Page:Popular Astronomy - Airy - 1881.djvu/287

Rh opposite problem; knowing the length of the line through which the earth's attraction pulls the moon in one hour, we have to find what is the length of GM, the semi-diameter of the orbit in which it revolves. Having found this, we find EG; and then, as in the last method, the proportion of EG to GM is the same as the proportion of the mass of the moon to the mass of the earth.

All these different methods agree very well in giving the result that the mass of the moon is about $1⁄80$ of the earth's mass. And when this mass, and the known mass of the sun, are used in combination with a law of density of the strata of the earth which will well explain the observed ellipticity of the earth, it is found that they explain almost exactly the observed amount of precession.

There remains but one set of bodies whose masses can be determined, namely, Jupiter's satellites. It so happens that these little bodies disturb each other very much. In consequence of the periodic time of Jupiter's second satellite being very nearly double that of the first, and the periodic time of the third being very nearly double that of the second, there is a kind of "inequality of long period" in their motions which admits of tolerably accurate observation, by the observation of their eclipses. From this their masses are computed in the same manner as the masses of the planets from their mutual perturbations. Computations are made of the effect of one satellite upon the others, on the assumption, for instance, that the satellite is $1⁄1000$ part of the mass of Jupiter; if this does not produce, in calculation, the perturbations which are actually observed, the assumed mass must be altered in the proper proportion. For the fourth satellite, there are no perturbations of the nature of