# [Cosmology] Fundamental Plane to find distance

I have been given data for the Coma and S639 clusters, including their velocity distances. For part a I calibrated the fundamental plane using the Coma data, and got:

log(Re) = 1.24log($$\sigma$$) - .82log<I> - .259

I am now supposed to use the S639 data along with the above fit to get a distance to S639. I think that this is related to the difference in zero points for the two clusters. My zero point for S639 is -.137, which is a difference of .122 in log(Re). I feel like there's some big thing that I'm missing that would make this a lot easier. I've done this type of problem before with the Tully-Fisher relation, which was easy enough, because M1 - M2 = -5log(d1/d2).

When I read papers in which they do this, they jump from saying "our zero points were x and y" to "this gave us a relative distance of z." Apparently it's fundamental enough that I should know it.

I realize <I> is given in units of Lsolarpc-2, so I feel like that may help.

I also know that Re=101.24log($$\sigma$$)-.82log<I>+ZP, which I can see helping.

I have tried to make so many things work and failed, I'm not sure what values are important to me anymore. I just have a bunch of stuff and I don't know what to do with it.

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