Fig. 85.—The outer planets.

134. Distances of the planets from the sun.—It is a comparatively simple matter to observe these planets year after year as they move among the stars, and to find from these observations how long each one of them requires to make its circuit around the sun—that is, its periodic time, T, which figures in Kepler's Third Law, and when these periodic times have been ascertained, to use them in connection with that law to determine the mean distance of each planet from the sun. Thus, Jupiter requires 4,333 days to move completely around its orbit; and comparing this with the periodic time and mean distance of the earth we find—

a3 / (4333)2 = (93,000,000)3 / (365.25)2,

which when solved gives as the mean distance of Jupiter from the sun, 483,730,000 miles, or 5.20 times as distant as the earth. If we make a similar computation for each planet, we shall find that their distances from the sun show a remarkable agreement with an artificial series of numbers called Bode's law. We write down the numbers contained in the first line of figures below, each of which, after the second, is obtained by doubling the preceding one, add 4 to each number and point off one place of decimals; the resulting number is (approximately) the distance of the corresponding planet from the sun.

0.40.71.01.62.85.210.019.638.8
0.40.71.01.52.85.29.519.230.1
Mercury.Venus.Earth.Mars.Jupiter.Saturn.Uranus.Neptune.
03612244896192384
444444444

The last line of figures shows the real distance of the planet as determined from Kepler's law, the earth's mean distance from the sun being taken as the unit for this purpose. With exception of Neptune, the agreement between Bode's law and the true distances is very striking, but most remarkable is the presence in the series of a number, 2.8, with no planet corresponding to it. This led astronomers at the time Bode published the law, something more than a century ago, to give new heed to a suggestion made long before by Kepler, that there might be an unknown planet moving between the orbits of Mars and Jupiter, and a number of them agreed to search for such a planet, each in a part of the sky assigned him for that purpose. But they were anticipated by Piazzi, an Italian, who found the new planet, by accident, on the first day of the nineteenth century, moving at a distance from the sun represented by the number 2.77.

This planet was the first of the asteroids, and in the century that has elapsed hundreds of them have been discovered, while at the present time no year passes by without several more being added to the number. While some of these are nearer to the sun than is the first one discovered, and others are farther from it, their average distance is fairly represented by the number 2.8.

Why Bode's law should hold true, or even so nearly true as it does, is an unexplained riddle, and many astronomers are inclined to call it no law at all, but only a chance coincidence—an illustration of the "inherent capacity of figures to be juggled with"; but if so, it is passing strange that it should represent the distance of the asteroids and of Uranus, which was also an undiscovered planet at the time the law was published.