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 1/3093500 that of
the sun-quotient. Hence we conclude that the mass of Mars is
1/3093500 that of the sun. By the corresponding quotient, the mass
of Jupiter is found to be about 1/1047 that of the sun, Saturn
1/3500, Uranus 1/22700, Neptune 1/19500.
We have set forth only the great principle on which the astronomer
has proceeded for the purpose in question.
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