How many Kuiper Belt objects have moons? How do we know this?
&quot;Moons&quot; is a misnomer here, the majority of Kuiper Belt Objects (KBOs) with companions are binaries.
Now there are several populations in the Kuiper Belt, characterized by their eccentricities and inclinations. The cold classicals are hereby the most important ones, having mostly circular, low inclination orbits and a high binarity fraction of about 30% (Noll et al. 2008).
Hot classicals, with eccentric and inclined orbits possess a binarity fraction of about or less than 1 in 40.
The other important KBO populations, i.e. the scattered disc, the resonant ones and the centaurs possess negligible binarity. In terms of numbers, the classicals make up about 2/3 of the entire KBO population by numbers, and the cold classicals are about 50-60% of the total classical population.
So in total you'd get a fraction of at least $f_{\rm Moon}\approx 0.66*0.5*0.3\approx10\%$ of KBOs having 'moons'.
In order to find and characterize binary orbits, strange light curves pose a first hint, but only high spatial resolution actually helps to discern the two binary components. As most KBOs are low-mass objects, their binary orbital times are long. Prolonged, 5-15 year snapshot observations with the HST allowed recently to characterize the spin direction, for example (Grundy et al. 2019).