How does the movement of stars compare to the movement of planets

Not sure what you mean.
If you mean the apparent position ( where they ae in the sky) stars don't move very much - they are so far away that they appear stationary.
The planets are moving around the sun, they are much closer than the stars and so move accross them.

 

Oddly enough, most stars in the galaxy however near or far from the center are moving at 210-240 km/s relative to the center. The Earth moves at just under 30 km/s relative to the Sun, while Mercury moves at 48 km/s. And just for good measure, the Andromeda galaxy is heading at us at 118 km/s (radial velocity), but the tangential velocity is a little bit uncertain. (see https://www.physicsforums.com/archive/index.php/t-64107.html). Oh, and the speed of light is as always 300,000 km/s.

 

To quote the famous cosmologist Eric Idle:

The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at forty thousand miles an hour,
Of the galaxy we call the "Milky Way".

That's why I said 'apparent motion'

 

No. stars doesn't rotate just like planets do. normally planets revolve around stars instead.

 

Stars rotate just like planets - the sun's day is 609 hours or 25 earth days long.
The sun ( and all the planets around it ) orbits the centre of our galaxy, taking around 250 million years an orbit.
Then our galaxy including all the stars and planets in it are moving in the local group of galaixies at even higher velocities.

 

In just terms of casual observation the planets move daily while the stars appear fixed in place. Several 'near by' stars do move quickly enough to be noticed with careful observation. A couple of the fastest movers are Arcturus and Barnard's Star.

 

One more note about the difference between the apparent position of stars vs. planets is that a planet can appear to change the direction it's going and then go backwards and then forwards again. As far as I know a star can't do this, except for maybe the tiny wobble of a binary star which wouln't have been observed by the naked eye.

 

So your point would be?

 

What causes the local group to move? I mean, in a galaxy there's a black hole in the center that causes the stars to orbit around it, but in a cluster of galaxies, is there anything that can cause them to move so fast?

 

Actually, the seasonal movement of the Earth around the Sun causes nearby stars to shift apparent position. This is called parallax, and it is the only direct means of measuring the distance to objects outside our solar system. This indeed makes the apparent positions of nearby stars wobble back and forth, though the variations are small and require careful observation and measurement.

 

Yes, each galaxy exerts gravitational force on every other galaxy in the local group, just like the supermassive black hole in the center of our own galaxy that causes the stars to orbit around it. Also, a cluster of galaxies can be gravitationally attracted to other galaxy clusters, which causes it to move across space if space isn't expanding too fast.

 

Ok thanks for clarifying. Haha I was under the impression that the galaxies didn't move...