Figure fragment: The daily rotation of the celestial sphere westward as seen from Earth reference frame

Figure: The daily rotation of the celestial sphere westward as seen from Earth reference frame

Caption: An animation of the Earth rotating eastward within the celestial sphere marked with lines of right ascension (RA) and declination (Dec or δ), the celestial equator, and the ecliptic.

Features:

The celestial sphere is not-to-scale.
It should be quasi-infinite compared to the Earth---but that is undrawable.
If one took the Earth as an at-rest reference frame as we do often in everyday life and as an observational perspective in astronomy, then the celestial sphere rotates westward as, in fact, we usually consider it to be doing.
Remote astronomical objects (that we project onto to the celestial sphere for location purposes) must have enormous rotation velocities RELATIVE to the at-rest Earth reference frame. At some point far enough from the Earth, those rotation velocities become superluminal. See the calculations below.
However, these enormous rotation velocities are geometrical velocities, NOT physical velocities, since NO information (which includes all forms of mass-energy) is propagating at faster than the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s ≅ 1 ft/ns RELATIVE to local inertial frames: "local" meaning at the place the information is at any time. So they do NOT violate special relativity. Recall, special relativity is based on an axiom that the vacuum light speed to be the highest physical velocity.
NO physical thing (such as a light signal) traveling in a local inertial frame can move at a superluminal velocity: i.e., NO physical velocity is superluminal.
Thus, superluminal geometrical velocities are NOT a violation of special relativity and they are very common as our example with the Earth reference frame and remote astronomical objects shows.
In fact, most of the remote astronomical objects with enormous rotation velocities RELATIVE to the at-rest Earth reference frame are moving at far, far less than the vacuum light speed relative to their local inertial frames.
To be specific to the case of the animation, rotation relative to the observable universe (i.e., to the bulk mass-energy of the observable universe) is considered absolute rotation in our modern understanding of cosmology. If a physical body with rest mass is rotating relative to the observable universe, every bit of it must be moving with a physical velocity (necessarily less than the vacuum light speed relative to a local inertial frame) and the body is just said to have a physical rotation. So the Earth rotates physically relative to the observable universe and NOT vice versa.
To illustrate the enormous geometrical velocities, in the at-rest Earth reference frame, note that rotation velocity
```
  v =  r * (2πf)  ,  
```
where r is radius perpendicular to the rotation axis and f is the frequency of rotation. For the at-rest Earth reference frame, f=1/( 86164.1 s) where 86164.1 s = 1 sidereal day. We have the special cases:
```
  v = 0.4651 km/s = 1.551*10**(-6) * c for r = 6378.1 km/s = Earth equatorial radius,
  v = 1.091*10**5 km/s = 0.03639 * c   for r= 1.495978707*10**8 km =
                                        1 astronomical unit,
  v = 7506 * c                         for r= 3.0856775814671900*10**13 km = 1 parsec.  
```

Credit and/or file tracking information follows to the divider line:

Image Credit/Permission: David Jeffery, 2003 / Own work, Public domain.
Image link: Itself.
Local file: local link: celestial_sphere_rotating.html.
Small image file: Celestial sphere file: celestial_sphere_rotating_2.html.
Stand-alone image file: Celestial sphere file: celestial_sphere_rotating_3.html.
File: Celestial sphere file: celestial_sphere_rotating.html.