Podcast Episode 60
image source: https://en.wikipedia.org/wiki/Draco_(constellation) • https://en.wikipedia.org/wiki/Gamma_Draconis • https://upload.wikimedia.org/wikipedia/commons/5/56/Thor_und_die_Midgardsschlange.jpg
THE REVELATION OF THE LIES OF BRITISH BANKING, & ROYAL SOCIETY BACKED LEVIATHAN:
Episode 60: The Speed of Light Lie Exposed! Want to learn about James Bradley's new clothes?
E=MC Squared is meaningless. E=MV and impetus is important history.
Educational systems indoctrinate the mass public into believing in things they really should not.
The fallacious and nonsensical governmental approved "science" of September 11th 2001 NIST report is a fine example of fantasy based propaganda sold as demonstrable Natural principle to humanity that has been conditioned by centuries of 'catechismic' or cataclysmic, style programming.
There is no (measured) velocity of light. The so-called "speed of light" is just an idea and bad metaphysics, it is a religious artifact of a secular faith. It is propaganda with no basis in reality and the work of James Bradley avoids observable astronomy in favor of adherence to the artificial and fallaciously reasoned construct.
The James Bradley story is a great example of illogical metaphysics sold as settled and peer reviewed science.
Unquestioned assumptions lie at the foundation of what too many of us really believe is actual science.
Astronomy 101: Of the motions of the Fixed Stars
(Which is ignored by James Bradley.)
"If an observer notices soon after sunset a star somewhere in the west, and looks for it again a few evenings later at about the same time, he finds it lower down and nearer to the sun; a few evenings later still it is invisible, while its place has now been taken by some other star which was at first farther east in the sky. This star can in turn be observed to approach the sun evening by evening. Or if the stars visible after sunset low down in the east are noticed a few days later, they are found to be higher up in the sky, and their place is taken by other stars at first too low down to be seen. Such observations of stars rising or setting about sunrise or sunset shewed to early observers that the stars were gradually changing their position with respect to the sun, or that the sun was changing its position with respect to the stars. The changes just described, coupled with the fact that the stars do not change their positions with respect to one another, shew that the stars as a whole perform their daily revolution rather more rapidly than the sun, and at such a rate that they gain on it one complete revolution in the course of the year. This can be expressed otherwise in the form that the stars are all moving westward on the celestial sphere, relatively to the sun, so that stars on the east are continually approaching and those on the west continually receding from the sun. But, again, the same facts can be expressed with equal accuracy and greater simplicity if we regard the stars as fixed on the celestial sphere, and the sun as moving on it from west to east among them (that is, in the direction opposite to that of the daily motion), and at such a rate as to complete a circuit of the celestial sphere and to return to the same position after a year.:"
URSA MAJOR DEMONSTRATES WHY BRADLEY WAS WRONG
image source: AA Morrris
"If you’re in the northern U.S., Canada or at a similar latitude, the Big Dipper is circumpolar for you – always above the horizon. These images show the Dipper’s location at around midnight in these seasons. Just remember “spring up and fall down” for the Dipper’s appearance in our northern sky. It ascends in the northeast on spring evenings, and descends in the northwest on fall evenings."
James Bradley and the Royal Society officially ignore sidereal time.
"A sidereal year (from Latin sidus "asterism, star") is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It equals 365.25636 SI days for the J2000.0 epoch. The sidereal year differs from the tropical year, "the period of time required for the ecliptic longitude of the sun to increase 360 degrees", due to the precession of the equinoxes. The sidereal year is 20 min 24.5 s longer than the mean tropical year at J2000.0 (365.242189 days). Before the discovery of the precession of the equinoxes by Hipparchus in the Hellenistic period, the difference between sidereal and tropical year was unknown. For naked-eye observation, the shift of the constellations relative to the equinoxes only becomes apparent over centuries or "ages", and pre-modern calendars such as Hesiod's Works and Days would give the times of the year for sowing, harvest, and so on by reference to the first visibility of stars, effectively using the sidereal year."
"Sidereal, tropical, and anomalistic years"
"The relations among these are considered more fully in Axial precession (astronomy). Each of these three years can be loosely called an astronomical year.
The sidereal year is the time taken for the Earth to complete one revolution of its orbit, as measured against a fixed frame of reference (such as the fixed stars, Latin sidera, singular sidus). Its average duration is 365.256363004 days (365 d 6 h 9 min 9.76 s) (at the epoch J2000.0 = January 1, 2000, 12:00:00 TT)."
