# What is the accuracy of an artificial satellite at a certain magnitude?

When we say that 'accuracy of gaia satellite is 10 $\mu$as at $V = 10$ magnitude in position and annual proper motion'. What does this mean? Does it change over time?

What this means is that after the 5-year Gaia mission is complete, the angular position (or coordinates) of 10th magnitude stars on the sky will be determined with a relative precision of 10 millionths of an arcsecond. This will also be the accuracy with which the annual tangential motion (the so-called proper motion) of stars can be measured. i.e. 10th magnitude stars will have an uncertainty in their proper motion of $\pm 10 \mu$as/year.
• @raj ? It means that $a_1$ is determined to somewhat better than 10 microarcseconds, as are $b_1$, $a_2$ and $b_2$. All with respect to a coordinate frame which I believe is based on distant quasars. – Rob Jeffries Aug 5 '15 at 7:20