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134-466: Currently, Earth's pole stars are Polaris (Alpha Ursae Minoris), a bright magnitude 2 star aligned approximately with its northern axis that serves as a pre-eminent star in celestial navigation , and a much dimmer magnitude 5.5 star on its southern axis, Polaris Australis (Sigma Octantis). From around 1700 BC until just after 300 AD, Kochab (Beta Ursae Minoris) and Pherkad (Gamma Ursae Minoris) were twin northern pole stars, though neither

268-618: A burner or lamp and would reasonably be described as stella polaris from about the High Middle Ages and onwards, both in Greek and Latin. On his first trans-Atlantic voyage in 1492, Christopher Columbus had to correct for the "circle described by the pole star about the pole". In Shakespeare's play Julius Caesar , written around 1599, Caesar describes himself as being "as constant as the northern star", though in Caesar's time there

402-637: A case of addition of velocities . In the Sun's frame, consider a beam of light with velocity equal to the speed of light c {\displaystyle c} , with x and y velocity components u x {\displaystyle u_{x}} and u y {\displaystyle u_{y}} , and thus at an angle θ {\displaystyle \theta } such that tan ⁡ ( θ ) = u y / u x {\displaystyle \tan(\theta )=u_{y}/u_{x}} . If

536-609: A change of aberration of about 5 μas/yr. Highly precise measurements extending over several years can observe this change in secular aberration, often called the secular aberration drift or the acceleration of the Solar System, as a small apparent proper motion . Recently, highly precise astrometry of extragalactic objects using both Very Long Baseline Interferometry and the Gaia space observatory have successfully measured this small effect. The first VLBI measurement of

670-404: A circle. Since he only observed the deviation in declination, and not in right ascension, his calculations for the maximum deviation of a star in the pole of the ecliptic are for its declination only, which will coincide with the diameter of the little circle described by such star. For eight different stars, his calculations are as follows: Based on these calculations, Bradley was able to estimate

804-473: A declination of –82°, meaning it will rise and set daily for latitudes between 8°S and 8°N, and will not rise to viewers north of this latter 8th parallel north . Precession and proper motion mean that Sirius will be a future southern pole star: at 88.4° S declination in the year 66,270 AD; and 87.7° S declination in the year 93,830 AD. Pole stars of other planets are defined analogously: they are stars (brighter than 6th magnitude, i.e. , visible to

938-524: A direct line with the Earth's rotational axis "above" the North Pole —the north celestial pole—Polaris stands almost motionless in the sky, and all the stars of the northern sky appear to rotate around it. Therefore, it makes an excellent fixed point from which to draw measurements for celestial navigation and for astrometry . The elevation of the star above the horizon gives the approximate latitude of

1072-545: A distance of 5° from celestial north. Precession will eventually point the north celestial pole nearer the stars in the constellation Hercules , pointing towards Tau Herculis around 18,400 AD. The celestial pole will then return to the stars in constellation Draco (Thuban, mentioned above) before returning to the current constellation, Ursa Minor. When Polaris becomes the North Star again around 27,800 AD, due to its proper motion it then will be farther away from

1206-592: A distance of several degrees, in the early medieval period, and numerous names referring to this characteristic as polar star have been in use since the medieval period. In Old English, it was known as scip-steorra ("ship-star") . In the Old English rune poem , the T-rune is apparently associated with "a circumpolar constellation", or the planet Mars. In the Hindu Puranas , it became personified under

1340-434: A distant 7° from the pole, never close enough to be taken as marking the pole, while third-magnitude Delta Cygni will be a more helpful pole star, at a distance of 3° from celestial north, around 11,250 AD. Precession will then point the north celestial pole nearer the constellation Lyra , where the second brightest star in the northern celestial hemisphere , Vega , will be a pole star around 14,500 AD, though at

1474-495: A hiatus in 1963–1965. This was originally thought to be due to secular redward (a long term change in redshift that causes light to stretch into longer wavelengths, causing it to appear red) evolution across the Cepheid instability strip , but it may be due to interference between the primary and the first- overtone pulsation modes. Authors disagree on whether Polaris is a fundamental or first-overtone pulsator and on whether it

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1608-399: A major goal of the 19th century theories of luminiferous aether . Augustin-Jean Fresnel proposed a correction due to the motion of a medium (the aether) through which light propagated, known as "partial aether drag" . He proposed that objects partially drag the aether along with them as they move, and this became the accepted explanation for aberration for some time. George Stokes proposed

1742-427: A medium known as the luminiferous aether. His reasoning was the same as Bradley's, but it required that this medium be immobile in the Sun's reference frame and must pass through the earth unaffected, otherwise the medium (and therefore the light) would move along with the earth and no aberration would be observed. He wrote: Upon consideration of the phenomena of the aberration of the stars I am disposed to believe that

1876-487: A parallax for Polaris, but a distance inferred from it is 136.6 ± 0.5  pc (445.5 ly) for Polaris B, somewhat further than most previous estimates and several times more accurate. This was further improved to 137.2 ± 0.3  pc (447.6 ly), upon publication of the Gaia Data Release 3 catalog on 13 June 2022 which superseded Gaia Data Release 2. Polaris is depicted in the flag and coat of arms of

