1) On Spirographs and Standard Candles - Cosmic Markers for Mark Shea, 2) How Big is Kepler 452? A Geocentric Minority Report, 3) - But Parallax Guarentees the Distance of Kepler 452, Right? Right? Don't Tell Me It Doesn't!
- Bad news, pal! It doesn't.
There are a few quirks to that.
If we go to the articles on wiki entitled Stellar Parallax and Heliometer, we will show where the doubts occur.
Here is first a description of a heliometer:
The basic concept is to introduce a split element into a telescope's optical path so as to produce a double image. If one element is moved using a screw micrometer, precise angle measurements can be made. The simplest arrangement is to split the object lens in half; with one half fixed and the other attached to the micrometer screw and slid along the cut diameter. To measure the diameter of the sun, for example, the micrometer is first adjusted so that the two images of the solar disk coincide (the "zero" position where the split elements form essentially a single element). The micrometer is then adjusted so that diametrically opposite sides of the two images of the solar disk just touch each other. The difference in the two micrometer readings so obtained is the (angular) diameter of the sun. Similarly, a precise measurement of the apparent separation between two nearby stars, A and B, is made by first superimposing the two images of the stars and then adjusting the double image so that star A in one image coincides with star B in the other. The difference in the two micrometer readings so obtained is the apparent separation or angular distance between the two stars.
This means that parallax of one star is measured in relation to other stars.
And that in its turn means that if ALL stars have a movement same direction, it won't be detected by this method. For Heliocentrism that is no problem. The one movement all stars share in same direction and some size changing twice a year is - according to Heliocentrism, to the theory we are the ones moving - the aberration of light, changing their positions by 20 arcseconds a year through the speed we have (still according to Heliocentrics) and the speed light has.
For a Geocentric, there is a problem here. First of all, the Bradley phenomenon would not really be "aberration of light" - but some movement either in the stars or in the space between us and them (I settle for movement in the stars, as simpler, and as explainable by angels moving them). But second, for that reason we cannot tell "this belongs to aberration" (check the general size of all stars' quasi collective movement) and "this belongs to parallax" (the remaining differences between them). BOTH would be due to an angel for instance doing some liturgic dance in honour of God and in timing with Sun (which might have an angel functioning as "master of ceremonies") and all the movement would be that, and the differences of angles between stars would be the small différences in these movements of the stars - of the star to the right moves a little more to the left than the star to the left, the angle shrinks, and so on. If in ten stars exactly one moves half an arcsecond more to the left or right than the rest, these 9 will in a first time be registered as having "no visible parallax" (being very distant) and the one moving more will be registered as having 0.500 microarcseconds parallax. If the difference is in the direction parallax is supposed to be in, considering "earth moving opposite direction". But with angels, all could be moving without earth being involved at all except as stationary observer - and then the observation is not an observation of what parallax is according to heliocentrics supposed to mean.
This obviously means, notwithstanding the great precision of measurements taken by the heliometer, that parallax angles tell us nothing about the distance of stars. It is the very first rung of "cosmic distance ladder" which breaks down.
Let's do a little history on the matter! Other article, now:
Stellar parallax is so small (as to be unobservable until the 19th century) that it's apparent absence was used as a scientific argument against heliocentrism during the early modern age.
Note, as just noted, its apparent presence is not a proof for Heliocentrism, since it can, as just said, be explained by angelic movers (precisely as the spirograph patterns of some planetary orbits in Tychonian Geocentrism).
Note also, back in this time stars with own light (not counting Sun) and "fixed" (we would now say "relatively fixed") apparent position in relation to the whole cosmos as seen from us, were thought of as being one layer, as inner surface layer of a hollow sphere. This would give some expectations about parallax that have not been fulfilled.
Observing constellations, we do not see - as would have been expected then - the distance between stars in Virgo uniformly augment as Sun goes into Pisces or diminish as Sun goes toward Virgo (which Heliocentrics interpret as us going towards Pisces). If they did, astronomers would today conclude they do have some cohesion, as I read in a magazine (an article series debunking astrology), the stars in a constellation are considered, usually (example given was outside zodiac, it was Great Bear) as at very different distances from us - in other words, there is no "constellation uniform" either broadening or narrowing of distances between stars belonging to same or nearby ones, with corresponding narrowing or broadening of opposite constellation. The kind of parallax observations postulated as a consequence of Heliocentrism if it were true in those early modern debates (notably the one between Galileo and St Robert Bellarmine, who was judging Galileo's book) has in fact not been observed.
It would have involved Heliometer readings with "constellation uniform" widening and narrowing of angular distances as we approached or regressed around Sun from such and such a constellation.
