Therefore, DE441 is less accurate than DE440 for the current century, but covers a much longer duration of years −13,200 to +17,191, compared to DE440 covering years 1550–2650. The ephemerides DE440 and DE441 are fit to the same data set, but DE441 assumes no damping between the lunar liquid core and the solid mantle, which avoids a divergence when integrated backward in time. The orbit of Pluto has been improved from use of stellar occultation data reduced against the Gaia star catalog. The orbit of Saturn has been improved by radio range and VLBA data of the Cassini spacecraft, with improved estimation of the spacecraft orbit. The orbit of Jupiter has improved substantially by fitting to the Juno radio range and Very Long Baseline Array (VLBA) data of the Juno spacecraft. Compared to the previous general-purpose ephemerides DE430, seven years of new data have been added to compute DE440 and DE441, with improved dynamical models and data calibration. The planetary and lunar ephemerides called DE440 and DE441 have been generated by fitting numerically integrated orbits to ground-based and space-based observations. 222 © 2021 EQUINOX PUBLISHING LTD an extended presentation of the open-source project Stellarium, which in the last few years has been enriched with capabilities for cultural astronomy research not found in similar, commercial alternatives. With this paper, we provide Georg Zotti et al. Cultural astronomers also value the possibilities they give of simulating the skies of past times or other cultures. Modern incarnations are immensely versatile tools, mostly targeted towards the community of amateur astronomers and for knowledge transfer in transdisciplinary research. However, in recent decades, "desktop planetarium programs" running on personal computers have gained wide attention. The immer-sive sky simulator of the twentieth century, the optomechanical planetarium, provided new ways for representing and teaching about the sky, but the high construction and running costs meant that they have not become common. For centuries, the rich nocturnal environment of the starry sky could be modelled only by analogue tools such as paper planispheres, atlases, globes and numerical tables.
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