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What equations determine how a star wobbles in response to an orbiting planet, and can it be used to determine the mass of distant objects based on the wobble?

If there are other more reliable methods of determining mass than the one I am asking about here, I would appreciate a few links explaining these methods, or an explanation of those methods and their benefits/limitations.

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What constant are you talking about? You'll have to provide a formula in which this constant appears for us to be able to understand the question. – David Zaslavsky♦ May 11 '12 at 0:42
Do you means Newtonian gravity? You might want to read up on "reduced mass" in that context which will help. If your asking about measuring these things, my answer to physics.stackexchange.com/questions/22700/… is a mediocre job of explaining the work. Maybe one of the astronomers can jump in with more detail (or point us at a migrated question that already has it). – dmckee♦ May 11 '12 at 0:47
Do I really suck that bad at asking questions. – Argus May 11 '12 at 0:56
Let me try what factors determined how a star with a common surrounding solar system lets use our system for simplicity effect the wobble of the central star again our sun for simplicity – Argus May 11 '12 at 0:58
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@Argus: the "singularity" does not have a mass, neither does the "event horizon". The mass is a property of the whole system, and is only measured at infinity. Your question makes no sense, but at least now is a famous difficult question that makes no sense. The "singularity" is not a matter particle, the black hole is not a point mass surrounded by horizon, the sooner you get rid of that idea the better. – Ron Maimon May 12 '12 at 17:02
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Have a look at http://en.wikipedia.org/wiki/Barycenter#Astronomy (and the links from it to find out more about the subject).

If you take our Solar System as an example and consider just the heaviest planet Jupiter, the Sun attracts Jupiter, but Jupiter attracts the Sun as well. Jupiter is much lighter than the Sun, but it's heavy enough to significantly move the Sun as it orbits. The barycentre of the Sun-Jupiter system is slightly above the Sun's surface, so an anstronomer looking at the Solar System from the planet Zogg would see the Sun orbiting (i.e. wobbling) about a point just above the Sun's surface.

To calculate the mass of the planet you need to know it's orbital period and how much the star is moving. You also need the mass of the star, but we can estimate this from the star's brightness and colour. The period of the star's wobble tells us the radius of the planet's orbit, and from that and how much the star wobbles, i.e. how much the planet moves it, we can work out the mass of the planet. The maths isn't as hard as you might think. See http://en.wikipedia.org/wiki/Doppler_spectroscopy#Procedure for the details.

You ask about other methods of determining the mass. In the Solar System we can calculate the masses of planets, asteroids etc by observing their effects on their moons, other planets etc. For exoplanets we can generally only see the star, so that's the only way we have of estimating their mass.

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Sounds like this is the current way in use as yo said we can use this for smaller bodies what about larger is there an upper limit or can say the "wobble" of an entire galaxy be observed and mass calculated? – Argus May 12 '12 at 9:01
We can estimate the mass of galaxies by measuring the speeds of stars orbiting in them, or by using the virial theorem (these two methods were the first to suggest dark matter existed). In principle galaxies can orbit each other, but the orbital motion takes tens to hundreds of millions of years, so it's far too slow for us to observe. – John Rennie May 13 '12 at 6:23

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