What has been observed instead is a phenomenon which, if stars are in a cluster close enough to inner surface of a hollow sphere, then the phenomenon is due to own movements of stars (movements explainable now as well as back then by angels moving them), but if it is truly parallactic, if it is exactly due to the factors astronomers allege, namely "our own movement around the sun", then the cosmos is very much greater since stars are more like filling all of a hollow sphere which is a larger one - supposing it even has any kind of outer limit.
The reason astronomers prefer the latter explanation is not originally that "angels are not a scientific explanation, since they cannot be tested" (as if the explanations they currently accept could), nor was it any disproof of their existance, or proof that their powers are not adequate for stars or planets (something which would have surprised St Thomas Aquinas as well as Riccioli). No, it was that after Newton and after flirting around with his explanation, tied to masses and gravitation, it was apparent that a purely mechanistic cosmic explanation could not handle the universe of Galileo (with Sun in centre of hollow sphere whose inside is covered with stars) any more than St Robert Bellarmine's and Tycho Brahes. After some turns of the planets, the masses of the stars not turning would (in a Galileo type universe) fall into the Sun - and draw the planets in along with them. Only if the closest star in each direction had on its opposite direction a pull equal to and opposite to that of Sun, and that one an even further off behind it, and so on in infinity, only then would a Newton explainable cosmos not collapse. So, they preferred the latter explanation.
James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light, the nutation of Earth’s axis, and catalogued 3222 stars.
The 20 arcseconds or so annual movement would have done fine as a "parallax value" in a Galileo cosmos. But Bradley was into Newton's mechanics more than into Galileo's Geometry. So this was rejected.
I am not sure if "speed of light through vacuum" has been measured with exactitude independently of "aberration of starlight" + presumed speed of Earth in relevant direction (i e opposite one?) : if not, aberration of starlight measured by Bradley and presumed to be what he presumed it to be has been involved in measuring light's speed and therefore it is circular to use that plus speed of Earth to calculate a value identic to observed "annual aberration".
This makes it harder to know what in any stellar distance widening or narrowing is due to which star moving, since "aberration" movement of 20 arcseconds could be part of a dance (liturgic, not bawdy) that angels dance holding stars. And therefore, no, one cannot safely say that even angle of parallax is definitely known in itself, it is only deducible by assumptions on what the différences depend on.
But even if angle of parallax were very definitely known in itself, it would still only prove star is at such or such a distance if one assumed that Geocentrism with angelic movers could be excluded - an assumption which as a Christian believing in angels I cannot make.
If you say "half of my argument is very exact measurements", I not only note there is some doubt about the exactness, but also above all ask "where is the other half"? If the other half was a dubious explanation rather than an certain fact, well, then your whole argument is not a proof.
I won't spare you how the quest for parallax continued through 19th C:
Stellar parallax is most often measured using annual parallax, defined as the difference in position of a star as seen from Earth and Sun, i. e. the angle subtended at a star by the mean radius of Earth's orbit around the Sun. The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is normally measured by observing the position of a star at different times of the year as Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars. The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.
Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, mostly by use of the filar micrometer.
Yes, the intrinsic "movement" of a star (supposed to be a "movement" through our own, which is extrinsic to star, as opposed to a real intrinsic movement in it) is obviously difficult to measure if you measure it by difference between it and the extrinsic movements of nearby stars.
Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond.
But the stars are still only getting their parallax measured by comparisons to other stars.
Even so, if one could have known that each star was really and truly fixed in position to the others, parallax would have conclusively proven Heliocentrism. But on the contrary, we know they aren't. Proper movements per annum differ between stars, and 200 stars have one exceeding 1 arcsecond and going up to 10 arcseconds.
In other words, the stars do move, the movements we see are not JUST due to ourselves moving. And if so, unless you can exclude angels and therefore exclude proper movements that are circular, all the movements we observe could possibly be proper movements and explainable by angelic movers. It is hard to imagine a barrier blocking angels from moving alpha Centauri and 61 Cygni less than 1 arcsecond each direction back and forth per halfyear, if it is not blocking other angels to move like Barnard's star, which has the largest proper motion of all stars, 10.3 seconds of arc per year.
This was the consideration which made me loose all faith in Heliocentrism. AND in astronomic "distance measures" (me being aware that "parallax" based trigonometry was the first rung of the cosmic distance ladder). So, yes, as far as I am concerned, Kepler 452 could still be only 1 light day away and only 41 miles across (or 66 kilometers across). And its very famous planet Kepler 452b could still be also only a light day away, and only 41.91 meters or 137 feet and 6 inches across.
Hans Georg Lundahl
Finding of St Stephen's Relics
and those of Sts Gamaliel, Nicodemus and Abibon