Telescopes
Galileo's telescope was crudely created out of two, small glass lenses. A telescope made from lenses is called a refractor. The lenses are separated by the sum of their focal lengths and the eyepiece has a small focal length and the objective lens has a long focal length. Today, most telescopes are built using large mirrors because they are much lighter, cheaper, and more durable than glass (aside from other problems). The most common telescope is a Cassegrain telescope that uses two mirrors and an eyepiece as shown in the diagram below.
During every tour at an astronomical observatory, patrons always ask the magnification of the largest telescope. Astronomer always shudder at such a questions because magnification isn't why astronomers build large telescopes; rather, astronomers use big telescopes because they are often studying very faint objects. To observe a dim object such as a galaxy or a nebula, astronomers need to gather as much light from the object as possible and bring it to a focus. Telescopes are used to gather light; astronomers describe telescopes in terms of their diameter and light gathering power (LGP) rather than magnification power. Astronomers that study planets do appreciate magnification and it varies greatly depending on the eyepiece used in the telescope. In general, magnification is the objective focal length divided by the eyepiece focal length. The smaller the eyepiece focal length, the higher the magnification and the smaller the field of view seen.
Spectroscopy
Astronomer's do not have the ability to visit a star's surface to find out its composition. In fact, the only data that astronomers have is the light that we receive. Fortunately, light carries a large amount of information with it. The study of light information is called spectroscopy. Scientists are able to decode information carried by the light by splitting light into a rainbow or a spectrum. When atoms become electrically charged or heated, light is emitted as electrons change their energy levels. By splitting starlight using a prism or a spectroscope, it turns out that every element has its own individual and characteristic spectrum. A careful analysis of a star's spectrum reveals many important characteristics including temperature, composition, motion, and magnetic fields. This information would be impossible to ascertain if it were not for spectroscopic techniques.
Cosmology
Every culture has a cosmogony, a theory of where the universe came from. Science also has a cosmogony, one that is based on data and observations. This cosmogony that most scientists accept in one form or another, is called the Big Bang. This Big Bang Theory is the result of several observations. First, Edwin Hubble observed in 1927 that galaxies are red shifted; galaxies are becoming farther and farther away from us. Second, he determined that the farther away a galaxy is, the faster it is receding. If the universe is expanding, then one must assume that the galaxies that compose our universe were once much closer together than they are now. By simply measuring how far apart galaxies are and how fast they are moving, we determine what cosmologists call the Hubble Constant (which likely ranges from 50 to 100). IF we run the expansion process backward we get two results. First result is that it probably took on the order of 15 billion years for the Universe to grow to its present size. Second, some awesome event must have caused the galaxies to go flying away from one another. No one knows what exactly this phenomena could have been, but astronomers refer to it as the Big Bang. Recently, astronomers hypothesized that there would be some residual radiation left over from such an event in the cold of deep space. This radiation was observed by the COBE satellite in 1991 to further the amount of evidence that suggests there was a such an event some 15 billion years ago.