Page:Astronomy for Everybody.djvu/275

times that of the earth; that it would take this number of earths to make a body as heavy as the sun.

I give this calculation to illustrate the principle; it must not be supposed that the astronomer proceeds exactly in this way and has only this simple calculation to make. In the case of the moon and earth, the motion and distance of the former vary in consequence of the attraction of the sun, so that their actual distance apart is a changing quantity. So what the astronomer actually does is to find the attraction of the earth by observing the length of a pendulum which beats seconds in various latitudes. Then by very delicate mathematical processes he can find with great exactness what would be the time of revolution of a small satellite at any given distance from the earth, and thus can get the earth-quotient.

But, as I have already pointed out, we must, in the case of the planets, find the quotient in question by means of the satellites; and it happens, fortunately, that the motions of these bodies are much less changed by the attraction of the sun than is the motion of the moon. Thus, when we make the computation for the outer satellite of Mars, we find the quotient to be ${\displaystyle \scriptstyle {\frac {1}{3,093,500}}}$ that of the sun-quotient. Hence we conclude that the mass of Mars is ${\displaystyle \scriptstyle {\frac {1}{3,098,500}}}$ that of the sun. By the corresponding quotient, the mass of Jupiter is found to be about ${\displaystyle \scriptstyle {\frac {1}{1,047}}}$ that of the sun; Saturn, ${\displaystyle \scriptstyle {\frac {1}{3,500}}}$; Uranus, ${\displaystyle \scriptstyle {\frac {1}{22,700}}}$; Neptune, ${\displaystyle \scriptstyle {\frac {1}{19,500}}}$.

I have set forth only the great principle on which the astronomer has proceeded for the purpose in question. The law of gravitation is at the bottom of all his work.