In Chapter 1 we introduced the foundations of Newtonian gravity, and presented the equations that govern the gravitational potential of spherical and nearly spherical bodies. We also examined the center-of-mass motion of extended bodies, and witnessed the remarkable near-decoupling of the external dynamics – the motion of each body as a whole – from the internal dynamics – the internal fluid motions within each body. As we saw in Chapter 1, the details of internal structure, encapsulated in multipole moments of the mass distribution, have a limited influence on the motion of the body as a whole. In this chapter we take the focus away from the external dynamics and examine the internal structure and dynamics of extended, self-gravitating bodies. We shall return to the theme of the near-decoupling of the external and internal dynamics, and reveal the limited influence of the center-of-mass motion and the external bodies on the structure of a selected body.

We begin in Sec. 2.1 with a review of the equations of fluid mechanics that are relevant to the internal dynamics; these are best formulated in the moving reference frame of a selected body A in an N-body system. In Sec. 2.2 we examine the simplest models of internal structure, involving spherical symmetry, assuming that the body is non-rotating and not influenced by external bodies.