Stellar Mass Calculation - Question

[Fiery Phoenix]

Is it, by any chance, possible to determine the mass of a star by knowing a) the surface temperature and b) the orbital period of a planetary companion? Provided that the orbital distance of the planet is not known.

The reason I'm asking this is because, as of late, I started contributing to the wiki of the science fiction video game Mass Effect. Part of what I'm doing involves some math.

So, is that possible? If so, please provide the formula. Thanks.

[IsaacKuo]

No. For a given surface temperature, the star may be anything from an "X" dwarf to an "X" giant. And a planet may orbit around this star at any orbital period within reason.

[Fiery Phoenix]

No. For a given surface temperature, the star may be anything from an "X" dwarf to an "X" giant. And a planet may orbit around this star at any orbital period within reason.

I figured as much. Still wanted to know. Not that I lost anything. Thanks for the insight.

More comments are welcome.

[IsaacKuo]

On the other hand...are the planetary companions in question supposed to be habitable or something?

I am unfamiliar with Mass Effect, so I don't know whether, say, the characters can walk around on the planets in question without an environment suit.

[Fiery Phoenix]

On the other hand...are the planetary companions in question supposed to be habitable or something?

I am unfamiliar with Mass Effect, so I don't know whether, say, the characters can walk around on the planets in question without an environment suit.

For the most part, no.

[Spaceman Spiff]

Is it, by any chance, possible to determine the mass of a star by knowing a) the surface temperature and b) the orbital period of a planetary companion? Provided that the orbital distance of the planet is not known.

The reason I'm asking this is because, as of late, I started contributing to the wiki of the science fiction video game Mass Effect. Part of what I'm doing involves some math.

So, is that possible? If so, please provide the formula. Thanks.

To first order(**), a main sequence star's properties (e.g., R, L, T_eff) are determined by its mass (primarily) and its elemental composition (secondarily, because most stars' bulk elemental abundances do not differ greatly from one another). This is known as the Russell-Vogt Theorem.

So if you stipulate that that the star is a main sequence star of typical cosmic abundances (as opposed to some exotic helium star or something), then its surface temperature gives you a rough estimate of its mass. If you know how old it is and bulk composition, you can zero in further as these effects are reasonably well calibrated.

Once the star ages off the main sequence, star masses aren't as well segregated, but you can get in the ball park if you also know the star's luminosity. A star's spectrum can also reveal its luminosity class (contrary to the implication of a post, above). Also: is the star's parallax measured? If so, then its luminosity pops out.

You didn't say how the star's effective temperature was derived -- estimated via multi-color photometry or better constrained with a good spectrum? Fitting the star's detailed spectrum with a model atmosphere usually reveals M/R^2 (the star's surface acceleration due to gravity). Its spectral class and luminosity type (both derived from the star's spectrum) would provide decent to rough estimates of the star's mass. If the star happens to be luminosity class V (main sequence), then its spectrum provides a better constrained estimate of the star's mass. A star's spectrum measured over time will also reveal the star's time-dependent radial velocity due to the gravitational pull of the planet on the star; more on that next.

You also didn't say whether we knew anything about the planet. If we measure the maximum Doppler shift of the star (from the star's spectrum), then we can determine the following quantity:

{m_planet * sin(i)}³ / {m_star + m_planet}² ,

where i is the line of sight inclination of the planet's orbit around the star (and the planet's orbital eccentricity also factors in, but again that can be determined from the time-dependent Doppler shift of the star's spectrum). If the planet transits its star, then sin³(i) is ~1. Thus if properties of the planet (e.g., its mass) are prior specifications, the star's mass may be determined.

I could go on, but I think you get the idea.
Note the power of a good spectrum of the star!

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(**)Other effects, such as rapid rotation or strong winds can alter the star's structure from nominal.

[korjik]

Is it, by any chance, possible to determine the mass of a star by knowing a) the surface temperature and b) the orbital period of a planetary companion? Provided that the orbital distance of the planet is not known.

The reason I'm asking this is because, as of late, I started contributing to the wiki of the science fiction video game Mass Effect. Part of what I'm doing involves some math.

So, is that possible? If so, please provide the formula. Thanks.

If you know the mass of the companion, you should be able to use Kepler's laws, or just the law of gravitation.

Without at least one more piece of information, the situation you describe is not uniquely defined

[Fiery Phoenix]

If you know the mass of the companion, you should be able to use Kepler's laws, or just the law of gravitation.

Without at least one more piece of information, the situation you describe is not uniquely defined

I do know the mass of the planet, but how am I supposed to break out the mass of the star at this point? Kepler's laws, which one exactly? Second? Third? Law of gravitation, there's simply not enough information to use that one it appears.

[EDG]

I forget, does ME give you the star's radius at all?

You can generally assume that the stars are Main Sequence, though if you read some of the descriptions of the other planets in the systems in ME, it sometimes does mention that the star is a Giant. I think there are a few blue stars in there too (which most likely wouldn't have planets in a realistic setting).

If the stars are main sequence then you can at least estimate their mass if you have the surface temperature - the surface temperature and the colour as well would correspond to a spectral type, and main sequence spectral types are usually within specific mass ranges (e.g. type M red dwarfs are usually less than 0.45 solar masses, type K orange main sequence stars are usually between 0.88 and 0.45 solar masses, etc).

[EDG]

Oh, if you know the orbital period of the planet then you can use Kepler's third law to figure out the mass of the primary it orbits.

http://en.wikipedia.org/wiki/Orbital...a_central_body

If rearrange the first equation in the "small body..." section, you can make M the subject, and thus find the mass of the star. Though whether it'd be accurate is uncertain (I know games like EVE online just tend to make up the values).