sphere covered by 1, 2, $\dots$, 20 distinct observations according to the nominal scanning law of [*Gaia*]{}, as functions of duration. No dead time is assumed.\[fig:frac\]](FracDeadTime000an.pdf){width="45.00000%"}

Prerequisites for a [*Tycho*]{}–[*Gaia*]{} solution
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How much [*Gaia*]{} data are needed?
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A good astrometric solution for (apparently) single stars requires that five astrometric parameters $(\alpha,\delta,\varpi,\mu_{\alpha*},\mu_\delta)$ are determined for each star . A sixth parameter ($\mu_r$) representing the radial motion (along the line of sight) is formally required for a complete representation of the space motion. In the present context it can be ignored, except for a limited number of nearby, fast-moving stars with significant perspective acceleration for which it is assumed to be known. Thus, at least five distinct measurements are needed for every star, where ‘distinct’ means that the measurements differ significantly either in time or direction. The scanning law of [*Gaia*]{} causes the direction of its spin axis to change by $4^\circ$ day$^{-1}$ , so that any two scans of the same star separated by at least 5 days may count as distinct. Figure \[fig:frac\] shows that after 0.5 yr, more than 90% of the sky is covered by at least three distinct scans, which together with the two measurements 