Answer to Question #141947 in Astronomy | Astrophysics for Gibby

Question

Imagine that you live in a geometrically flat universe which is dominated by radiation. Hubble's constant in this universe is measured to be 70km s−1 Mpc−1 . A Mpc (Mega-parsec) is a million parsecs, and a parsec is 3.086×1016m .

How old is this universe (in billions of years)?

Answer 1

The universe has years

$t=\frac{1}{H}=\frac{1}{70 \cdot\frac{km}{s \cdot Mpc} }=\frac{1}{70 \cdot\frac{1000 \cdot m}{s \cdot 10^6 \cdot 3.086 \cdot 10^{16}m} }=\frac{1}{\frac{7 \cdot 10^4}{3.086 \cdot 10^{22}s}}=$

$=\frac{3.086 \cdot 10^{22}s}{7 \cdot 10^4}=4.4 \cdot 10^{17}s=\frac{4.4 \cdot 10^{17}s}{3.15 \cdot 10^7s/years}=1.4 \cdot 10^{10} years=14 \space billions \space \space of \space \space years$