"Today the mean tropical year is defined as the period of time for the mean ecliptic longitude of the Sun to increase by 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of the seasons; because of the biological and socio-economic importance of the seasons, the tropical year is the basis of most calendars. The modern definition of mean tropical year differs from the actual time between passages of, e.g., the northward equinox for several reasons explained below. Because of the Earth's axial precession, this year is about 20 minutes shorter than the sidereal year. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds, using the modern definition. (= 365.24219 days of 86400 SI seconds) The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 3 in 2011), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2011). The anomalistic year is usually defined as the time between perihelion passages. Its average duration is 365.259636 days (365 d 6 h 13 min 52.6 s) (at the epoch J2011.0)."
"The draconic year, draconitic year, eclipse year, or ecliptic year is the time taken for the Sun (as seen from the Earth) to complete one revolution with respect to the same lunar node (a point where the Moon's orbit intersects the ecliptic). The year is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within about a month of every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is 346.620075883 days (346 d 14 h 52 min 54 s) (at the epoch J2000.0). This term is sometimes erroneously used for the draconic or nodal period of lunar precession, that is the period of a complete revolution of the Moon's ascending node around the ecliptic: 18.612815932Julian years (6798.331019 days; at the epoch J2000.0)."
CIRCULAR REASONING IS THE ORDER OF THE DAY
The so-called "speed of light" is a lie. It is a concept that relies on James Bradley apparent ignoring of sidereal time.
"The Earth Does Move, After All
Now one thing of great importance should be stressed. Stellar aberration, produced by the direction of motion of the Earth (and as shown below the speed that it has compared to the speed of light) is different from stellar parallax, produced by the change in position of the Earth (which depends upon the size of our orbit, compared to the distance of the star); but it is still produced by our motion. In other words, although what Bradley discovered was not the stellar parallax he and others had been looking for during the previous century and a half, it was irrefutable proof that the Earth does move. In fact, it is also a measure of how fast the Earth moves, because the size of the aberration is a direct observation of a particular ratio, namely the speed of the Earth compared to the speed of light. For in the diagrams showing how the direction of falling rain or "falling" light would be altered by an observer's motion, the size of the angular change in direction is directly related to the ratio of the speed."
MAINSTREAM "SCIENCE" IS FILLED WITH EXAMPLES OF "GREAT MINDS" WHO GOT EVERYTHING WRONG BUT TURNED OUT TO BE RIGHT, ANYWAY
James Bradley's predecessor:
He got it wrong too. But so right at the same time. Modern education is indoctrination based upon what can best be described as fallaciously reasoned mathematical catechism.
"Ole Christensen Rømer (Danish: [ˈo(ː)lə ˈʁœːˀmɐ]; 25 September 1644 – 19 September 1710) was a Danish astronomer who in 1676 made the first quantitative measurements of the speed of light.
Rømer also invented the modern thermometer showing the temperature between two fixed points, namely the points at which water respectively boils and freezes.
In scientific literature alternative spellings such as "Roemer", "Römer", or "Romer" are common."
"By trial and error, during eight years of observations Rømer worked out how to account for the retardation of light when reckoning the ephemeris of Io. He calculated the delay as a proportion of the angle corresponding to a given Earth's position with respect to Jupiter, Δt = 22·(α⁄180°)[minutes]. When the angle α is 180° the delay becomes 22 minutes, which may be interpreted as the time necessary for the light to cross a distance equal to the diameter of the Earth's orbit, H to E. (Actually, Jupiter is not visible from the conjunction point E.) That interpretation makes it possible to calculate the strict result of Rømer's observations: The ratio of the speed of light to the speed with which Earth orbits the sun, which is the ratio of the duration of a year divided by pi as compared to the 22 minutes
65·24·60⁄π·22 ≈ 7,600.
In comparison the modern value is circa 99,792 km s−1⁄29.8 km s−1 ≈ 10,100.
Rømer neither calculated this ratio, nor did he give a value for the speed of light. However, many others calculated a speed from his data, the first being Christiaan Huygens; after corresponding with Rømer and eliciting more data, Huygens deduced that light travelled 6 2⁄3 Earth diameters per second.
Rømer's view that the velocity of light was finite was not fully accepted until measurements of the so-called aberration of light were made by James Bradley in 1727.
