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## Homework Statement

Calculate the comobile distance of a galaxy with z=7.3, H[itex]_{0}[/itex]=72 km/s/Mpc, universe with [itex]\Omega_{0}=\Omega_{0,m}=1[/itex]

Calculate the scale factor when the galaxy emitted the light we receive today.

## Homework Equations

Friedmann equation

[itex](\frac{\dot{a}}{a})^{2}=(H_{0})^{2}[ \Omega_{0,r}(\frac{a}{a_{0}})^{-4}+\Omega_{0,m}(\frac{a}{a_{0}})^{-3}+(1-\Omega_{0})(\frac{a}{a_{0}})^{2}+\Omega_{\Lambda}][/itex]

## The Attempt at a Solution

With this model of universe Friedmann equation becomes:

[itex](\frac{\dot{a}}{a})^{2}=(H_{0})^{2}[\Omega_{0,m}(\frac{a}{a_{0}})^{-3}][/itex]

so

[itex](\frac{\dot{a}}{a})=(H_{0})(\frac{a}{a_{0}})^{-3/2}[/itex]

I should use the equation:

[itex]X=\int^{t 0}_{t em}\frac{cdt}{a\dot{a}}[/itex]

[itex]X=[/itex] comobile distance

..but i don't know how to put the scale factor into it.