There is a certain relation between two quantities which at first sight seems quite independent. These quantities are the mass of the earth and the distance of the sun. The distance of the sun bears to a certain distance (which can be calculated when we know the intensity of gravitation at the earth's surface, the size of the earth and the length of the year) the same proportion that the cube root of the sun's mass bears to the cube root of that of the earth. There is no uncertainty about this result, and the consequence is obvious. If we have the means of weighing the earth in comparison with the sun, then the distance of the sun can be immediately deduced. How are we to place our great earth in the weighing scales? This is the problem which Le Verrier has shown us how to solve, and he does so by invoking the aid of the planet Mars.
If Mars in his revolution around the sun were solely swayed by the attraction of the sun, he would, in accordance with the well-known laws of planetary motion, follow for ever the same elliptic path. At the end of one century, or even of many centuries, the shape, the size, and the position of that ellipse would remain unaltered. Fortunately for our present purpose, a disturbance in the orbit of Mars is produced by the earth. Although the mass of our globe is so much less than that of the sun, yet the earth is still large enough to exercise an appreciable attraction on Mars. The ellipse described by the planet is consequently not invariable. The shape of that ellipse and its position gradually change, so that the position of the planet depends to some extent upon the mass of the earth. The place in which the planet is found can be determined by observation; the place which the planet would have had if the earth were absent can be found by calculation. The difference between the two is due to the attraction of the earth, and, when it has been measured, the mass of the earth can be ascertained. The amount of displacement increases from one century to another, but as the rate of growth is small, ancient observations are necessary to enable the measures to be made with accuracy.
A remarkable occurrence which took place more than two centuries ago fortunately enables the place of Mars to be determined with great precision at that date. On the 1st of October, 1672, three independent observers witnessed the occultation of a star in Aquarius by the ruddy planet. The place of the star is known with accuracy, and hence we are provided with the means of indicating the exact point in the heavens occupied by Mars on the day in question. From this result, combined with the modern meridian observations, we learn that the displacement of Mars by the attraction of the earth has, in the lapse of two centuries, grown to about five minutes of arc (294 seconds). It has been maintained that this cannot be erroneous to the extent of more than a second, and hence it would follow that the earth's mass is determined to about one three-hundredth part of its amount. If no other error were present, this would give the sun's distance to about one nine-hundredth part.
Fig. 50.—Relative Sizes of Mars and the Earth.
Notwithstanding the intrinsic beauty of this method, and the very high auspices under which it has been introduced, it is, we think, at present hardly worthy of reliance in comparison with some of the other methods. As the displacement of Mars, due to the perturbing influence of the earth, goes on increasing continually, it will ultimately attain sufficient magnitude to give a very exact value of the earth's mass, and then this method will give us the distance of the sun with great precision. But interesting and beautiful though this method may be, we must as yet rather regard it as a striking confirmation of the law of gravitation than as affording an accurate means of measuring the sun's distance.
