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Although he admired the Almagest, Regiomontanus was keenly aware that its geometric models led to inconsistencies (notably between predictions of planetary position and predictions of planetary size).
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Almost immediately he found that the existing almanacs and ephemerides, which record stellar and planetary positions, were grossly inaccurate.
Ptolemy's mathematical models permitted accurate predictions of planetary positions and eclipses of the sun and moon.
Copernicus's recognition that the sun was at the center of planetary motion did not automatically lead to more accurate predictions of planetary positions.
The inscriptions imply that there may originally have been a display of planetary positions, most likely on the front face, but nearly all the relevant parts are missing.
Three-dimensional models using concentric spheres would, he believed, yield good mathematical predictions of planetary positions without jeopardizing the physical principles of natural philosophy.
Ideally, the geometrical models that allowed prediction of planetary positions could be imagined as real, physical, three-dimensional spheres rotating around Earth.
It led directly to the work of Tycho Brahe, who measured stellar and planetary positions more accurately than had anyone before him.
Similarly, he buys only organic ingredients and sells biodynamic wines, which are not only organic but are made taking the phases of the moon and planetary positions into consideration.
Along with W.J. Eckert, he developed a method of calculating orbit corrections (1937) that has been widely accepted, and, with Eckert and G.M. Clemence (1951), Brouwer was the first to use a computer to calculate planetary positions accurately.
When Johannes Kepler was preparing tables of celestial events and planetary positions for the years 1629 to 1636, he paid special attention to any possible transits of Mercury and Venus in front of the Sun.
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