In 1809, again making use of observations of Io, but this time with the benefit of more than a century of increasingly precise observations, the astronomer Jean Baptiste Joseph Delambre reported the time for light to travel from the Sun to the Earth as 8 minutes and 12 seconds. Depending on the value assumed for the astronomical unit, this yields the speed of light as just a little more than 300,000 kilometres per second. The modern value is 8 minutes and 19 seconds, and a speed of 299,792.458 km/s.
A plaque at the Observatory of Paris, where the Danish astronomer happened to be working, commemorates what was, in effect, the first measurement of a universal quantity made on this planet."
"Rømer's determination of the speed of light was the demonstration in 1676 that light has a finite speed, and so does not travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer (1644–1710),[note 1] who was working at the Royal Observatory in Paris at the time.
By timing the eclipses of the Jupiter moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun. This would give light a velocity of about 220,000 kilometres per second in SI units, about 26% lower than the true value of 299,792.458 km/s.
Rømer's theory was controversial at the time he announced it, and he never convinced the director of the Paris Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period, such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley."
There are numerous examples of this propaganda phenomena of inverted reasoning and the replacing of mathematical fallacy for actual and demonstrable reality.
Royal Society indoctrinated and peer reviewed and approved minds demand adherence to heliocentric catechism no matter how irrational such belief is.
BEHOLD THE BIBLICAL BEAST: THE DRAGON OF THE INTERNATIONAL BANKING CITY OF LONDON ITSELF
"Gamma Draconis (γ Draconis, abbreviated Gamma Dra, γ Dra), also named Eltanin, is a star in the northern constellation of Draco. Contrary to its gamma-designation (historically third-ranked), it is the brightest star in Draco at magnitude 2.4, outshining Rastaban (Beta Draconis) by nearly half a magnitude. In 1.5 million years, Eltanin will pass within 28 light years of Earth. For a period, if its current absolute magnitude does not change, it will be the brightest star in the night sky, nearly as bright as Sirius is at present. It is by far the brightest star having a zenith above a point near London (and thus Leipzig, Dusseldorf, Astana and Calgary) which occurs near midnight (24:00h) at London which led to its vaunting in these places as the "zenith star" or "London zenith star".[n 1] From other locations it has a nearby bright, well-known star in Lyra in night sky; finding Vega, Eltanin is the red star just north-northwest of it. Eltanin is at a distance of 154.3 light-years (47.3 parsecs) from the Sun, as determined by parallax measurements from the Hipparcos astrometry satellite. In 1728, while unsuccessfully attempting to measure the parallax of this star, James Bradley discovered the aberration of light resulting from the movement of the Earth. Bradley's discovery confirmed Copernicus' theory that the Earth revolved around the Sun."
A CIRCULAR FALLACY CASE STUDY
"Circular reasoning (Latin: circulus in probando, "circle in proving"; also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. The components of a circular argument are often logically valid because if the premises are true, the conclusion must be true. Circular reasoning is not a formal logical fallacy but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Begging the question is closely related to circular reasoning, and in modern usage the two generally refer to the same thing.
Circular reasoning is often of the form: "A is true because B is true; B is true because A is true." Circularity can be difficult to detect if it involves a longer chain of propositions. Academic Douglas Walton used the following example of a fallacious circular argument:
Wellington is in New Zealand.
Therefore, Wellington is in New Zealand.
He notes that, although the argument is deductively valid, it cannot prove that Wellington is in New Zealand because it contains no evidence that is distinct from the conclusion. The context – that of an argument – means that the proposition does not meet the requirement of proving the statement; thus, it is a fallacy. He proposes that the context of a dialogue determines whether a circular argument is fallacious: if it forms part of an argument, then it is. Citing Cederblom and Paulsen 1986:109, Hugh G. Gauch observes that non-logical facts can be difficult to capture formally:
'Whatever is less dense than water will float, because whatever is less dense than water will float' sounds stupid, but 'Whatever is less dense than water will float, because such objects won't sink in water' might pass."
THE ABOVE CONCEPT RELIES ON THE BELOW CONCEPT:
Peer reviewed "Royal Society" methods rely on inverted reasoning.
"An argument from authority, also called an appeal to authority, or argumentum ad verecundiam is a form of defeasible argument in which a claimed authority's support is used as evidence for an argument's conclusion. It is well known as a fallacy, though it is used in a cogent form when all sides of a discussion agree on the reliability of the authority in the given context."
The magic of authority – failure becomes success by means of "alchemy".
