Page:The Solar System - Six Lectures - Lowell.djvu/41



pair their united mass. It comes out twice that of our Sun. Now, as gravity is as $$\textstyle \frac{m}{d^{2}} \,\!$$, we have, calling the whole distance from us to them a, the following quadratic to give us d, the boundary distance between the two domains, our Sun's and Centauri's, $$\textstyle \frac{m}{a-d^{2}}=\frac{m}{d^{2}} \,\!$$; from which we find the dividing line between the Sun's domain and  Centauri's to be 114,000 astronomical units.

Neptune, the farthest known planet at present, is but thirty astronomical units away, or about $$\textstyle \frac{1}{4000} \,\!$$ only of the distance to the limit of the Sun's domain. How nestled we all are under the Sun's protecting wing is evident. It is no wonder that the remotest comets seem almost infinitely distant at their aphelion, though part and parcel of the brood.

Coming back now from these chill outer confines of the Sun's territory to the inner family circle gathered about the hearth or focus of all these ellipses, occupied by the Sun,—for such is