Parallax Prelude

The first step towards solving the puzzle of the Stellar Parallax Clusterfuck is to open the box and familiarise yourself with the individual pieces of the puzzle.

Caveat Emptor
The History of Science informs us it’s totally inappropriate to assume the picture on the box accurately represents the pieces in the box.

In other words:

The picture on the box of the Stellar Parallax Clusterfuck is [in all probability] just as misleading as the classic Geocentric Clusterfuck packaging.

Under the geocentric model, the Sun, Moon, stars, and planets all orbited Earth.

The astronomical predictions of Ptolemy’s geocentric model, developed in the 2nd century CE, served as the basis for preparing astrological and astronomical charts for over 1500 years. The geocentric model held sway into the early modern age, but from the late 16th century onward, it was gradually superseded by the heliocentric model of Copernicus (1473-1543), Galileo (1564-1642), and Kepler (1571-1630).

There was much resistance to the transition between these two theories. Some Christian theologians were reluctant to reject a traditional theory [citation needed] that agreed with Biblical passages.

https://en.wikipedia.org/wiki/Geocentrism

Cosmic Distance Ladder
Inside the Stellar Parallax Clusterfuck packaging the astronomers have squeezed a Cosmic Distance Ladder that reaches out to the furtherest flung corners of the universe dreamt about by Space Cadets and Buzz Lightyear.

The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects.

The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy.

Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on.

Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

https://en.wikipedia.org/wiki/Cosmic_distance_ladder

Mere mortals who have plumbed the depths of Settled Science are fully justified to wonder: What could possibly go wrong with such a massive megaparsec mathematical model?

A distance of one million parsecs is commonly denoted by the megaparsec (Mpc). Astronomers typically express the distances between neighbouring galaxies and galaxy clusters in megaparsecs.

https://en.wikipedia.org/wiki/Megaparsec

The first rung of this colossal cosmic concept is the astronomical unit.

Direct distance measurements are based upon the astronomical unit (AU), which is the distance between the Earth and the Sun.

Kepler’s laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, but provides no measurement of the overall scale of the orbit system.

Radar is used to measure the distance between the orbits of the Earth and of a second body.

From that measurement and the ratio of the two orbit sizes, the size of Earth’s orbit is calculated.

https://en.wikipedia.org/wiki/Cosmic_distance_ladder#Astronomical_unit

The astronomical unit (symbol: au, ua, or AU) is a unit of length, roughly the distance from Earth to the Sun.

However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year.

Originally conceived as the average of Earth’s aphelion and perihelion, since 2012 it has been defined as exactly 1.495978707×1011 m, or about 150 million kilometres (93 million miles).

https://en.wikipedia.org/wiki/Astronomical_unit

The astronomical unit is a mathematical kludge that defines a calculation constant that’s said to represent the continuously varying distance between the Earth and the Sun.

A kludge or kluge is a workaround or quick-and-dirty solution that is clumsy, inelegant, inefficient, difficult to extend and hard to maintain.

https://en.wikipedia.org/wiki/Kludge

149,597,870.7 kilometres = 92,955,807.273 miles

https://www.unitconverters.net/length/km-to-miles.htm

In astronomy, where immense distances have to be very frequently expressed, a common unit is the mean radius of the earth’s orbit, the “astronomical unit” of length, i.e. 92,900,000 miles.

Encyclopædia Britannica – 1911 – Volume 27 – Physical Units
https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Units,_Physical

Building upon the astronomical unit the second shaky step of the Cosmic Distance Ladder is the Trigonometric Parallax [aka Stellar Parallax].

The most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background.

https://en.wikipedia.org/wiki/Cosmic_distance_ladder#Parallax

Stellar parallax remains the standard for calibrating other measurement methods.

https://en.wikipedia.org/wiki/Stellar_parallax

Click to access Design_Of_The_Universe-Fritz_Kahn-1954-377pgs-PHY.pdf

The shenanigans start with the Stellar Parallax [aka Trigonometric Parallax].

This is where the fudge starts to hit the fan as the astroturfing astronomers stoop to scoop up their deliciously deceptive Double Fudge Sundae.

Astroturfing is the practice of masking the sponsors of a message or organization (e.g., political, advertising, religious or public relations) to make it appear as though it originates from and is supported by grassroots participants.

It is a practice intended to give the statements or organizations credibility by withholding information about the source’s financial connection.

https://en.wikipedia.org/wiki/Astroturfing

The Double Fudge Sundae is designed to smooth over the astronomical unit kludge because the astronomers need to sweet talk you into swallowing the absurd assertion that their conceptually crippled Stellar Parallax triangle has “equal length legs”.