"This discovery of what became known as the aberration of light was, for all realistic purposes, conclusive evidence for the movement of the Earth, and hence for the correctness of Aristarchus' and Kepler's theories; it was announced to the Royal Society in January 1729 (Phil. Trans. xxxv. 637). The theory of the aberration also gave Bradley a means to improve on the accuracy of the previous estimate of the speed of light, which had previously been estimated by the work of Ole Rømer and others."
So wrong it is right!
Ad hoc patchwork acts like very real mental cement, binding nonsense into what is sold as "science".
"While classical reasoning gives intuition for aberration, it leads to a number of physical paradoxes observable even at the classical level (see history). The theory of special relativity is required to correctly account for aberration. The relativistic explanation is very similar to the classical one however, and in both theories aberration may be understood as a case of addition of velocities."
This expiation, which is 'peer reviewed' and Royal Society sanctioned, and accepted catechism and dogma or rather, mass marketed "settled science":
"Aberration may be explained as the difference in angle of a beam of light in different inertial frames of reference. A common analogy is to consider the apparent direction of falling rain. If rain is falling vertically in the frame of reference of a person standing still, then to a person moving forwards the rain will appear to arrive at an angle, requiring the moving observer to tilt their umbrella forwards. The faster the observer moves, the more tilt is needed."
The spell binding power of peer reviewed and officially sanctioned authority has over human imagination and subsequent behavior is truly magical.
Light as actual and Natural phenomena is demonstrably nothing like rain.
James Bradley conducted no real world experiment to establish his concept. In fact he was looking for parallax which he failed to find. Instead of the Royal Society promoting the logical conclusion, that heliocentric theory is flawed and the model of Ptolemy and geocentric theory better describes natural and demonstrable reality, we get peer approved and pavlovian rewarded Royal stamped propaganda nonsense.
"The Search for (Circularly Reasoned) Proof That the Earth Moves"
"Prior to the Copernican revolution the Earth was presumed to be fixed in place, neither rotating on its axis nor revolving around the Sun. The daily westward motion of the stars caused by our rotation was thought to be a real motion of the Celestial Sphere around the Earth; and the annual eastward motion of the Sun caused by our orbital motion was thought to be an orbital motion of the Sun around the Earth. But if Copernicus was correct in putting the Sun in the center of the Solar System, then the Earth must be moving, and there are presumably effects caused by its motion that we ought to be able to see.
This had been realized even in ancient times, in discussions about the rotation of the Earth (though as is the case today, these were often more heated arguments than reasoned discussions). The general feeling was that the Earth could not move, because if it did (1) we would feel a strong wind blowing in the opposite direction to our motion, due to the difference between the motion of the air and the Earth; and (2) things thrown upwards would fall to the west of their expected position, because of the eastward motion of the Earth underneath them, while they were in flight.
In modern thinking (Galilean relativity, to be specific), such effects are not expected, because at any given time everything which is at rest relative to us is moving eastward with us, while we rotate, at the same rate that we are; and any motion that we might observe things to have if we were at rest would appear the same even if we were moving, insofar as our motion is uniform.
But if we can't observe the effects of our motion directly, how are we to tell whether we are moving at all?
Very early on, it was realized that if the Earth moved around the Sun the positions of the stars would change, due to stellar parallax. And in fact, many observers in the late 1500's claimed to have actually observed such changes; but the much more accurate observations of Tycho Brahe showed that there was no change in stellar positions which could be attributed to anything other than observational errors; and given the lack of any reliable observations of stellar parallax, Tycho rejected the idea that the Earth moved. The exact reason he did so isn't entirely clear (though it may have had to do with erroneous interpretations of the apparent size of stars of different brightness), but we can be certain that if he hadobserved stellar parallax, he would have adopted the Copernican view of things.
We "Know" Copernicus Was Right; But Can We Prove It?
By the early 1600's Galileo's thought and physical experiments on the nature of motion and his astronomical observations had led him to the basic premise of Galilean relativity: the laws of nature should appear the same no matter how you are moving. Whatever you can hope to observe when at rest should appear the same in terms of the laws of nature if you are moving (though the actual observations might need some minor corrections caused by non-uniform motions). In other words, ancient objections that if we moved we would see various effects caused by that movement (which we do not see) are incorrect. In general, things should look the same whether (as in the case of students in my classroom at LBCC) we are moving to the east at 850 miles per hour, or we are at rest.
