William Herschel (1738-1822), music master at Bath, surveyed the heavens for whatever he could find. On March 13, 1781, while he was sweeping the heavens with a reflector not even as large as ours, Herschel came across an object with a disk-like appearance, which he thought might be a comet. About a year later it was established that the new object was in a nearly circular orbit far beyond the planet Saturn, at about 19.2 AU. The new planet was eventually named Uranus, a name suggested by Bode, who had popularized a strange sequence of numbers discovered by Titius. To construct this sequence proceed as follows:
| .0 | .3 | .6 | 1.2 | 2.4 | 4.8 | 9.6 | 19.2 |
| .4 | .4 | .4 | .4 | .4 | .4 | .4 | .4 |
| .4 | .7 | 1.0 | 1.6 | 2.8 | 5.2 | 10.0 | 19.6 |
Compare these numbers with the radii of the planetary orbits in AU:
| .39 | .72 | 1.00 | 1.52 | ? | 5.20 | 9.54 | 19.20 |
During the 2nd quarter of the 19th century small discrepancies were noted in the elliptical path of Uranus. These variations could not be accounted for as a result of the influence of the known planets. Hence a suspicion grew that some unknown planet was perturbing the orbit of Uranus. Independently Adams and Leverrier calculated the probable location of the hypothetical planet, assuming it would be at the distance which the Titius-Bode law suggested; namely, 38.8 AU.
The British astronomers didn't take the prediction of Adams seriously, but the Berlin observatory looked carefully for the unknown object at the position suggested by Leverrier, and almost immediately located it on September 23, 1846. However, the actual radius of Neptune's orbit was later found to be 30.07 AU, quite far from the Titius-Bode value.
Only one more planet was ever discovered, the planet Pluto. It was discovered in 1930 in an unusual orbit of mean radius 39.5 AU which is tilted quite far out of the ecliptic plane.
Much effort was expended in the futile search for a hypothetical planet Vulcan closer to the Sun than Mercury. There was a tiny discrepancy in the orbit of Mercury which could not be accounted for on the basis of the interaction with known planets.
The explanation of this apparent discrepancy came in 1916 when Einstein showed that Newton's theory is not quite correct when applied to an object as close to the Sun as Mercury. For most purposes, however, it is unnecessary to employ Einstein's general theory of relativity. Newton's theory of gravitation works quite well.
It takes light about 10 1/2 hours to cross the entire solar system. While this represents a vast distance, it is a small distance compared to the distance to the nearest star other than the Sun, from which the light takes over 4 years to make the journey. This vast distance is in turn small compared to the distance 105 light years across the galaxy of stars comprising the Milky Way, or the distance 2 x 106 light years between our galaxy and the Andromeda galaxy. Finally, this vast distance is small compared to the overall dimensions of the universe itself, about 1010 light years. How do you suppose that this picture of the vastness of the universe was pieced together?
The music master Herschel did things in a big way, constructing big organs and big telescopes. He received a government grant for the construction of a 48 inch reflecting telescope, with which he surveyed the heavens, discovering many interesting nebulae.
Concerning these nebulae J. H. Lambert had the prophetic idea that all the stars in the Milky Way constitute one large cluster in motion about its center, and that the nebulae seen by Herschel are other galaxies of stars located outside the Milky Way galaxy. This view was not generally accepted until the 1920's, about 150 years later. The reason was the apparent avoidance by nebulae of the galactic plane, which suggested that they are associated with the Milky Way. Actually, we know today that some of the nebulae seen by Herschel are within the Milky Way system, while others are distant galaxies outside the Milky Way. Furthermore, the reason we do not see more nebulae near the galactic plane is that there is a great deal of light-absorbing dust within our galaxy.
Unfortunately, during the 18th century such ideas as these could be nothing but unprovable speculations. It was necessary to learn more about light, its emission and absorption, before solid evidence could be obtained.
Nevertheless, during the early 19th century it was possible to reach out to stars in the immediate neighborhood of the Sun. Herschel observed many binary stars such as Castor, the brightest star in the constellation Gemini. Comparison of the positions with those recorded earlier by Bradley led Herschel to conclude that these are actually stars rotating about one another, indicating that Newton's theory of gravitation applies universally.
The systematic study of binary stars was initiated by F. W. Struve, who found binary stars to be quite common. Such systems are invaluable because they permit us to learn the masses of some distant stars, through the application of Kepler's 3rd law. However, we shall first have to discuss how the distances to stars are inferred, since we need that information to figure out the actual size of the orbit of a binary star from its apparent angular size as viewed from the earth.
The first stellar distance was measured by F. W. Bessel in the year 1838 using a device called the heliometer, a telescope with a split objective. By tilting the one half of the split objective relative to the other half, double images could be produced. The tilt is arranged so that the image of the object to be recorded coincides with some reference image. The angle between the two celestial objects can then be read off. Over a period of time the measured angle will change if the object being studied is relatively close to us, for the earth moves back and forth over a distance of 2 AU. Of course, this parallax method is applicable to relatively few stars, perhaps 6,000 in all. However, only the nearest 700 have been located to a 10% accuracy.
After the development of photography the heliometer gave way to the comparison of photographic plates taken 6 months apart.