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 you are referring to is the precision with which the astrometry (position) of stars will be measured with the Gaia satellite.

The sentences you refer to in Perryman et al. (2014) are "Gaia will achieve accuracies of some 10μas (microarcsec) in positions and annual proper motions for bright stars (V ∼ 10), degrading to around 25μas at V = 15, and to around 0.3 mas (300μas) at V = 20 (Lindegren et al. 2008)."

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.

• Could you give the author name (or a link) please. Commented Aug 4, 2015 at 7:44
• iopscience.iop.org/0004-637X/789/2/166
– user7330
Commented Aug 4, 2015 at 8:38
• Thanks for the reply. However, I still didn't understand the sentence 'will be determined with a relative precision of 10 millionths of an arc second'. Lets say there are 2 stars A & B with equatorial coord. (a1, b1) and (a2, b2) then how does the above sentence fits in this context.
– user7330
Commented Aug 5, 2015 at 3:29
• @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. Commented Aug 5, 2015 at 7:20