The most important fundamental distance measurements come from trigonometric parallax.

As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background.

These shifts are angles in an isosceles triangle, with 2 AU (the distance between the extreme positions of Earth’s orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal length legs.

https://en.wikipedia.org/wiki/Cosmic_distance_ladder#Parallax

Note: The fudge is seen hitting the fan in a later post!

The Double Fudge Sundae is also intended to sweet talk you into swallowing their misdirection that determining the distance to a Star is “essentially similar” to a land survey.

Chapter IX – Parallax

The method of determining the distance of a heavenly body is, in principle, essentially similar to that adopted in land surveys.

Textbook on Spherical Astronomy – W M Smart – 1949
https://archive.org/details/SphericalAstronomy/page/n207

https://en.wikipedia.org/wiki/Trigonometry

Note: The fudge is seen hitting the fan in a later post!

That Damned Elusive Parallax!
The revival of Heliocentrism left many Natural Philosophers wondering Is he in heaven? – Is he in hell? because the Stellar Parallax was damned elusive.

Stellar parallax is so small (as to be unobservable until the 19th century) that its apparent absence was used as a scientific argument against heliocentrism during the early modern age.

https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_and_attempts

Tycho Brahe found “no measurable parallax” with his equipment.

It is clear from Euclid’s geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho Brahe’s principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere (the fixed stars).

https://en.wikipedia.org/wiki/Stellar_parallax#Early_theory_and_attempts

In the year 1572, on November 11th, Tycho discovered in Cassiopeia a new star of great brilliance, and continued to observe it until the end of January, 1573. So incredible to him was such an event that he refused to believe his own eyes until he got others to confirm what he saw. He made accurate observations of its distance from the nine principal stars in Cassiopeia, and proved that it had no measurable parallax.

Later he employed the same method with the comets of 1577, 1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had no measurable parallax and must be very distant.

History of Astronomy- George Forbes – 1909
https://archive.org/details/historyofastrono00forbrich/page/45

Newton was sure the elusive Stellar Parallax was less than 1 arc minute.

Concerning the Distance of the Stars

Thus I have given an account of the system of the planets.

As to the fixed stars, the smallness of their annual parallax proves them to be removed to immense distances from the system of the planets: that this parallax is less than one minute is most certain; and from thence it follows that the distance of the fixed stars is above 360 times greater than the distance of Saturn from the sun.

Newton – Principles of Natural Philosophy
From Newton’s “Principia,” third edition, 1726;
translated by Andrew Motte, 1729, first American edition, 1848.
Source Books In Astronomy – Mcgraw Hill – 1929

https://archive.org/details/in.ernet.dli.2015.177246/page/n100

A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn (or complete rotation), one minute of arc is 1/21600 of a turn.

https://en.wikipedia.org/wiki/Minute_of_arc

The first observed Stellar Parallaxes were reported in arc seconds.

Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years. It was first observed in 1806 by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work “Osservazione e riflessione sulla parallasse annua dall’alfa della Lira”.

https://en.wikipedia.org/wiki/Stellar_Parallax

Apparently, Calandrelli reported a parallax of 4.4 arc seconds for Vega, which is clearly too large – it would represent a distance of less than a quarter of a parsec, less than a light year.

https://en.wikipedia.org/wiki/Talk:Stellar_parallax

Abbot Giuseppe Calandrelli (1749-1827) was an Italian astronomer and mathematician.

https://it.wikipedia.org/wiki/Giuseppe_Calandrelli

Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr.

This star is relatively close at only 25 light-years from the Sun, and, together with Arcturus and Sirius, one of the most luminous stars in the Sun’s neighborhood. It is the fifth-brightest star in the night sky, and the second-brightest star in the northern celestial hemisphere, after Arcturus.

https://en.wikipedia.org/wiki/%CE%91_Lyrae

A second of arc, arcsecond (arcsec), or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn…

https://en.wikipedia.org/wiki/Second_of_arc

milliarcseconds (mas), or thousandths of an arcsecond.

https://en.wikipedia.org/wiki/Second_of_arc#Astronomy

The early Stellar Parallaxes reported by John Brinkley were derived from pairs of celestial co-ordinates i.e. not offsets from neighbouring stars.

