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parallax nor any
Martian daily parallax at that time. However, insofar as it was accepted that comets are superlunary and sphere-busting, whereby solid celestial orbs are impossible and thus intersecting orbits cease to be impossible, then this thereby also admitted the model of Ursus (and Origanus) as also observationally tenable, along with Wittich's Capellan system (and thus also Praetorius's), whilst the Ptolemaic model was ruled out by the phases of Venus, all heliocentric models by the perceived absence of any annual stellar parallax, and both the Copernican and Tychonic models were also refuted by the absence of any Martian daily parallax. Renowned anti-Copernican adherents of the Capellan planetary model included
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valid observational support in this respect. It seems its credibility rested solely upon his aristocratic social status rather than any scientific evidence. And this failure to find any
Martian parallax in effect also refuted Copernicus's heliocentric model in respect of its Martian orbit, and supported the geocentric models of Ptolemy and the Capellan geoheliocentric model of Wittich and Praetorius and also Ursus's more Tychonic model. The latter differed from Tycho's only in respect of its non-intersecting Martian and Solar orbits and its daily rotating Earth.
157:, refuted the Ptolemaic geocentric model, which implied they are only crescents in conjunction, just as in opposition, whereas they are gibbous or full in conjunction. This crucial novel fact was logically implied by the Heraclidean, Capellan and Tychonic geoheliocentric planetary models, according to all of which at least the orbits of Venus and Mercury are centred on the Sun rather than the Earth, as well as by the pure heliocentric model. Consequently this left only the Copernican and Wittichan Capellan models compatible with both solid orbs and the
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orb containing the orbs of Venus and of
Mercury and itself in turn wholly circumscribed by a Martian orb. This was in significant contrast with Ursus's geoheliocentric model in which the orbits of Mercury and Venus intersect the Martian orbit but the Solar orbit does not, and also with the Tychonic model in which the Martian orbit also intersects the Solar orbit in addition to those of Mercury and Venus, and whereby both these models rule out solid celestial orbs that cannot interpenetrate, if not excluding interpenetrating fluid orbs.
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contradicting his earlier conclusion by 1584 that his observations of Mars at opposition in 1582-3 established it had no discernible parallax, whereas he put the Sun's parallax at 3 arcminutes. Thus Brahe's 1588 model crucially contradicted both
Wittich's and also Ursus's geoheliocentric models at least in respect of the dimensions of the Martian orbit, by positing its intersection with the Solar orbit.
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argued that showed that Mars's parallax was never greater than 4', which put a limit of 2' on the Sun's parallax...". See p109 Taton & Wilson 1989. But inasmuch as this seems to assert Kepler found Brahe's observations showed Mars's parallax to be as great as 4', it is contrary to the impression
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in adopting the
Capellan system to explain the motion of the inferior planets. It is evident from Wittich's diagram of his Capellan system that the Martian orbit does not intersect the solar orbit nor those of Mercury and Venus, and would thus be compatible with solid celestial orbs, with the Solar
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Thus by 1610 it seems the only observationally tenable candidate for a planetary model with solid celestial orbs was
Wittich's Capellan system. Indeed it also seems it was even the only planetary model that was generally observationally tenable, given the twin failures to find any stellar annual
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Having failed to find any
Martian parallax greater than the Solar parallax, Tycho had no valid observational evidence for his 1588 conclusion that Mars comes nearer to the Earth than the Sun, and nor did anybody else at that time, whereby Tycho's uniquely distinctive geoheliocentric model had no
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of Mars was ever greater than that of the Sun was crucial to whether
Wittich's (and indeed also Praetorius's and Ursus's) model was observationally tenable or not. It seems Tycho Brahe eventually came to the conclusion by 1588 that Mars does come nearer to the Earth than the Sun is, albeit
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It seems a primary purpose of
Wittich's Capellan model, evident from the drafting markings in his drawing, was to save the integrity of solid celestial orbs, and the only planetary models compatible with solid celestial orbs were the Ptolemaic, Copernican and Wittichan Capellan (including
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However, Wittich's
Capellan model of the Martian orbit contradicted Copernicus's model in which Mars at opposition is nearer to the Earth than the Sun is, whereby if true the Solar and Martian orbits must intersect in all geoheliocentric models. Thus the question of whether the
161:. But only the Wittichan system was also compatible with the failure to find any stellar parallax predicted by all heliocentric models, in addition to also being compatible with the failure to find any Martian parallax that refuted both the Copernican and Tychonic models.
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Newton's crucial Phenomena 3, 4 and 5 were notably studiously neutral between the heliocentric and Tychonic planetary models in only admitting 5 primary planets orbited the Sun, thus not including the Earth, and remained so even in its 1726 third
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In fact given the modern values of some 9" for solar parallax and a maximum of some 23" for Martian parallax, they were indetectable by naked eye or even by telescopic instrumentation at the time.
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given by Gingerich & Westman 1988 and also by Dreyer's 1890 and Gingerich's 1982 that Kepler found no justification in Brahe's observations for any discernible Martian parallax.
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model, in which the inner planets Mercury and Venus orbit the Sun but the outer planets Mars, Jupiter and Saturn orbit the Earth, may have directly inspired
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Longomontanus's semi-Tychonic model would also have been ruled out if it put Mars closer to the Earth than the Sun at any point.
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model in which all the 5 known primary planets orbited the Sun, which in turn orbited the stationary Earth.
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Paul Wittich's 1578 Capellan geoheliocentric planetary model - as annotated in his copy of Copernicus's
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by Gingerich & Westman, 'Transactions of the American Philosophical Society' Vol 78, Part 7, 1988
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Planetary astronomy from the Renaissance to the rise of astrophysics Part A: Tycho Brahe to Newton
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Goulding, Robert (1995). "Henry Savile and the Tychonic World-System".
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The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus
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has a full set of phases like the Moon, published in his 1613
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354:The telescope and cosmic dimensions
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