# Parsecs/Distance accuracy

## 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

## 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.

I'm not sure what value this question actually wants as an answer Last edited by a moderator:

Dick
Homework Helper
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).

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

Dick
Homework Helper
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.

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

Last edited:
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