Transactions of the Royal Irish Academy – Volume XII – 1815
https://archive.org/details/transactionsofro012oya/page/n151

John Mortimer Brinkley (1763-1835) was the first Royal Astronomer of Ireland and later Bishop of Cloyne. He was President of the Royal Irish Academy (1822–35), President of the Royal Astronomical Society (1831–33).

https://en.wikipedia.org/wiki/John_Brinkley_%28astronomer%29

In some 18th and 19th century astronomical texts, declination is given as North Pole Distance (N.P.D.), which is equivalent to 90 – (declination).

For instance an object marked as declination -5 would have a NPD of 95, and a declination of -90 (the south celestial pole) would have a NPD of 180.

https://en.wikipedia.org/wiki/Declination

Altair, designation α Aquilae (Latinised to Alpha Aquilae, abbreviated Alpha Aql, α Aql), is the brightest star in the constellation of Aquila and the twelfth brightest star in the night sky.

Right ascension 19h 50m 46.99855s
Declination +08° 52′ 05.9563″

Parallax (π) 194.95 ± 0.57 mas

https://en.wikipedia.org/wiki/Alpha_Aquilae

In these early years even negative Stellar Parallaxes were encountered.

Page 139

By 1815 the time had obviously arrived for putting the theory into practice.

But Bessel was to be disappointed again : when he had finished the reduction of the position of 61 Cygni relative to the six different stars he was forced to the conclusion that its parallax was negative!

Attempts To Measure Annual Stellar Parallax
Mari Elen Wyn Williams -1981

Click to access Williams-MEW-1981-PhD-Thesis.pdf

Nowadays, all Stellar Parallaxes are less than 1 arc second.

https://archive.org/details/encyclopaediabri25chisrich/page/789

The angles involved in these calculations are very small and thus difficult to measure. The nearest star to the Sun (and thus the star with the largest parallax), Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec.

This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away.

https://en.wikipedia.org/wiki/Parallax#Stellar_parallax

This is because Friedrich Bessel broke the arc-second-barrier in 1838.

Then in 1838 Friedrich Bessel made the first successful parallax measurement, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.

https://en.wikipedia.org/wiki/Stellar_Parallax

61 Cygni is a binary star system in the constellation Cygnus, consisting of a pair of K-type dwarf stars that orbit each other in a period of about 659 years.

When Joseph von Fraunhofer invented a new type of heliometer, Bessel carried out another set of measurements using this device in 1837 and 1838 at Königsberg.

He published his findings in 1838 with a value of 369.0±19.1 mas to A and 260.5±18.8 to B, and estimated the center point to be at 313.6±13.6. This corresponds to a distance of about 600,000 astronomical units, or about 10.4 light-years. This was the first direct and reliable measurement of the distance to a star other than the Sun.

https://en.wikipedia.org/wiki/61_Cygni#Parallax_measurement

Friedrich Wilhelm Bessel (1784-1846) was a German astronomer, mathematician, physicist and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method of parallax.

In January 1810, at the age of 25, Bessel was appointed director of the newly founded Königsberg Observatory by King Frederick William III of Prussia.

https://en.wikipedia.org/wiki/Friedrich_Bessel

Breaking the arc-second-barrier then became all the rage.

Early in 1839 Thomas Henderson (1798-1844) announced a parallax of nearly 1″ for the bright star α Centauri which he had observed at the Cape, and in the following year Friedrich Georg Wilhelm Struve (1793-1864) obtained from observations made at Pulkowa a parallax of ¼” for Vega ; later work has reduced these numbers to ¾” and ⅒” respectively.

A Short History of Astronomy – Arthur Berry – 1899
https://archive.org/details/ashorthistoryas00berrgoog/page/n428

Uniformitarianism, also known as the Doctrine of Uniformity, is the assumption that the same natural laws and processes that operate in our present-day scientific observations have always operated in the universe in the past and apply everywhere in the universe. … Hutton’s work was later refined by scientist John Playfair and popularised by geologist Charles Lyell’s Principles of Geology in 1830.

https://en.wikipedia.org/wiki/Uniformitarianism_%28science%29

Afterwards, Stellar Parallaxes started slowly shrinking.

61 Cygni is a binary star system in the constellation Cygnus, consisting of a pair of K-type dwarf stars that orbit each other in a period of about 659 years.

61 Cygni first attracted the attention of astronomers when its large proper motion was first demonstrated by Giuseppe Piazzi in 1804.

