The Doppler effect has made it possible to discover the doubles stars which are so distance that their resolution by means of a telescope is impossible. The spectral lines of such stars periodically become doublets indicating that the radiations does come 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) = 1.2.10^(-4)` and occurs every `tau = 30` days.

Explanation

Maximum splitting of the spectral lines
will occur when both of the stars are moving in the direction of line of observation as shown.
we then have the equations
`((Delta lambda)/(lambda))_(m) = (2v)/(c )`
`(mv^(2))/(R ) = (gamma m^(2))/(4R^(2))`
`tau = (pi R)/(v)`
from these we get
`d = 2R = ((Delta lambda)/(lambda))_(m) c tau//pi = 2.97 xx 10^(7) km`
`m = ((Delta lambda)/(lambda))_(m)^(3) c^(3)tau//2pi gamma = 2.9 xx 10^(29) kg`