Can we separate the "normal " velocities of a galaxy from its velocity from the expansion? why or why not?

Question

Can we separate the "normal " velocities of a galaxy from its velocity from the expansion? why or why not?

Answer 1

There actually is no velocity due to expansion, it is the rate of  expansion of space that causes the increasing separation.

Answer 2

Yes we can.  Velocity is a vector and vectors are additvie.  For example V = vu + vg; where V is the observed velocity wrt some convenient space-time coordinate, vu is a component, and vg is another component of the observed velocity.  

Let V1 = vu + vg1 be the observed velocity of galaxy 1

Let V2 = vu + vg2 be the observed velocity of galaxy 2

vu is the universal expansion velocity and it is the same everywhere in the known universe.

vg1 = V1 - vu and vg2 = V2 - vu, which are the respective velocities of the galaxies.  vu can also be measured as a red shift (discovered by Hubble) in the light coming from the horizon of the universe (14-15 billion ly away from us).  So we can solve for the galactic velocities through vector analysis.

It is noteworthy that the vg velocities are quite variable in direction and magnitude.  For example, some galaxies are headed for collisions with each other...the Milky Way is headed for a collision with Andromeda for example.  Other galaxies are pulling away from their neighbors.  

On the other hand, vu, the universal expansion is uniform throughout the known universe.  The model I like is of a balloon expanding with our galaxies and known universe on the surface of the balloon.  As the balloon gets bigger, the dots on the balloon (the galaxies) get farther and farther apart; not because they are moving (vg) but because the space between them is getting bigger (vu).

BTW: Space  does have a velocity...it is expanding at a rate over time.  In fact dS/dt = vu is the expansion velocity where dS is the change in spatial size (the surface of the balloon) and dt is the time interval to make that change.  When anything, including space, moves over time, that's velocity by definition.  In fact the rate of expansion is accelerating, which prompted the invention of dark energy to account for the force that causes that acceleration.