All Problems Optics of Moving Sources
Problem 5.228
The Doppler effect has made it possible to discover the double stars which are so distant that their resolution by means of a telescope is impossible. The spectral lines of such stars periodically become doublets indicating that the radiation does come from two stars revolving about their centre of mass. Assuming the masses of the two stars to be equal, find the distance between them and their masses if the maximum splitting of the spectral lines is equal to \((\Delta \lambda / \lambda)_{m}=1.2 \cdot 10^{-4}\) and occurs every \(\tau=30\) days.
\[ \text { 5.228. } d=(\Delta \lambda / \lambda)_{m} c \tau / \pi=3 \cdot 10^{7} \quad \mathrm{~km}, \quad m=(\Delta \lambda / \lambda)_{m}^{3} c^{3} \tau / 2 \pi \gamma= \] \(=2.9 \cdot 10^{29} \mathrm{~kg},\) where \(\gamma\) is the gravitational constant.