Planets and Asteroids

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The planet mars is a member of the solar system; that is to say, it is one of the bodies which revolve in orbits about the Sun. During the early years of the 17th century, when Kepler's views of a Sun-centered system were beginning to find acceptance, six planets were known. In order of increasing distance from the Sun, they were Mercury, Venus, Earth, Mars, Jupiter, and Saturn.

These bodies are all visible, at appropriate times, by the unaided eye. In spite of the development of the telescope, they remained the only known planets until 1781. In that year, however, William Herschel identified the planet Uranus, beyond Saturn. Herschel's discovery was made by careful observation of the skies, but the two remaining planets Neptune and Pluto were discovered, in 1846 and 1930, respectively, as a result of mathematical calculations of the perturbations of the orbit of Uranus.

In addition to the nine planets, the solar system contains a group of small bodies, known as asteroids or planetoids, which also orbit around the Sun. More than 30 000 of these bodies, with diameters ranging from 760 kilometers (470 miles) down to a few kilometers (1 or 2 miles), have been observed in the telescope. The orbits of some 1600 of the asteroids have been determined, and the majority are found to lie between the orbits of Mars and Jupiter. This region has therefore become known as the asteroid belt.

A comparison of the orbits of the planets shows that there is an exceptionally large gap between Mars and Jupiter (fig. 3.1). In fact, Kepler had suggested that a previously unknown planet might be found in this region of the solar system. This conclusion appeared to find support from a rule based on the work of the German astronomer J. D. Titius, but brought to public notice by his fellow countryman J. E. Bode in 1771. By this rule, the distances of the successive planets from the Sun, in terms of the distance of Earth from the Sun, could be represented by adding 0.4 to each of the following series of numbers: 0, 0.3, 0.6, 1.2, 2.4, 4.8, and 9.6. Apart from the zero, these numbers

FIGURE 3.1. The solar system showing planetary orbits.

FIGURE 3.1. The solar system showing planetary orbits.

form a simple geometric progression, in which the ratio of successive terms is two.

Bode's rule, sometimes inappropriately called Bode's law, was found to correlate the distances of the six planets known before 1781, except that there was no planet with a distance corresponding to the number 2.4. Such a distance would lie between the orbits of Mars and Jupiter. When Uranus was discovered and its orbit determined, its distance from the Sun was found to agree with Bode's rule, using the next number in the geometrical series; namely, 19.2. Consequently, it appeared that there should be a planet between Mars and Jupiter, and at the end of the 18th century a group of astronomers made plans to look for this missing planet.

Before a systematic search began, however, the first asteroid was discovered by an Italian, Giuseppe Piazzi, in 1801. He observed a small object moving against the background of fixed stars and thought it might be a comet. But the famous German mathematician Karl F. Gauss calculated its orbit and showed that it was similar to the orbits of the planets. The average distance from the Sun of this new member of the solar system, which was called Ceres, appeared to be in good agreement with that required for the missing member, 2.4, of the Bode series.

For a time, it was thought that Ceres, with its orbit between those of Mars and Jupiter, was the missing planet. But by 1807, three other similar bodies had been found with orbits in the same general region. No further asteroids were observed until 1845 when a fifth was added, and subsequently the number has increased steadily almost from year to year. The smallest observable asteroids have diameters of a few kilometers, but there is little doubt that there are many more of smaller size which have not been detected. These very small members of the solar system, which are relatively easily deflected from their orbits by collisions, have probably played a role in shaping the surface of Mars (p. 131).

The asteroids may have resulted from the disruption or explosion, perhaps in the early stages of development of the solar system, of a planet between Mars and Jupiter. It is possible, on the other hand, that the considerable mass of Jupiter, the largest and most massive of the planets, may have prevented the formation of a single planet by accumulation of material in the nebular cloud from which the solar system evolved. Many small planetoids would then have formed instead.

Elliptical Orbits

Kepler's contention that the orbits of the planets (and asteroids) are elliptical has been confirmed. Although there are important minor deviations (or perturbations), they can be ignored here. It will be recalled from chapter II that the characteristic of an ellipse is that it has two focal points (or foci) ; the sum of the distances from any point on the ellipse to the two foci is the same for all points on the ellipse. The line XY passing through the foci F± and F2 in figure 3.2 is called the major axis of the ellipse. It can be easily shown that the constant sum of the distances to the two foci mentioned above is equal to the length of the major axis.

Consider, for example, the point X; this is a point on the ellipse and the distances to the foci are XF2 and XF1. The foci are located symmetrically within the ellipse; consequently, the distance XF1 is equal to F2Y. Hence the sum of the distances from X (or Y) to the two foci is XF2+F2Y, which is equal to the length XY, the major axis of the ellipse. By definition, the sum of the distances from any point on the ellipse to the two foci is always the same; hence, this sum is equal to the length of the major axis.

Another important property of an ellipse is known as the eccentricity. It provides an indication of the departure of the shape from that of a circle. If O in figure 3.2 is the midpoint of the major axis of the ellipse, then XO, which is half the length of the major axis, is called the semimajor axis. The eccentricity of the ellipse is defined by

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