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Hierarchical structure is clearly visible in the Universe. The "observable universe" includes almost empty voids, between which lie large cosmic filaments. The filaments consist of galactic superclusters, organized from groups and clusters of galaxies of many different sizes and shapes. Depending on the galaxy's morphological type, a galaxy may have several structural components, including spiral arms, a halo, and a core. Galaxies can have satellites in the form of dwarf galaxies and globular star clusters. The constituent parts of galaxies, star clusters, and other smaller star systems (orbiting each other or a center of mass) are formed from stars. Planetary systems and small bodies such as asteroids, comets and objects in fragment disks are formed by accretion processes in the protoplanetary disk surrounding newborn stars.

If we depict this hierarchy very roughly and very schematically, it will look as shown in the figure (small bodies revolve around satellites, satellites around planets, planets around stars, etc.).

enter image description here

What determines the existence of this hierarchy and why on cosmological scales does rotational motion turn into translational motion towards the great attractor? I assume that the gravitational field on a wide range of scales (from planetary to cosmological) has many minima of gravitational potential. Potential minima are the most favorable state of the field, since in them the field energy is minimal. Thus, the gravitational field on a wide range of scales (from planetary to cosmological) has more than one ground state (that is, the state with minimum energy).

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No, gravitation has, as far as we know it, the same form on all scales. There is some nonlinearity when gravitation gets very strong due to general relativity, but this is not relevant for the hierarchy in this question. A system with bodies of masses $m_1, m_2, m_3, \ldots$ behaves the same as a system where you scale the masses to $sm_1, sm_2, sm_3, \ldots$ and rescale all distances by $s$. So it is not strange that systems on very different scales behave roughly the same.

Gravitational collapse occurs when some sort of dispersed mass can lose energy by radiating it away (or shed parts of itself carrying off energy). Dark matter halos appear unable to do this, and end up diffuse blobs. Normal matter can do it, and this is why galaxies and stars can do it. But when a large cloud of gas starts to collapse, the critical length scale that determines the size of the collapsing region also starts to change. This leads to Jeans fragmentation: the big cloud starts to collapse, but now the size scale in the denser cloud is smaller so parts of the cloud starts to collapse on their own, and so on.

Radiated energy, friction and other factors influence and limit this and set the size distribution of stars formed (which is relatively scale-free). Once fusion can start the collapse ends, and this also sets a scale for solar system bodies through the different accretion process they undergo. Here issues of gas, ice and rock availability determine the size distribution.

In short, there are different processes for placing small and medium satellites in orbit around planets (tidal interactions), planets around stars (accretion processes), stars around each other (fragmentation), stars in galaxies (gravitation from other stars and dark matter halos), galaxy clusters (dark matter halos) and supercluster (overall structure formation from initial baryon oscillations in the big bang). This is scale free, and the size distributions are pretty broad - with some cut-offs due to the limits of the above processes. But they are all shaped by angular momentum conservation and gravitation that makes stuff orbit other stuff.

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  • $\begingroup$ Still, I didn’t quite understand your answer. Yes, there are various physical effects that appear on different scales (I'm talking about radiation, friction, temperatures of matter in accretion disks). But are they the reason that the rotation of planets around a star and the rotation of galaxies around the center of a galaxy cluster is a manifestation of essentially the same central phenomenon that you mentioned - the conservation of angular momentum? $\endgroup$
    – dtn
    Dec 27, 2023 at 8:14

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