File talk:Lunaparallax.png

Purpose of the diagram

This diagram illustrates the historically crucial fact that, contrary to the mistaken standard definition of ‘parallax’ as a change in the perceived orientation of an object due to a locomotion of the observer, in fact a fixed observer can also perceive parallax purely due to the motion of the objects themselves or even just to the observer’s viewpoint without any motion of the observer nor of the objects observed. Indeed even in secondary school physics pupils are taught to avoid scientific instrument needle reading errors due to parallax caused by an oblique viewpoint of the dial and needle, rather than due to any motion of object or observer.

The diagram shows for the case of geocentric-geostatic cosmology how the fact that a fixed observer on the Earth’s surface at the equator is displaced from the Earth’s centre by an Earth radius entails that at moonrise in the East the Moon would appear below a given fixed star, whereas at moonset in the West it would appear to have moved ahead of it, and when overhead it would appear in line with it. But for a hypothetical observer at the centre of the Earth they would always appear in alignment. The parallax of the Moon (or a planet) is the angle subtended at that body by the Earth’s equatorial radius. (The parallax is exaggerated here by the lunar and stellar distances being drawn radically under scale for expository purpose.) It seems a daily Lunar parallax apparent to a fixed observer on the surface of a supposedly central and non-rotating Earth was first recorded in the 2nd century BC by Hipparchus in his book On Sizes and Distances.

Because greater distance implies less parallax, calculations of planetary and cometary daily parallax and thus of their relative distances played crucial roles in ‘the astronomical revolution’. For the conclusion that Martian parallax at opposition is greater than Solar parallax, and thus that Mars is sometimes nearer the Earth than the Sun is, refuted the Ptolemaic geocentric solid orbs model because the Martian orb would have had to interpenetrate the Solar orb. In the Ptolemaic model depicted in Copernicus’s De Revolutionibus, Mars is never nearer the Earth than the Sun is, but in the semi-heliocentric Tychonic model it is when at opposition. Tycho mistakenly thought his observations showed that Mars had greater parallax at opposition than the Sun’s, which he took on faith to be 3’ without ever measuring it himself. And the calculation that comet parallax is less than Lunar parallax, whereby comets are superlunary and so must pass through various planets’ celestial orbs, refuted solid orbs more generally. Modern values for the maximum daily parallaxes of the Moon, Mars and Sun are respectively almost 1 degree (i.e. approximately two Moon diameters), some 23 arcseconds and some 9 arcseconds. Thus the Moon, for example, is apparently displaced by almost 2 degrees from moonrise to moonset.

The diagram provides a corrective pedagogical alternative to the somewhat misleading and confusing diagram of daily parallax in Kuhn’s 1957 The Copernican Revolution [See Fig 39, p207 1959 Vintage Books edition] that misrepresents this parallax as due to the transportation of the observer rather than to their displacement from the centre of the Earth, and also mistakenly claims “The large size of the moon and its rapid orbital motion disguise the parallactic effect.” It was crucially Kuhn’s inattention to observations and his neglect of analysing the logical role of crucial observations and observational conclusions in the heliocentric revolution, such as daily parallax, the phases of Venus and stellar aberration, combined with the traditional failure initiated by Galileo to compare the most scientifically and culturally relevant Tychonic geocentric model with the heliocentric model and also the traditional failure to date and quantify the conversion in the scientific community from the post-Ptolemaic geoheliocentric models of geocentrism dominant in the 17th century to pure heliocentrism, that led him to invalidly conclude this ‘scientific revolution’ was empirically irrational, and which in turn inspired his general Wittgensteinian-Koyrean irrationalist theory of scientific revolutions as incommensurable ‘paradigm‘ changes rather than empirically rational progress, published in his 1962 The Structure of Scientific Revolutions.