When the astronomer studies the motions of a binary star in the sky, he generally finds that the two components do not move in circles about one another but in ellipses[6]. Once again, Newton’s law is confirmed, and we are entitled to assume that the forces which keep binary stars together are the same gravitational forces as keep the moon from running away from the earth, or the planets from the sun. By a study of these ellipses it becomes possible to weigh the stars. If one of the component masses were enormously heavier than the other, the former would stand still while the lighter component described an ellipse around it, the motion being essentially similar to that of a planet around the sun. Such cases are not observed in actual binary stars because the two components are generally comparable in weight, and this brings new complications into the question. There is no need to enter into mathematical details here. Suffice it to say that neither star stands still; the two components describe ellipses of different sizes, and from a study of these two ellipses the weights of both the components can be determined. [6] What he actually observes is the “projection” of the orbit on the sky, but it is a well-known theorem of geometry that the projection of an ellipse is always an ellipse. The following table shews the result of weighing the four binary systems nearest the sun in this way, the sun’s weight being taken as unity: _Stellar Weights_ Binary systems near the sun. +----------------+-------------+-----------------------+-----------+ | | Distance in | Weights of components | | | Star | light-years | in terms of sun’s |Luminosity | | | from the sun| weight |(see p. 49)| +----------------+-------------+-----------------------+-----------+ | α Centauri _A_ | 4·31 | 1·14 | 1·12 | | ” _B_ | | 0·97 | 0·32 | +----------------+-------------+-----------------------+-----------+ | Sirius _A_ | 8·65 | 2·45 | 26·3 | | ” _B_ | | 0·85 | 0·0026 | +----------------+-------------+-----------------------+-----------+ | Procyon _A_ | 10·5 | 1·24 | 5·5 | | ” _B_ | | 0·39 | 0·00003| +----------------+-------------+-----------------------+-----------+ | Kruger 60 _A_ | 12·7 | 0·25 | 0·0026 | | ” _B_ | | 0·20 | 0·0007 | +----------------+-------------+-----------------------+-----------+