In the about the same era (though concluding a bit earlier) Kepler showed that the motions of the planets could be far more easily and elegantly explained as being due to elliptical motions around the Sun, rather than some complex combination of circular motions around the Earth; and the result of the combination of Galileo's principles of motion and Kepler's analysis of planetary motions was that most natural philosophers (that is, scientists) of the early to mid 1600's came to accept the reality of the Earth's motion without any observational proof that it did move. But that didn't affect the desire to observe the effects of that motion, and in some ways made that desire even stronger, for it is unsettling to believe in a scientific theory without any observational proof to support it.
Unfortunately, the parallactic movement of stars caused by our orbital motion around the Sun is incredibly small (smaller, even, than the size of the smallest stellar images on every photograph of the sky taken more than a few years ago), and the technology required to observe that motion would not be achieved until the 1800's. So for over two hundred years, astronomers and other scientists might have believed the Copernican theory without any observational proof that it was correct; but during that interval the fact that stellar parallax was so incredibly small (meaning that the stars are so incredibly far away) wasn't known, and it was always hoped that "any day now" more accurate observations would provide the evidence needed to prove that we are moving. And so the search went on and on.
By the late 1600's it had been shown that Polaris, whose altitude is relatively constant on account of its position near the North Celestial Pole, and as a result is a little easier to accurately measure than for stars whose altitudes change dramatically (which required corrections due to atmospheric refraction that were much larger than the quantities being measured; meaning that any error in those corrections could destroy the evidence being looked for), changed its position in a regular manner by 40 seconds of arc (40") each year. Unfortunately, the direction of the change was not what one would have expected if it were caused by stellar parallax, so additional observations of other stars were attempted, to clarify the matter.
Bradley's Efforts to Observe Stellar Parallax
The star of greatest importance at this point in the story is γ (gamma) Draconis, also known as Eltanin, or Etamin (it is this sort of confusion in common names that led Bayer to adopt Greek letters for enumerating the stars), which was soon found to have an alteration in its position similar to that of Polaris. (The reason Eltanin/Etamin was chosen for this purpose is that it passes nearly overhead in London, and by observing it as it passed near the zenith on different dates the effects of atmospheric refraction, which are zero at the zenith, could be ignored.)
In 1725 James Bradley, who held a position at Oxford as astronomer and natural philosopher, began observations of γ Draconis at the home of a friend, Samuel Molyneux. Using a telescope attached to a chimney so that it pointed nearly vertically, he changed the position of the telescope very slightly, and very accurately measured its change in position using a screw and plumb-line; and over the course of a year or so found that the star did indeed vary in position during the course of the year by 40 arc-seconds, just like Polaris. But, exactly like Polaris, the change in motion was in the wrong direction for stellar parallax, as shown in the following diagram:
How Bradley's observations differed from the expected effects of parallax. As shown on the left, as the Earth moves to one side of its orbit, γ Draconis should move to the opposite side of its parallactic ellipse (the path the star seems to follow during the year as a result of our motion around the Sun). Thus, when the Earth is at points A, B and C, the star should appear to be at points a, b and c. Instead, as shown on the right, as the Earth moves from one point to the next the apparent positions are shifted in the direction of the Earth's motion, which is a quarter circle ahead of the expected parallactic shift. In addition (although not demonstrated here), the amount of the parallactic shift should depend upon the star's distance, being larger for closer stars and smaller for more distant stars; whereas the so-called stellar aberration observed by Bradley is the same for every star in a given region, regardless of its distance. (Parallax produces an elliptical motion, circular at the Ecliptic poles and linear at the Ecliptic plane, whose semi-major axis equals the reciprocal of each star's distance in parsecs, which is of course different for different stars. Stellar aberration produces an elliptical motion, circular at the Ecliptic poles, and linear at the Ecliptic plane, whose semi-major axis equals a constant regardless of the distance or angular position of the star, that constant being equal to one radian multiplied by the ratio of the Earth's orbital velocity to the speed of light. Said statements to be explained in later revisions of this page.)"
"Confronted by observations which made no sense in terms of the Earth's supposed motion, Bradley decided to make additional observations,..."
"A Fortuitous Discovery"
"Confronted by observations which made no sense in terms of the Earth's supposed motion, Bradley decided to make additional observations, first of other stars that passed very nearly overhead, then, by improving the mount of the telescope so that it could be just as accurately aligned over an angle of more than three degrees from the vertical, still other stars. But no matter which stars he observed the annual motion presumably produced by the Earth's motion around the Sun was always in the wrong direction, and always the same size, despite the probably different distances of the stars involved. What in the world could possibly be the cause of this inexplicable result?
