Caption: A cartoon illustrating the hierarchy of celestial frames (CEFs) (called center-of-mass inertial frames in the cartoon) in the observable universe and an astrophysical rotating frame (attached, e.g., to a moon, planet or star). In our discussion below, we do NOT consider rotating frames. For those, see the Mechanics file: frame_rotating.html.

Features:

1. Celestial frames (CEFs) (which is a term invented by yours truly) are discussed at length in Mechanics file: frame_basics.html: Celestial Frames (CEFs). Implicit in that discussion is that there is a whole hierarchyhierarchy of them in observable universe.

   Note the term celestial frame can be used as a synonym for the system of astro-bodies for which the celestial frame is defined. Context as usual determines the meaning of celestial frame.

2. Celestial frames are, in fact, a way of dividing astro-bodies into systems that are useful (i.e., efficient) for analysis of their internal motions.

   So there is choice in defining celestial frames, but quite often the choice is obvious.

   When the internal gravitational forces of a system of astro-bodies are large relative to the external tidal forces caused by the external gravitational field, then the internal structure and motions are mostly independent of the external gravitational field. The external gravitational field always determines the motion of the center of mass of the system of astro-bodies.

   The ideal celestial frame is one where the external gravitational field is uniform over the celestial frame. In this case, the external gravitational field does NOT affect the internal motions at all. In particular, a perfectly uniform external gravitational field CANNOT change the total angular momentum of celestial frame about the center of mass (CM): i.e., the celestial frame has conservation of angular momentum.

   The ideal case actually virtually holds, for example, for most planetary systems and most multiple star systems. They are usually so small that the external gravitational field is close to be uniform over them, and thus tidal forces are negligible.

3. Now relatively strong tidal forces tend to tear apart identifiable systems of astro-bodies.

   So the ones that persist as identifiable systems (mostly because they are gravitationally bound) are those for which celestial frames are most useful for analysis.

4. So the hierarchy of celestial frames mostly consists of identiable gravitationally-bound systems: i.e., moons, moon systems, planets, planetary systems stars, multiple star systems, compact remnants, (white dwarfs, neutron stars, and black holes) star clusters, clouds of gas and cosmic dust, galaxies, galaxy groups (which are just very poor galaxy clusters in yours truly's opinion and won't be mentioned explicitly hereafter), galaxy clusters, etc. Gravitationally-unbound systems that can be treated as celestial frames (CEFs) are galaxy superclusters and comoving frames (see Mechanics file: frame_basics: Comoving Frames).

   Why do these systems of astro-bodies and NOT others?

   They are the most obvious systems of astro-bodies, and so the most obvious ones to analyze.

5. The goodness-for-analysis of relatively isolated celestial frames means you should NOT try to extend their application much beyond their actual size: i.e., beyond the physical extent of the systems of astro-bodies defining them. This is just a practical desideratum.

   If you need to analyze motions of astronomical objects outside of the celestial frame you are using, then you should probably use a larger celestial frame in the hierarchy of celestial frames that includes those astro-bodies.

   If you need to to deal with the observable universe as a whole, then you do NOT use celestial frames at all. You use cosmological model. The most standard of these are Friedmann equation models which are solutions for the Friedmann equation which is derived from general relativity plus simplifying cosmological assumptions.

6. The above discussion omits mention of the cosmological constant force as simplification. See Mechanics file: frame_basics.html: Cosmological Constant Qualification 2 for the qualifications needed by the cosmological constant force.

   Credit/Permission: © David Jeffery, 2021 / Own work.
   Image link: Itself.
   Local file: local link: frame_hierarchy_astro.html.
   Extended file: Mechanics file: frame_hierarchy_astro_4.html.
   File: Mechanics file: frame_hierarchy_astro.html.
   

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