I read in Neil deGrasse Tyson's book Astrophysics for People in a Hurry that scientists can tell if a star has a planet orbiting it because the light appears to shake.

So if in the case of a binary star which is quite obviously shaking because its orbiting another star how would I know a planet is orbiting the 2 stars?


1 Answer 1


The light from the two stars would be Doppler shifted in a sinusoidal pattern (for a circular orbit). The signals from the two stars would be in anti-phase and would oscillate at the orbital period of the binary.

The planet would cause a small pull on the binary system which would superimpose a further small sinusoidal signal (again, assuming a circular orbit), but at the longer orbital period of the planet around the binary system.

The process is illustrated below by adding two (red and blue) sine waves together, where the blue sine wave has a much smaller amplitude and lower frequency than the red sine wave. These sine waves encode the Doppler shift that would be measured from the absorption lines of one of the binary components. Thus the red wave would indicate the Doppler shift due to the motion of the binary system and the blue sine wave the additional modulation due to the smaller motion induced by the tug of the planet as it orbits. The black line then gives the superposition of these (they can basically be added if the velocities are non-relativistic) and you can see that it is subtly different from a monochromatic sine wave of fixed amplitude.

enter image description here

For non-circular orbits, the pattern of Doppler shifts would be non-sinusoidal but still periodic in a similar way.

  • 3
    $\begingroup$ Your diagram illustrates perfectly why stiff glassware on a stiff surface is susceptible to reproducing powerful AM transmissions - I never understood that phenomenon before. $\endgroup$
    – dotancohen
    Nov 17, 2022 at 13:36
  • $\begingroup$ @dotancohen actually my comparison with amplitude modulation was erroneous. The signals are added rather than being multiplied together. $\endgroup$
    – ProfRob
    Nov 17, 2022 at 13:58
  • $\begingroup$ see also Fourier Transforms applied to Doppler shifts, position, intensity of the received light... $\endgroup$ Nov 17, 2022 at 19:20

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