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

Caption: An image of the Earth at rest as the celestial sphere (marked with the north celestial pole (NCP), the south celestial pole (SCP), the celestial equator, Ursa Minor (AKA the Little Dipper) Polaris, and a small circle) rotates west once per day.

Further explication

  1. The celestial sphere is not-to-scale.

    It should be quasi-infinite compared to the Earth---but that is undrawable.

  2. If one took the (at-rest) Earth reference frame as a standard 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.

  3. Remote astronomical objects (that we project onto to the celestial sphere for location purposes) must have enormous rotation velocities RELATIVE to the Earth reference frame. At some point far enough from the Earth, those rotation velocities become superluminal. See the calculations below.

    In fact, if the universe is infinite, there is NO upper limit on the rotation velocities.

  4. However, these enormous rotation velocities are geometrical velocities, NOT physical velocities with "physical" having the special meaning of velocity relative to a local inertial frame. It is an axiom special relativity that the upper limit on physical velocities is the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s ≅ 1 ft/ns.

    To emphasize, the enormous geometrical velocities transmit NO information faster the vacuum light relative any local inertial frame.

  5. 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.

  6. In fact, most of the remote astronomical objects with enormous rotation velocities RELATIVE to the Earth reference frame are moving at far, far less than the vacuum light speed relative to their local inertial frames.

  7. To be specific to the case of the image, 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.

  8. To illustrate the enormous geometrical velocities, in the 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 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.