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when you take such a given galaxy and it is said that you are moving away from us with a speed $v$, what do you mean really? Let me explain: is the galaxy itself which has an intrinsic velocity of recession , or the galaxy is at rest (sorry for the forcing), but is that the whole universe is expanding (see the famous example of the balloon that is inflated ) and then we see the Milky Way Galaxy get away with speed ( boh ) of 20,000 km / s? Or these 20,000 km / s are the combined action of both ( ie that the Universe is expanding and an actual speed of removal of the galaxy ) ..

Always referring to the example of a separation speed of 20,000 km / s , and pretending that someone has already replied saying that this speed is due solely to the expansion of the Universe , I can say that the 20,000 km / s are due to the sum of 10,000 km / s + 10,000 km / s speed of removal of Milky Way Galaxy and that I'm looking at a point equidistant between the two galaxies ?

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  • $\begingroup$ The separation speed depends on the distance of a galaxy. The real expension should be explained in terms of "speed per lightyear", so that a lightyear expands by such meters per year. Two lightyears expand by twice this amount per year... I hope I didn't make this too confusing! $\endgroup$ – PhilMacKay Mar 19 '14 at 19:52
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Basically, your idea that "...the combined action of both (i.e. that the Universe is expanding and an actual speed of removal of the galaxy)." is correct. The one due to expansion might be called "comoving velocity" while the one due to the "actual" motion of the galaxy through the expanding universe is usually called the "peculiar velocity".

The observed difference in velocity between two galaxies has two components, one is the comoving velocity (due to the expansion of space) and the other is the "peculiar velocity", which is the velocity due to motion distinct from the expansion. This is pretty easy to define mathematically. If we take a coordinate system that expands at the same rate as the universe, and call the radial coordinate $\chi$ ("comoving coordinates"), then the radial coordinate in the expanding universe $r$ ("proper coordinates") is related to the comoving coordinate by the scale factor $a(t)$, which describes the size of the relative size of the universe as a function of time (so if $a(t_1)=0.5$ and $a(t_2)=1.0$ the universe is twice as large at $t_2$ than it was at $t_1$).

$$r(t)=a(t)\chi(t)$$

The "proper velocity" (e.g. the example measurements you give in your question) is, intuitively, $\dot{r}=\frac{dr}{dt}$. This breaks down into two components:

$$\dot{r} = a\dot{\chi}+\dot{a}\chi = v_\mathrm{peculiar} + v_\mathrm{comoving}$$

A galaxy will have some peculiar velocity due to its $\dot{\chi}$, and all galaxies have (sort of) random peculiar velocities which lie in some typical range. So as you look further away (bigger $\chi$), the comoving velocity begins to dominate over the comoving velocity ($\dot{\chi}$ is the same everywhere, within some scatter).

You can measure velocities relative to any reference point you choose, it is completely equivalent to say one galaxy is moving away from another at $2000\;\mathrm{km}/\mathrm{s}$ or that they are both moving away from some central point at $1000\;\mathrm{km}/\mathrm{s}$ in opposite directions. In practice we usually measure everything from our vantage point, at rest with respect to the Milky Way (the motion of the Earth around the Sun and the Sun around the galaxy are known and usually corrected for).

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