How might you determine what part of a galaxy's redshift is caused by the galaxy's orbital motion about the center of mass of its cluster?

Homework problem
please help ><

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

You have to look at the red shifts of several galaxies in the cluster and find the average. If the cluster has one giant galaxy in the center [such as the Virgo cluster] you might count that as sitting still in the middle of the cluster and measure all the other galaxies red-shift against that one.

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So all I have to do is look at the other galaxies in the cluster and then compare to the one that I am looking right now?

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

How do they work out the Milky Way's rotation?

In fact, why do galaxies rotate?

For that matter, why does EVERYTHING rotate? - eg planets, stars, solar systems, galaxies, clusters, superclusters...the Universe?

Does the Universe rotate? Against what perspective does it rotate? How can something "rotate" amidst nothingness?

Sorry for thread-jumping, couldn't help myself!

The only word I can answer your question is gravitational force

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We come without a thing and gone without a thing. We need simple life. A cup of teas and a couple of meals per day, that is good enough. And this is my standard of living.

Everything rotates for the same reason as water rotates when running out of the bath. A non-rotating motion is unstable and all it takes is a slight nudge one way or the other to set it spinning. Like balancing a pencil on its point - it's possible but much more likely that it falls one way or the other. The only time things are likely to move in straight lines is when there aren't any other objects in the vicinity to perturb their movement.

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For each extended object, larger than a point, i.e., dust, moons, planets, stars, groups of stars, galaxies, groups of galaxies, etc., in a state of mutual attraction with its neighbors, there is a gravitational gradient because parts of the object will be closer to each center of net gravitational force than will other parts. The gravitational gradient produces a torque which will either cause each object to be ripped apart (in extreme gradients of black holes) or to rotate.

When considered at the level of the entire universe and assuming the big bang, I'm not sure what would give it non-zero angular momentum and since angular momentum is believed to be conserved, my wild guess is that the net rotation is zero. Then there's the problem of no center in the normal sense about which the universe could rotate; yet if one assumed the electric and magnetic fields generated by the plasma (of which most of the universe is constituted) could somehow cause huge chunks of the universe to rotate about some "local" center more rapidly than gravity of the chunk could constrain, that huge chunk of the universe would be observed to be expanding due to the centrifugal force and observers within the chunk would conclude that the universe is expanding whether or not there was a big bang.

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

In nature all objects will travel in a straight line unless they are influenced by unbalanced force(s). The fact that objects are in an orbit, circular or elliptical, is a result of the combination of forces of attraction between the orbiting object and other objects close enough to exert attractive forces. The direction and magnitude of the acceleration of the object is referred to as centripetal force which is perpendicular to the objects instantaneous velocity and in the direction of the center of its orbit.