/cosmocalc/input.php .  Compare the age of the universe with various other ages. The age of the  Earth is thought to be about $4.6 \times 10^9$ years. The age of the Sun   and the rest of the solar system is probably similar. The age of our  galaxy is estimated as about $10^{10}$ years, but some star clusters orbiting  our galaxy (globular clusters) are thought to be at least $1.5 \times 10^{10}$  years old (their age is estimated by computer modelling the nuclear burning  of their stars). Is this embarrassing for your value of the age of the  universe? What is the age of the universe if $H_0 = 80\ {\rm km}s^{-1}{\rm   Mpc}^{-1}$? Anything wrong with this? years.  \subsection{Advanced problems}