The Solar Orbiter mission, with an orbit outside the Sun Earth line and leaving the ecliptic plane, opens up opportunities for the combined analysis of measurements obtained by solar imagers and spectrometers. For the first time, different space spectrometers will be located at wide angles to each other, allowing three-dimensional (3D) spectroscopy of the solar atmosphere. The aim of this work is to prepare the methodology to facilitate the reconstruction of 3D vector velocities from two stereoscopic LOS Doppler velocity measurements using the Spectral Imaging of the Coronal Environment (SPICE) onboard the Solar Orbiter and the near-Earth spectrometers, while widely separated in space. We develop the methodology using the libraries designed earlier for the STEREO mission but applied to spectroscopic data from the Hinode mission and the Solar Dynamics Observatory. We use well-known methods of static and dynamic solar rotation stereoscopy and the methods of EUV stereoscopic triangulation for optically thin coronal EUV plasma emissions. We develop new algorithms using analytical geometry in space to determine the 3D velocity in coronal loops. We demonstrate our approach with the reconstruction of 3D velocity vectors in plasma flows along open and closed magnetic loops. This technique will be applied to an actual situation of two spacecraft at different separations with spectrometers onboard (SPICE versus the Interface Region Imaging Spectrograph (IRIS) and Hinode imaging spectrometer) during the Solar Orbiternominal phase. We summarise how these observations can be coordinated.
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