How Accurately Will Gaia Measure Cepheid Distances?

[odoital]

Homework Statement

The planned Gaia satellite is a successor to Hipparcos. It will have an astrometric accuracy of 24 micro-arcseconds, and be able to detect Cepheid variable stars in the Magellanic clouds (~ 70kpc away). Estimate how accurately Gaia will determine distances to these Cepheids

Homework Equations

The Attempt at a Solution

I haven't really done any cosmology before so this is new to me. I've just defined a parsec in the previous question as a star 1pc away having a parallax of one arcsecond.

http://upload.wikimedia.org/wikipedia/en/a/a8/Parsec.png

I'm not sure what value this question actually wants as an answer

 

[Dick]

Take your picture and replace the base distance with the approximate distance to the Magellanic cloud. Now what is the angle. (Hint: this is really trigonometry - not cosmology).

 

[odoital]

Hmm, i tried that and the angle came out as virtually 0 arc seconds

 

[Dick]

You're right! It is virtually zero. But it is NOT zero. Express the answer in micro-arcseconds. This whole game is about tiny angles.

 

[odoital]

ok, well converting to meters:

1AU = 149.6 x 10^9 m
70kpc = (70,000) * (3.086 x 10^16) m

Angle, say, x = 3.97 x 10^-9 degrees = 14.28 microarcseconds

 

[Dick]

So given the astrometric accuracy of Gaia, will it be able to accurately measure distances on this scale using parallax?

 

[odoital]

Given that it can only(!) read to 24micro-arcseconds, no - as the calculated angle is 14.28 microarcseconds. But I'm confused at the way the question's worded - "estimate HOW ACCURATELY Gaia will determine distances to these Cepheids", I'm not sure what physical quantity it's asking for

 

[Dick]

Aside from saying "not very accurately at all", I'm not sure. You could say if the true parallax is 14, Gaia could measure anything between 0 and 38, implying it's somewhere between around half the true distance and infinity. Not very satisfying, eh? If it's any consolation, if you measured LOTS of stars and averaged the results - you could do a lot better. And I think that's what they do.