  Despite years of high accuracy observations, none of the available
theoretical techniques has yet allowed the confirmation of a moon beyond the
solar system. Methods are currently limited to masses about an order of
magnitude higher than the mass of any moon in the solar system. I here present
a new method sensitive to exomoons similar to the known moons. Due to the
projection of transiting exomoon orbits onto the celestial plane, satellites
appear more often at larger separations from their planet. After about a dozen
randomly sampled observations, a photometric orbital sampling effect (OSE)
starts to appear in the phase-folded transit light curve, indicative of the
moons' radii and planetary distances. Two additional outcomes of the OSE emerge
in the planet's transit timing variations (TTV-OSE) and transit duration
variations (TDV-OSE), both of which permit measurements of a moon's mass. The
OSE is the first effect that permits characterization of multi-satellite
systems. I derive and apply analytical OSE descriptions to simulated transit
observations of the Kepler space telescope assuming white noise only. Moons as
small as Ganymede may be detectable in the available data, with M stars being
their most promising hosts. Exomoons with the 10-fold mass of Ganymede and a
similar composition (about 0.86 Earth radii in radius) can most likely be found
in the available Kepler data of K stars, including moons in the stellar
habitable zone. A future survey with Kepler-class photometry, such as Plato
2.0, and a permanent monitoring of a single field of view over 5 years or more
will very likely discover extrasolar moons via their OSEs.
