Compared to the size of the Solar system, about ten light hours across, the nearest star is quite far, about four light years away. It is mind-boggling to contemplate the size of the Milky Way galaxy, some 1011 stars in a disk of diameter 105 light years. The entire history of the development of human civilization is dwarfed by the time it has taken for light to reach us from the most distant stars in our galaxy.
Perhaps we can put this all in perspective by imagining that the Sun is represented by a pea that is one-quarter of an inch in diameter. On this scale the Earth would be 2 1/2 mils in diameter and located about 4 1/2 feet from the pea. The solar system would extend out about 175 feet from the pea. On the other hand, a light year would be approximately 26 miles, the distance run by a marathon runner, and the nearest star would be represented by another pea 100 miles away. Except for interstellar dust and gas, the galaxy is largely empty space! In this model the entire galaxy would be represented by a dish 2 1/2 million miles in diameter with the pea Sun not too far from one of the edges of the dish. To picture the size of that dish, recall that the actual distance to the moon is one-quarter million miles.
Aside from the Magellanic clouds, which may be viewed in the southern hemisphere, the closest extragalactic bodies are some 2 million light years distant. Compared to the size of our galaxy, that's not all that far away. The most famous example is the Andromeda galaxy M31, which is believed to resemble our own Milky Way galaxy. Through the analysis of Cepheid variables in the nearby galaxies their distance can be inferred.
Suppose now that we shrink our dish galaxy so that it is represented by a quarter dollar, which is about one inch in diameter. The Andromeda galaxy would be represented by another quarter only twenty inches away. The galaxies are not very far from one another in terms of their own sizes! A sphere 2/3rds of a mile in diameter would be full of such quarters. This would be the entire universe!
In 1926 Edwin Hubble classified 600 galaxies as elliptical, spiral, barred spiral, or irregular. We shall begin by showing an elliptical galaxy near M31. These comprise about 20% of all galaxies, and are characterized by having little gas and dust from which new stars may form. In fact, elliptical galaxies contain no young stars such as blue giants. Consequently the ellipticals tend not to be very bright for their size.
The Milky Way and the Andromeda galaxy are examples of spiral galaxies, the most common type, comprising about 50% of all galaxies. Here are a few other examples of spiral galaxies characterized by various degrees of openness of the spiral arms.
Similar in appearance to the Sc spiral galaxies are the barred spiral galaxies, which comprise about 30% of all galaxies. The reason for the name is apparent from some photographs of such galaxies.
It is believed that galaxies formed before the stars of which they are now composed. The theory of formation of galaxies is even more speculative than the theory of the origin of stars from galactic gas, for no one has ever witnessed the birth of a galaxy.
Since all types of galaxies contain some very old stars, it is not possible to regard the different types as representing ages in the evolution of a galaxy. A theory must account for the different galactic types in some other way. A popular opinion now is that angular momentum distinguishes one galactic type from another, the spirals forming with more spin than the ellipticals.
A problem concerned with the spiral arms should be mentioned. If one thinks of the spiral arms as objects subject to the universal law of gravitation, then an open spiral (type Sc) should gradually wind up tighter, because the matter farther from the galactic center moves more slowly. Calculation shows that this winding up would change an Sc galaxy into an Sb galaxy in a short period of time, comparable to the rotation period (108 years). Too many Sc spirals are seen for this to be the case.
Consequently it is believed that the spiral arms are a "condition" of matter in the galaxy, representing an instability. However, the theory of such instability is very rudimentary.
It was Hubble who first observed that in general the Doppler shift of light from other galaxies increases as the distance to the galaxy increases. If one plots recessional velocity as determined spectroscopically versus the distance determined by the observation of Cepheid variables, one gets a crude straight-line graph. The fit to a straight line improves significantly if one treats clusters of galaxies rather than individual galaxies. That galaxies tend to cluster into groups was discovered relatively recently. The Milky Way and Andromeda are two members of the Local Group.
The proportionality constant (Hubble constant) between recessional velocity and the distance is about 30 km/sec per million light years. The speed of light is 3 x 105 km/sec, so by the Hubble law a galaxy 10 billion light years distant should recede with the velocity of light. The red shift of such a galaxy would be infinite. Thus, ten billion light years away is truly the "horizon of our universe!"
Before the expansion of the universe was observed, it was predicted by the 1916 Einstein general theory of relativity. Later Einstein remarked that the greatest mistake he ever made was not to take this prediction seriously. Instead, he modified the theory, introducing the so-called cosmological constant. By the time Hubble established the law that bears his name, the idea of the cosmological constant became a permanent fixture in cosmological theory, much to the chagrin of Einstein.
These figures have all increased a bit since I first gave this course in 1974. I am now trying to acquaint myself with more recent discoveries and with current thinking with regard to cosmology.