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Position-position-velocity space (P-P-V Space or just PPV) is a conceptual space where two dimensions are the normal "space" dimensions and the third dimension is the velocity component in the direction along what would normally be the third spatial dimension. The concept is an organizing principle of 3D sets of data (3D matrices, or data cubes) where across two dimensions, the data applies to the two physical dimensions across the sky, and the third dimension applies to the radial velocity component of the movement of material seen along that line of sight. E.g., if along a line of sight, there is some material moving at 1 km/sec away from the viewer and apparently even more material moving 2 km/sec toward the viewer, then in that column within the cube, there would be two data points, with differing values in the V dimension, corresponding to those two radial velocities. This format is now common for astronomical data, e.g., for molecular clouds that include star-forming regions, in which internal structure is of high interest.
This is in contrast to "ordinary" position-position-position space (P-P-P space or PPP) which is undoubtedly useful when it can be reliably determined. The motivation for PPV space is: it represents the data that can be observed: the two spatial dimensions (e.g., based on astrometry) and taking as the third dimension, the radial velocity indicated by spectrography (or the equivalent radio astronomy observations). Naturally one wants the data in all six such dimensions, but the other positional and velocity dimensions are only determined through analysis that is subject to possible future improvement: PPV is closer to raw observation data. The more-straightforward analysis required to produce PPV data is identification of Doppler shifted spectral lines, whose shift indicates a that gas movement's radial velocity component. The radial velocity offers clues to the third positional-dimension, e.g., to distinguish between two clouds lined up with us (one close than the other) that are moving at different velocities.
PPV data is the natural result of an imaging spectrometer, or the equivalent radio observations. Position-velocity space (P-V space) similarly describes data resulting from similar analysis of a slit spectrograph, and position-position space (P-P space) represents just a normal image of the sky.