(Solved) Mastering Astronomy: What are the masses of the two stars?

Mepheston0

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12 years ago

Mastering Astronomy: What are the masses of the two stars?

The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 6 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 5.0×10^4. What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass. Unit is Msun. Thank you soo much

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sci_expert

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12 years ago

You have to use that mv^2/r = GmM/r^2, where M is the total mass of the system (twice the mass of each star), r their separation and v the orbital velocity.

Post Merge: A year ago

For example, say the question was "the spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 6.00 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 1.20×10^5 m/s"

We don't know r, but it can be eliminated because we now the orbit time T = 2 pi r/v

Combining the two equations we find: M = v^3 T/(2 pi G)

By comparing with the Earth-Sun system, I find that each of the stars has a mass of 16 times the solar mass.

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Mepheston0 Author

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12 years ago

I keep getting the wrong answer. I'm getting around 79,000 for some reason. Can you show me please?

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George

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12 years ago

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Mastering Astronomy: What are the masses of the two stars?

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