Page:Astronomy for Everybody.djvu/180

of the planets from the sun are proportional to the squares of their times of revolution. This law requires some illustration. Suppose one planet to be four times as far from the sun as another. It will then be eight times as long going around it. This number is reached by taking the cube of four, which is sixty-four, and then extracting the square root, which is eight.

The unit of measure which the astronomer uses to express distances in the solar system being the mean distance of the earth from the sun, it follows that the mean distances of the inferior planets will be decimal fractions, as we have just shown, while those of the outer ones will vary from 1.5 in the case of Mars to 30 in the case of Neptune. If we take the cubes of all these distances and extract their square roots we shall have the times of the revolution of the planets, expressed in years.

It will be seen that the outer planets are longer in getting around their orbits, not only because they have farther to go, but because they actually move more slowly. If, as in the case first supposed, the outer planet is four times as far from the sun, it will move only half as fast. This is why it takes eight times as long to get around. The speed of the earth in its orbit is about 18.6 miles per second. But that of Neptune is only about 3.5 miles per second, although it has thirty times as far to go. This is why it takes more than one hundred and sixty years to complete a revolution.