Part II - Infinite inhomogeneous systems – galaxy clustering

Summary

And much harder it is to suppose all the particles in an infinite space should be so accurately poised one among another as to stand still in a perfect equilibrium. For I reckon this as hard as to make, not one needle only, but an infinite number of them (so many as there are particles in an infinite space) stand accurately poised upon their points.

Newton

Having introduced the basic descriptions of gravitational many-body physics, it is time to attend to some astronomical applications. Many basic processes still remain to be explored, but they are best introduced in their astrophysical contexts.

Occasionally in Part 1 I have mentioned that infinite homogeneous systems – indeed all homogeneous gravitational systems – are anomalies, idealizations which do not exist in nature. However convenient they may be for mathematical analyses they are too unstable to represent anything we see, except as a first approximation. Newton recognized this and described it qualitatively in his letter to Bentley. Jeans (see Section 15) formulated it quantitatively for a static universe. Important complications, and a new richness of results, occur in the expanding Universe. This is a fundamental problem, for it begins to describe how matter is distributed around us on the largest scales.