In 1838, Friedrich Bessel measured its distance from Earth at about 10.4 light-years, very close to the actual value of about 11.4 light-years; this was the first distance estimate for any star other than the Sun, and first star to have its stellar parallax measured.

https://en.wikipedia.org/wiki/61_Cygni

Transactions of the Royal Irish Academy – Volume XII – 1815
https://archive.org/details/transactionsofro012oya/page/n151

The shrinking of Stellar Parallaxes was helped along by new technology.

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.

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.

https://en.wikipedia.org/wiki/Stellar_parallax

A large heliometer was installed at Kuffner Observatory (In Vienna) in 1896, and was used for measuring the distance to other stars by trigonometric parallax.

https://en.wikipedia.org/wiki/Stellar_parallax

The instrument was installed in 1896, an by 1910 it had computed 16 parallax distances to other stars, out of only 108 total known to science at that time.

https://en.wikipedia.org/wiki/Kuffner_Observatory

Breaking the arc-second-barrier transformed Friedrich Bessel into a glittering Star of Settled Science lauded by the Space Cadets.

The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.

https://en.wikipedia.org/wiki/Parallax#Stellar_parallax

Bessel’s breakthrough used a 200 year old method detailed by Galileo.

https://archive.org/details/bub_gb_rfnVXUgSnkcC/page/n346

Bessel‘s improvements in methods and his construction of a great star catalogue based on Bradley’s observations, were both very notable contributions.

But the most memorable of his investigations was the definite detection of the parallax of a star. For this he chose the double star 61 Cygni, not because of its brightness, one obvious criterion of nearness and therefore of large parallax, but for its large proper motion of 5.2 seconds of arc per annum, which is also an indication of relative proximity.

He used Galileo’s method, measuring with the heliometer, at frequent intervals during a year, that star’s distances on the sky from two neighbouring stars, both faint and without sensible proper motions and thus in all probability much more distant from
us than 61 Cygni.

At the end of 1838 he announced that the parallax was about a third of a second of arc, corresponding to a distance of 10 light years.

The remarkable accuracy of this first reliable determination of parallax may be gathered from the fact that the most recent value is not ten per cent different.

A Concise History of Astronomy – Peter Doig -1950
https://archive.org/details/AConciseHistoryOfAstronomy/page/n156

https://archive.org/details/ashorthistoryas00berrgoog/page/n426

Bessel’s brilliance placed the Stars in an expanded light year scale Universe.

Alpha Centauri is the closest star system and closest planetary system to the Solar System at 4.37 light-years (1.34 parsec) from the Sun.

Parallax (π) 754.81 ± 4.11 mas

https://en.wikipedia.org/wiki/Alpha_Centauri

In astronomy, where immense distances have to be very frequently expressed, a common unit is the mean radius of the earth’s orbit, the “astronomical unit” of length, i.e. 92,900,000 miles.

But while this unit serves well for the region of our solar system, its use involves unwieldy numerical coefficients when stellar distances are to be expressed.

Astronomers have therefore adopted a unit of length termed the “light year,” which is the distance traversed by light in a year; this unit is 63,000 times the mean radius of the earth’s orbit.

The relative merits of these units as terms in which astronomical distances may be expressed is exhibited by the values of the distance of the star α. Centauri from our earth, namely, 25,000,000,000,000 miles = 275,000 astronomical units = 4.35 light years.

Encyclopædia Britannica – 1911 – Volume 27 – Physical Units
https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Units,_Physical

But, as always, it’s worth remembering:

All that glitters is not gold.

Gallery | This entry was posted in Astrophysics, Books, Parallax, Science, Solar System, Uniformitarianism. Bookmark the permalink.

4 Responses to Parallax Prelude

  1. Hello,

    I have enjoyed reading all of what has been said and agree with a great deal of it.
    My only comment pertains to the planet’s distances from the Sun and Kepler’s 3rd Law.

    A recent breakthrough provides an easier and extremely accurate way to calculate the distance: (10^7 X AU X 18.59267746 = major axis measured in imperial miles).

    This one equation works for all planets. To calculate the elliptical circumferences, multiply the major axes by Pi(3.1536) instead of the Pi(3.14159). Finally, to validate the orbital distances, divide the circumferences by 216 and then by their individual AUs. They all should end up with the same result which is the Sun’s photospheric circumference (2,714,530.909 imperial miles).

    Thanks,

    Ron

  2. Pingback: Parallax Problems | MalagaBay

  3. Pingback: Parallax Patterns | MalagaBay

  4. Pingback: Parallax Perspective | MalagaBay

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