Page:Popular Science Monthly Volume 10.djvu/433

This mass, if we express it in pounds or tons, is too enormous to be conceived: it is 2 octillions of tons—that is, 2 with 27 ciphers annexed; it is nearly 750 times as great as the combined masses of all the planets and satellites of the solar system—and Jupiter alone is more than 300 times as massive as the earth. The sun's attractive power is such that it dominates all surrounding space, even to the fixed stars, so that a body at the distance of our nearest stellar neighbor, α Centauri, which is more than 200,000 times remoter than the sun, could free itself from the solar attraction only by darting away with a velocity of more than 300 feet per second, or over 200 miles an hour; unless animated by a greater velocity than this, it would move around the sun in a closed orbit—an ellipse of some shape, or a circle, with a period of revolution which, in the smallest possible orbit, would be about 31,600,000 years, and if the orbit were circular, would be nearly 90,000,000. We say it would revolve thus—that is, of course, unless intercepted or diverted from its course by the influence of some other sun, as it probably would be. And we may notice here that in many cases certainly, and in most cases probably, the stars are flying through space at a far swifter rate, with velocities of many miles per second.

If we calculate the force of gravity at the sun's surface, which is easily done by dividing its mass, 325,600, by the square of 10834 (the number of times the sun's diameter exceeds the earth's), we find it to be 2712 times as great as on the earth; a man who on the earth would weigh 150 pounds, would there weigh nearly two tons; and, even if the footing were good, would be unable to stir. A body which at the earth falls a little more than 16 feet in a second would there fall 443. A pendulum which here swings once a second would there oscillate more than five times as rapidly, like the balance-wheel of a watch—quivering rather than swinging.

Since the sun's volume is 1,280,000 times that of the earth, while its mass is only 325,600 times as great, it follows at once that the sun's average density (found by dividing the mass by the volume) is only about one-quarter that of the earth. This is a fact of the utmost importance in its bearing upon the constitution of this body. As we shall see hereafter, we know that certain heavy metals, with which we are familiar on the earth, enter largely into the composition of the

and r the mean radius of the earth; T, the length of the sidereal year, reduced to seconds; and 12 g the distance a body falls in a second at the earth's surface. Now, the distance the earth falls toward the sun in a second, or the curvature of her orbit in a second, is equal to $\scriptstyle {\tfrac {2\pi ^{2}R}{T^{2}}}$ (about 0.119 inch). Hence, by the law of gravitation, 12 g : $\scriptstyle {\tfrac {2\pi ^{2}R}{T^{2}}}={\tfrac {m}{r^{2}}}:{\tfrac {M}{R^{2}}}$, whence, $\scriptstyle M=m\left({\tfrac {4\pi ^{2}R^{3}}{T^{2}r^{2}g}}\right)$ In this formula make it = 3.14159 ; R, 92,250,000 miles ; T = 31,558,149.3 seconds ; r = 3,956.179 miles ; and g = 0.0061035 mile (16.113 feet), and we shall. get the result given in the text, viz., M = 325,600 m.