Mass is clearly a physically important parameter for a star, as it will determine the strength of the gravity that tries to pull the star’s matter together. We discuss one basic way we can determine mass, from orbits of stars in stellar binaries, and see the range of stellar masses. This leads us to the virial theorem, which describes a stably bound gravitational system.

We conclude our discussion of stellar properties by considering ways to infer the rotation of stars. All stars rotate, but in cool, low-mass stars like the Sun the rotation is quite slow. In hotter, more-massive stars, the rotation can be more rapid, with some cases (e.g., the Berillium stars) near the "critical" rotation speed at the star’s surface.

This chapter considers stellar ages. Just how old are stars like the Sun? What provides the energy that keeps them shining? And what will happen to them as they exhaust various available energy sources? We show that the ages and lifetimes of stars like the Sun are set by long nuclear burning timescales and the implications that high-mass stars should have much shorter lifetimes than low-mass stars.

The timescale analyses in Chapter 8 show that nuclear fusion provides a long-lasting energy source that we can associate with main sequence stars in the H-R diagram. This chapter addresses the following questions: What are the requirements for H to He fusion to occur in the stellar core? And how is this to be related to the luminosity vs. surface temperature scaling for main sequence stars? In particular, how might this determine the relation between mass and radius? What does it imply about the lower mass limit for stars to undergo hydrogen fusion?

Much as stars within galaxies tend to form within stellar clusters, the galaxies in the universe also tend to collect in groups, clusters, or even in a greater hierarchy of clusters of clusters, known as "super-clusters." Plots of galaxy positions versus redshift distance reveal the large-scale structure of the universe as a "cosmic web," with galaxies lying along extended, thin "walls" and densely clustered intersections, surrounded by huge voids with few or no galaxies in between.

Observations of binary systems indicate that main sequence stars follow an empirical mass-luminosity relation L ~ M^3. The physical basis for this can be understood by considering the two basic relations of stellar structure, namely hydrostatic equilibrium and radiative diffusion. In practice, the transport of energy from the stellar interior toward the surface sometimes occurs through convection instead of radiative diffusion; this has important consequences for stellar structure and thus for the scaling of luminosity.

We walk through the different epochs and eras of the universe, going forward in time from the Hot Big Bang. In the earliest universe, radiation (photons) dominated over matter. As the universe cools, electrons are able to recombine with protons, then helium and other light elements were formed in the first few minutes. Cosmic inflation is posited to overcome several problems, but investigations to probe and perhaps confirm inflation are ongoing.

In our everyday experience, there is another way we sometimes infer distance, namely by the change in apparent brightness for objects that emit their own light, with some known power or luminosity. For example, a hundred watt light bulb at close distance appears a lot brighter than the same bulb from far away. Similarly, for a star, what we observe as apparent brightness is really a measure of the flux of light, i.e. energy emitted per unit time per unit area.

Radiation generated in the deep interior of a star undergoes a diffusion between multiple encounters with the stellar material before it can escape freely into space from the stellar surface. We define the optical depth by the number of mean free paths a photon takes from the center to the surface. This picture of photons undergoing a random walk through the stellar interior can be formalized in terms of a di usion model for radiation transport in the interior.

Compared to stars, the region between them, called the interstellar medium or "ISM," is very low density; but it is not a completely empty vacuum. A key theme in this chapter is that stars are themselves formed out of this ISM material through gravitational contraction, making for a star-gas-star cycle. We explore the characteristics of cold and warm regions of the ISM and their roles in star formation.

Hubble’s law gives us the simple and obvious interpretation that we currently live in an expanding universe. The inverse of Hubble’s constant defines the "Hubble time" which effectively marks the time in the past since the expansion began. more realistically, one would expect the universe expansion to be slowed by the persistent inward pull of gravity from its matter. We consider how various theoretical models for the universe connect with the observable redshift that indicates its expansion.