astronomy lesson

[Michael Koppelman <lolife@bitstream.net>]

So GSC 748-1618 may well be a RR Lyrae star. Just for fun, I wanted to 
assume it was and see if I could figure out it's distance. I'm making a 
lot of assumptions at first.

According to Santis et al 2002 a fairly accurate relation is:

Mv = -1.842 log P - 0.137Ab + 0.26

where Mv = the absolute visual magnitude and Ab = the amplitude in the 
color B.

For my star P=0.7774 days. I do not know the blue amplitude but the V 
amplitude is 0.29m. I could probably assume that the blue amplitude is 
somewhat bigger than this. Just using the V amplitude for now I get:

Mv= -1.842 log(0.7774) - 0.137(0.29) + 0.26 = 0.42

This gives a distance modulus of 10.90. To convert this to distance:

d = 10^(mv-Mv+5-A)

If we assume that A is zero (incorrectly) we get a distance of 1.51 kpc 
or almost 5000 ly. If I bump the blue amplitude up to 0.4m I get 1.52 
kpc -- not a huge difference. A, however, makes a huge difference. I 
don't really have a way to estimate that at this point. A=1 brings the 
star closer to 3100 ly and A=5 all the way to 500 ly. Clearly, as Arne 
warned me, extinction is going to be a big factor. If I try to solve 
for A using nearby stars where the distance is known, I get very small 
values -- like 0.04 or less.

My questions to you are:

1. Does an absolute visual magnitude of 0.42 seem at all reasonable? 
According to Astrophysical Quantities, these things should be around 
Mv=0.7 but it mentions that this depends on the metallicity.
2. Is there a relation between metallicity (Fe/H) and BVRI photometry? 
Any other way (for me) to determine metallicity?
3. How can I start to get an estimate of the interstellar extinction A?
4. Where else am I off base?

It seems safe to say at this point that this star is less than 5000 ly 
away.

Thanks!
Michael Koppelman