Undergrad How Does the Hubble Parameter Relate to Galaxy Movement?

[Komorebi]

This is the time derivative to calculate the speed which a galaxy moves away from another galaxy. I don't understand how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1). Could anyone explain this? vi(t) = d/dt (ri(t) − r1(t))
= d/dt a(t)(xi − x1)
= da/dt (xi − x1)
= (∙a)/a a(t). (xi − x1) !
=(∙a)/a (ri(t) − r1(t))
= H(t) (ri(t) − r1(t))

[ ∙a= da/dt ]

 

[sophiecentaur]

It's a good idea to define the variables in an equation. Not everyone uses the same 'conventions'.

 

[Bandersnatch]

how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1)

Since $\frac{da}{dt}=\dot a$
and $\frac{a}{a}=1$
You have $\frac{da}{dt} \Delta x$ multiplied by 1 to net you $\frac{\dot a}{a}a\Delta x$.

If it still doesn't click, Leonard Susskind derives this here in a slightly different, but essentially the same manner:

(starting at 21:22 mark)