Red/blueshift due to orbiting planet

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The discussion centers on calculating the observed wavelengths of the NaI double line due to the presence of an orbiting planet around a star with a mass of 1.2 solar masses. The oscillations in spectral lines suggest a planet with a 2.1375-day orbital period, but the negligible mass of the planet implies that it does not significantly affect the star's motion. Consequently, the expected Doppler shift in wavelength is minimal or nonexistent. Participants express confusion over the problem's premise, noting that if the planet's mass is negligible, it should not cause a red or blueshift. The conclusion drawn is that the problem may be flawed in its assumptions.
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Homework Statement


The periodical oscillations of the spectral lines of a star incicate that there is a planet orbiting around it with a period of 2.1375 days.Calculate what the observed wavelengths of the NaI double line will be,which is normally observed at 586.6nm and 589.6nm.
Star's mass=1.2 solar masses
Assume the planet's mass is negligible compared to the mass of the star and that its orbit is circular.

Homework Equations


Kepler's law
Doppler effect

The Attempt at a Solution


I would guess the shift in wavelength is because the gravitational force acting on the star because of the planet's mass at the points radially away from the earth,cause the star to move with a miniscule speed u,resulting in a red/blueshift.
But,firstly, I can't calculate the mass of the planet in order to get the star's acceleration
and secondly,even if I did,the phrase "Assume the planet's mass is negligible" leads me to believe this is not the correct solution.
 
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You are right. If the planet's mass is negligible, then there is no Doppler shift. Whoever wrote the problem is confused.
 
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