The distance of the Sun from the Earth is often spoken of as the “astronomical unit”; it is the fundamental measure of astronomy, and all our information as to the sizes and distances of the various planets rests upon it. And, as we shall shortly see, the particular problem with which we are engaged—the habitability of worlds—is directly connected with these two factors: the size of the world in question, and its distance from the Sun.
The distance of the Sun has been determined by several different methods the principles of which do not concern us here, but they agree in giving the mean distance of the Sun as a little less than 93,000,000 miles; that is to say, it would require 11,720 worlds as large as our own to be put side by side in order to bridge the chasm between the two. Or a traveller going round the Earth at its equator would have to repeat the journey 3730 times before he had traversed a space equal to the Sun’s distance.
But knowing the Sun’s distance, we are able to deduce its actual diameter, its superficial extent, and its volume, for its apparent diameter can readily be measured. Its actual diameter then comes out as 866,400 miles, or 109·4 times that of the Earth. Its surface exceeds that of the Earth 11,970 times; its volume, 1,310,000 times.
But the weight of the Sun is known as well as its size; this follows as a consequence of gravitation. For the planets move in orbits under the influence of the Sun’s attraction; the dimensions of their orbits are known, and the times taken in describing them; the amount of the attractive force therefore is also known, that is to say, the mass of the Sun. This is 332,000 times the mass of the Earth; and as the latter has been determined as equal to about
6,000,000,000,000,000,000,000 tons
that of the Sun would be equal to
2,000,000,000,000,000,000,000,000,000 tons.
It will be seen that the proportion of the volume of the Sun to that of the Earth is greater than the proportion of its mass to the Earth’s mass—almost exactly four times greater; so that the mean density of the Sun can be only one-fourth that of the Earth. Yet, if we calculate the force of gravity at the surfaces of both Sun and Earth, we find that the Sun has a great preponderance. Its mass is 332,000 times that of the Earth, but to compare it with the attraction of the Earth’s surface we must divide by (109·4)2, since the distance of the Sun’s centre from its surface is 109·4 times as great as the corresponding distance in the case of the Earth, and the force of gravity diminishes as the square of the increased distance. This gives the force of gravity at the solar surface as 27·65 times its power at the surface of the Earth, so that a body weighing one ton here would weigh 27 tons 13 cwt. if it were taken to the Sun.[8]
This relation is one of great importance when we realize that the pressure of the Earth’s atmosphere is 14·7 lb. on the square inch at the sea level; that is to say, if we could take a column of air one square inch in section, extending from the surface of the Earth upwards to the very limit of the atmosphere, we should find that it would have this weight. If we construct a water barometer, the column of water required to balance the atmosphere must be 34 feet high, while the height of the column of mercury in a mercurial barometer is 30 inches high, for the weight of 30 cubic inches of mercury or of 408 cubic inches of water (34 × 12 = 408) is 14·7 lb.
If, now, we ascend a mountain, carrying a mercurial barometer with us we should find that it would fall about one inch for the first 900 feet of our ascent; that is to say, we should have left one-thirtieth of the atmosphere below us by ascending 900 feet. As we went up higher we should find that we should have to climb more than 900 feet further in order that the barometer might fall another inch; and each successive inch, as we went upward, would mean a longer climb. At the height of 2760 feet the barometer would have fallen three inches; we should have passed through one-tenth of the atmosphere. At the height of 5800 feet, we should have passed through one-fifth of the atmosphere, the barometer would have dropped six inches; and so on, until at about three and a third miles above sea level the barometer would read fifteen inches, showing that we had passed through half the atmosphere. Mont Blanc is not quite three miles high, so that in Europe we cannot climb to the height where half the atmosphere is left below us, and there is no terrestrial mountain anywhere which would enable us to double the climb; that is to say, to ascend six and two-third miles. Could we do so, however, we should find that the barometer had fallen to seven and a half inches; that the second ascent of three and a third miles had brought us through half the remaining atmosphere, so that only one-fourth still remained above us. In the celebrated balloon ascent made by Mr. Coxwell and Mr. Glaisher on September 5, 1861, an even greater height was attained, and it was estimated that the barometer fell at its lowest reading to seven inches, which would correspond to a height of 39,000 feet.