Red/blueshift due to orbiting planet

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SUMMARY

The discussion centers on calculating the observed wavelengths of the NaI double line (586.6nm and 589.6nm) due to the red/blueshift caused by a planet orbiting a star with a mass of 1.2 solar masses and an orbital period of 2.1375 days. The key equations involved are Kepler's law and the Doppler effect. It is concluded that since the planet's mass is negligible compared to the star's mass, there is no significant Doppler shift, contradicting the initial assumption that the planet's gravitational influence would cause a measurable effect.

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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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