It is well known that galaxies falling into clusters can experience gas stripping due to ram-pressure by the intra-cluster medium (ICM). The most spectacular examples are galaxies with extended tails of optically-bright stripped material known as jellyfish. We use the first large homogeneous compilation of jellyfish galaxies in clusters from the WINGS and OmegaWINGS surveys, and follow-up MUSE observations from the GASP MUSE programme to investigate the orbital histories of jellyfish galaxies in clusters and reconstruct their stripping history through position vs. velocity phase- space diagrams. We construct analytic models to define the regions in phase-space where ram-pressure stripping is at play. We then study the distribution of cluster galaxies in phase-space and find that jellyfish galaxies have on average higher peculiar velocities (and higher cluster velocity dispersion) than the overall population of cluster galaxies at all clustercentric radii, which is indicative of recent infall into the cluster and radial orbits. In particular, the jellyfish galaxies with the longest gas tails reside very near the cluster cores (in projection) and are moving at very high speeds, which coincides with the conditions of the most intense ram-pressure. We conclude that many of the jellyfish galaxies seen in clusters likely formed via fast (~1- 2 Gyr), incremental, outside-in ram-pressure stripping during first infall into the cluster in highly radial orbits.
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