Calculating Earth's Orbital Speed Using Star Spectra

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How can the earth’s orbital speed be determined from observations of the spectrum of a star?

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on Phys.org
Not sure if you want the entire answer, but here's a hint: over the course of a year, the direction of the Earth's orbital motion around the sun rotates through a full 360 degrees. How does this change the component of the velocity towards or away from the star being observed? What effect would this have on the observed spectrum?
 
Right, I've been thinking about this, but I'm just not sure. Do you have an answer?
 
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