Physics 110: Homework #11 Solutions

11.1

Matter is considered ``dark'' in astronomy if it is not as bright as a normal star, for example, and therefore not visible across vast distances of space. With the advent of the space program in the 60's and 70's, this definition had to be generalized as other wavelength bands became accessible to astronomers (such as the X-ray band) and we detected visible matter in these bands. Nevertheless, even considering emission from all wavebands, there is not enough luminous matter to explain many dynamical systems (like the rotation curves of galaxies and the motions of galaxies in clusters of galaxies). Baryonic matter is ordinary matter composed of protons and neutrons. (Technically, a baryon is a particle made from three quarks, which are a type of fundamental particle.) Nonbaryonic matter consists of all other kinds of matter including electrons and neutrinos, as well as more exotic particles like WIMPS that have not been discovered yet. Our bodies are made of protons, neutrons, and electrons. Virtually all of our mass comes from the protons and neutrons in the atoms we are made of, so we are therefore made of baryonic matter.

11.2

On the largest scales, redshift surveys of large numbers of galaxies reveal that clusters and superclusters are arranged in patterns of sheets that surround voids, within which few galaxies can be found. In general it has been found that the largest void seen is limited only by the size of the volume sampled by the redshift survey. The Great Wall is an immense sheet-like structure of galaxies measuring  Mpc in size.

11.3

The age of the Universe is inversely proportional to the Hubble constant, t = 1/H. The age of the Universe also depends on the mass density, , which is a measure of how much the Universe has decelerated. If is non-zero, then the Universe must have been expanding more rapidly in the past than it is now, implying that the age of the Universe should be less. If the Universe is critical, i.e., , then the age of the Universe is t = 2/3H.

11.4

Astronomers rejected the steady state theory because they found that the Universe changes with time. In addition, this theory did not have a good explanation for the origin of the cosmic microwave background radiation.

11.5

A flat universe is infinite, boundless, and has no center. A positively curved universe is finite, boundless, and also has no center.

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