Isaac Newton was fully aware of the fact that a prism could disperse a ray of light into its constituent colors. (Demonstrate) However, he never accepted Huygens's essentially correct wave theory of light. By the beginning of the 19th century, however, this phenomenon assumed an extremely important role in astronomy.
If sunlight is allowed to pass through a narrow slit and then a prism, the spectrum formed shows not only a continuous colorful spectrum but also dark lines superimposed thereon. What is the significance of such lines?
Each chemical element, when stimulated in an appropriate way, emits a characteristic bright line spectrum. Each bright line corresponds to a particular wavelength. Using a simple spectrometer these wavelengths can be determined. (Demonstrate the use of a student spectrometer and gas discharge tube.) Note that instead of a prism one may use a "diffraction grating" consisting of many closely spaced etched slits. (Demonstrate)
During the 19th century there was no understanding of the origin of the spectural lines, but it was recognized that each element has its own characteristic spectrum. By comparing laboratory spectra with the solar spectrum one could infer that certain elements must be found on the Sun.
Such studies were greatly facilitated by the introduction of photography about 1850. In 1868 N. Lockyer discovered in the spectrum of a solar prominence a line which he could not identify. This line he attributed to a new element which he named Helium after the Sun. Just before the turn of the century this elusive element was discovered on the earth by W. Ramsay. (Release Helium filled balloon.)
When the light of other stars is caused to pass through a prism or diffraction grating it is found that their spectra are not always similar to the spectrum of the Sun. During the 19th century astronomers began classifying stellar spectra. Today the classification system into which this has evolved is quite complex, so we shall oversimplify the picture.
The temperatures which we have associated with these spectral types are determined on the basis of 20th century atomic theory. These are the presumed temperatures of the photospheres of the stars. During the 19th century, of course, these surface temperatures were not known, because the processes of emission and absorption of light by atoms was not yet understood.
It should be noticed that the lines observed in stellar spectra are usually dark lines upon a continuous background. The continuous background is produced by electrons as they are scattered by atoms, while the dark lines are due to absorption of light of selected wavelengths in the cooler gas of the photosphere.
Modern quantum theory enables one to infer a great deal from spectra. However, one of the most important concepts in the analysis of stellar spectra was developed much earlier, toward the middle of the 19th century, by Doppler. (Demonstrate Doppler effect by swinging a small loudspeaker at the end of a wire.)
When there is relative motion of the source and the observer of light, the spectral lines undergo a shift similar to the shift in pitch of sound waves. The shift Dl in the wavelength is given approximately by Dl/l = v/c, where l is the wavelength, v is the velocity of separation, and c is the velocity of light. The shift is, therefore, a direct measure of the recessional velocity.
The Doppler effect has been used in many ways in astronomy. For example, through spectroscopy one knows that the rings of Saturn rotate about the planet, more slowly at the outer edge than at the inner edge. The rotation of the planet can also be confirmed in this way, corroborating the impression we get of the rotation of the surface features.
In the case of a spectroscopic binary star the appearance of the spectral lines is time-dependent. From the spectrum one can infer the period of the binary system accurately. Some spectroscopic binaries have periods measured in days! Two stars similar to our Sun would have to be only 3 million miles apart to revolve about one another in one day. Three million miles is not a very great distance considering the fact that the diameter of the Sun is about 3/4 million miles. Stars this close would have to be highly distorted spheroids!
From the spectrum of a binary star one can also infer the maximum velocities of approach and recession of the component stars. Of course, most of the time one does not know the tilt of the rotational plane of the binary system. Thus, one can only get a lower limit upon the actual velocities of the two stars.
From the known period and the lower limit on the velocity one can evaluate a lower limit to the separation of the two stars. Finally, a lower limit to the total mass of the binary system can be calculated using Kepler's 3rd law.
If the two stars are of comparable luminosity one can get separate velocity measurements for the two stars, and hence evaluate the mass ratio of the stars quite accurately. Thus, in such cases one can get lower limits upon the masses of the individual stars comprising the binary system.
In the case of eclipsing binaries we may infer that the plane of the orbit is such that we are viewing it edge on. In this case the actual masses of the constituent stars can sometimes be ascertained. From an analysis of the light curve of an eclipsing binary the radii of the individual stars and their relative surface brightnesses can also be calculated occasionally. The surface brightness, however, is directly related to the surface temperature, by a 20th century atomic physics law called the Stephan-Boltzmann law.
Thus the properties of distant stars may be inferred, providing they are members of binary systems. Among the thousands of eclipsing binaries only a couple dozen allow complete identification of all the important attributes of the constituent stars. Nevertheless, it is astounding that so much can be learned from a little light about objects which are so very far away.
No star is close enough to resolve its disk (except, of course, for the Sun). However, some stars are almost close enough to be resolved by the largest telescopes. The diameters of such stars have been ascertained using a device called the Michelson interferometer, which exploits the fact that light arriving at the telescope along two slightly different paths can be made to interfere with itself. The diameters of seven nearby stars have been determined in this way. The first was the red giant Betelgeuse, whose immense size was measured in 1920. (Physics Today, April 1974.)
More recently electronic techniques have been developed for correlating intensity data for light received at two separated telescopes. This approach is extremely common with radio telescopes, but has also been used with optical telescopes to determine the sizes of about 15 additional stars.
Many of the stars which have been successfully measured with interferometers are huge compared to the Sun, with diameters several hundred times greater. In spite of the tremendous size of these stars, it should be noted that they are not particularly massive. In fact, the most massive star ever identified has a mass equal to only 60 solar masses. Hence the average density of these giant stars is very low.
Actually, the detailed analysis of stellar structure indicates that most of the mass of these giant stars is concentrated in a small volume in the center, so the major portion of the body of the star is so tenuous that it is a better vacuum than has ever been made on earth.