can i use heliocentric velocity as a rotation speed? In the research of the galaxies, does heliocentric velocity involves space's expanding velocity? and can i use heliocentric velocity by galaxy's rotation speed?
It's a little unclear what you're asking for, but...
&quot;Heliocentric velocity&quot; means measured radial velocity of an object relative to the Sun. (Which basically means relative to us, except you take out the variations due to the Earth's motion around the Sun.) For galaxies more distant than, say, the Local Group, the heliocentric velocity is the combination of a) the Sun's motion in our Galaxy; b) the local peculiar motion of our Galaxy; c) the local peculiar motion of the other galaxy; and d) the cosmic expansion of the universe (&quot;cosmological redshift&quot;). The first three never vary that much, but the fourth increases with distance, so for distant galaxies, it's (almost) all due to the cosmic expansion.
&quot;Rotation velocity&quot; for a galaxy generally means the speed of stars and gas clouds about the center of that galaxy; it is not one single number but a function of distance from the galaxy's center -- though in the outer parts of the galaxy it often settles to a nearly constant value, which may indeed be referred to as &quot;the&quot; rotation velocity.
The two have nothing to do with each other, though. For example, the rotation velocity in the outer part of M31 (the Andromeda Galaxy) is about 230 km/s, while its heliocentric velocity is about $-300$ km/s. If it were 100 megaparsecs away in the Coma Cluster, its heliocentric velocity would be something like 7000 km/s, but its rotation velocity would be the same.