One possibility was that the axis of the Earth did not maintain a constant position in space, or even move (causing the precession of the Equinoxes) around the pole of the Earth's orbit, as shown by Copernicus, at a constant rate; but had an additional annual motion -- a sort of "nodding", or nutation -- that made the stars merely seem to change their positions, because those positions were being measured relative to the (changing) position of the Earth's axis of rotation. And in fact, nearly twenty years later, after a careful study of the motions of the stars during the 18-year cycle of lunar orbital changes, Bradley announced that there was indeed a nutation of the Earth's axis, related to the motion of the Moon. However, this was not the cause of the annual changes in stellar position, and a completely different explanation was required.
As often happens in science (recall Newton's "discovery" of the nature of gravity when an apple fell to the ground while he was in his orchard), the answer came from a completely unscientific pursuit. While sailing on the Thames Bradley noticed that as he turned the boat the direction of a vane on the mast changed, and being aware that the change was not due to a change in the wind, but in the direction of the boat, he realized that the puzzling change in the direction of the stars might be caused not by the changing position of the Earth, but by the its changing motion.
To understand this, consider the diagram below:
The "aberration" of rain and light "falling" toward a moving observer. On the left an observer is running in the rain. The moving observer will not see the rain falling from its true direction, but at an angle to that direction determined by his speed divided by the rain's speed, and the angle of his motion relative to the rain's actual motion (shown here as being vertical, and therefore perpendicular to his motion). The faster he goes the more nearly the rain will appear to fall horizontally; the slower he goes, the more nearly it will appear to fall vertically. Similarly, as shown on the right, a beam of light from a distant star will appear to be coming from a little "in front" of its true position because of the motion of the Earth, at an angle to its true position determined by the Earth's speed, divided by the speed of light, times the sine of the angle between the direction to the star and the direction of the Earth's motion. Since the Earth's orbital velocity is one ten-thousandth (1/10,000) of the speed of light, the star's position changes by up to one ten-thousandth of a radian (360 degrees divided by 2π, divided by 10,000), or approximately 20 seconds of arc whether the star is near the Ecliptic Pole, or in the plane of the Ecliptic, but at right angles to the Earth's current direction of motion.
Now let's use another diagram, to apply this to the orbit of the Earth:
The change in stellar position (stellar aberration) caused by the Earth's velocity of motion around the Sun. In the diagrams on the left, the Earth is shown at point A, moving in the direction of the arrow. This produces a change in the position of the star relative to its "correct" position, shown by the arrow going from the star's average position, to point b. In the diagrams on the right, the Earth is shown at point B, moving in the direction of the arrow shown there. This produces the change in position shown by the arrow going from the star's average position, to point c. Thus the change in position (stellar aberration) caused by the Earth's velocity is three months ahead of the change expected for a stellar parallax produced by a change in the position, which is exactly what Bradley had observed.
The Earth Does Move, After All
Now one thing of great importance should be stressed. Stellar aberration, produced by the direction of motion of the Earth (and as shown below the speed that it has compared to the speed of light) is different from stellar parallax, produced by the change in position of the Earth (which depends upon the size of our orbit, compared to the distance of the star); but it is still produced by our motion. In other words, although what Bradley discovered was not the stellar parallax he and others had been looking for during the previous century and a half, it was irrefutable proof that the Earth does move. In fact, it is also a measure of how fast the Earth moves, because the size of the aberration is a direct observation of a particular ratio, namely the speed of the Earth compared to the speed of light. For in the diagrams showing how the direction of falling rain or "falling" light would be altered by an observer's motion, the size of the angular change in direction is directly related to the ratio of the speed. Without going into the geometrical details,
the speed of the Earth / the speed of light = the angle of stellar aberration / the size of a radian,
where a radian is the angle in a circle / 2 π = 360 * 3600 / 6.28318531 = 206264.806, or
the speed of the Earth / the speed of light = the angle in seconds of arc / 206264.806
Using the 20 arc-seconds observed by Bradley (the total change in stellar positions was 40 arc-seconds, but half of that is when the star goes one way, when we are on one side of our orbit, and half is when the star goes the other way, when we are on the other side of our orbit) in this equation, we find that the orbital velocity of the Earth is approximately one ten-thousandth of the speed of light. Given our present knowledge of the speed of light (186,400 miles or 300,000 kilometers per second), the Earth's orbital velocity is hence measured as 18 1/2 miles or 30 kilometers per second."