  We present Pandora, a new software to model, detect, and characterize
transits of extrasolar planets with moons in stellar photometric time series.
Pandora uses an analytical description of the transit light curve for both the
planet and the moon in front of a star with atmospheric limb darkening and it
covers all cases of mutual planet-moon eclipses during transit. The orbital
motion of the star-planet-moon system is computed with a high accuracy as a
nested Keplerian problem. We have optimized Pandora for computational speed to
make it suitable for large-scale exomoon searches in the new era of space-based
high-accuracy surveys. We demonstrate the usability of Pandora for exomoon
searches by first simulating a light curve with four transits of a hypothetical
Jupiter with a giant Neptune-sized exomoon in a one-year orbit around a
Sun-like star. The 10 min cadence of the data matches that of the upcoming
PLATO mission and the noise of 100 parts per million is dominated by photon
noise, assuming a photometrically quiet, $m_V = 11$ Sun-like star for
practicality. We recovered the simulated system parameters with the UltraNest
Bayesian inference package. The run-time of this search is about five hours on
a standard computer. Pandora is the first photodynamical open-source exomoon
transit detection algorithm, implemented fully in the Python programming
language and available for the community to join the search for exomoons.