2010-403: A pardon by saying, "I am as constant as the northern star/Of whose true-fixed and resting quality/There is no fellow in the firmament./The skies are painted with unnumbered sparks,/They are all fire and every one doth shine,/But there's but one in all doth hold his place;/So in the world" (III, i, 65–71). Of course, Polaris will not "constantly" remain as the north star due to precession , but this

2144-479: A period of 29.59 ± 0.02 years and an eccentricity of 0.608 ± 0.005 . In 2019, a study by R. I. Anderson gave a period of 29.32 ± 0.11 years with an eccentricity of 0.620 ± 0.008 . There were once thought to be two more widely separated components—Polaris C and Polaris D—but these have been shown not to be physically associated with the Polaris system. Polaris Aa, the supergiant primary component,

2278-427: 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 net effect is that light rays striking the moving observer from the sides in a stationary frame will come angled from ahead in the moving observer's frame. This effect is sometimes called the "searchlight" or "headlight" effect. In

2412-589: A point on the Arctic Circle . Such an observer will see the star transit at the zenith , once every day (strictly speaking sidereal day ). At the time of the March equinox , Earth's orbit carries the observer in a southwards direction, and the star's apparent declination is therefore displaced to the south by an angle of κ {\displaystyle \kappa } . On the September equinox ,

2546-462: A result of ten years ' observations, that Polaris , the Pole Star, exhibited variations in its position amounting to 40″ annually. Some astronomers endeavoured to explain this by parallax, but these attempts failed because the motion differed from that which parallax would produce. John Flamsteed , from measurements made in 1689 and succeeding years with his mural quadrant, similarly concluded that

2680-528: A similar theory, explaining that aberration occurs due to the flow of aether induced by the motion of the Earth. Accumulated evidence against these explanations, combined with new understanding of the electromagnetic nature of light, led Hendrik Lorentz to develop an electron theory which featured an immobile aether, and he explained that objects contract in length as they move through the aether. Motivated by these previous theories, Albert Einstein then developed

2814-526: A small oscillation of the eyepiece, the amount of which (i.e. the deviation from the vertical) was regulated and measured by the introduction of a screw and a plumb line. The instrument was set up in November 1725, and observations on γ Draconis were made starting in December. The star was observed to move 40″ southwards between September and March, and then reversed its course from March to September. At

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2948-450: A table of the first two batches of names approved by the WGSN; which included Polaris for the star α Ursae Minoris Aa. In antiquity, Polaris was not yet the closest naked-eye star to the celestial pole, and the entire constellation of Ursa Minor was used for navigation rather than any single star. Polaris moved close enough to the pole to be the closest naked-eye star, even though still at

3082-473: A telescope of his own erected at the Rectory, Wanstead . This instrument had the advantage of a larger field of view and he was able to obtain precise positions of a large number of stars over the course of about twenty years. During his first two years at Wanstead, he established the existence of the phenomenon of aberration beyond all doubt, and this also enabled him to formulate a set of rules that would allow

3216-550: A very close F6 main-sequence star with a mass of 1.26  M ☉ . Polaris B can be resolved with a modest telescope. William Herschel discovered the star in August 1779 using a reflecting telescope of his own, one of the best telescopes of the time. In January 2006, NASA released images, from the Hubble telescope , that showed the three members of the Polaris ternary system. The variable radial velocity of Polaris A

3350-488: Is 2.5 times brighter today than when Ptolemy observed it, changing from third to second magnitude. Astronomer Edward Guinan considers this to be a remarkable change and is on record as saying that "if they are real, these changes are 100 times larger than [those] predicted by current theories of stellar evolution ". In 2024, researchers led by Nancy Evans at the Harvard & Smithsonian , have studied with more accuracy

3484-450: Is a low-amplitude Population I classical Cepheid variable , although it was once thought to be a type II Cepheid due to its high galactic latitude . Cepheids constitute an important standard candle for determining distance, so Polaris, as the closest such star, is heavily studied. The variability of Polaris had been suspected since 1852; this variation was confirmed by Ejnar Hertzsprung in 1911. The range of brightness of Polaris

3618-401: Is barely visible on a clear night , making it less useful for casual navigational or astronomy alignment purposes. It is a yellow giant 294 light years from Earth. Its angular separation from the pole is about 1° (as of 2000). The Southern Cross constellation functions as an approximate southern pole constellation, by pointing to where a southern pole star would be. At the equator , it

3752-552: Is called stella maris , the sterre of the see, for he ledeth in the see men that saylle and have shyppemannes crafte. Polaris was associated with Marian veneration from an early time, Our Lady, Star of the Sea being a title of the Blessed Virgin. This tradition goes back to a misreading of Saint Jerome 's translation of Eusebius ' Onomasticon , De nominibus hebraicis (written ca. 390). Jerome gave stilla maris "drop of

3886-511: Is crossing the instability strip for the first time or not. The temperature of Polaris varies by only a small amount during its pulsations, but the amount of this variation is variable and unpredictable. The erratic changes of temperature and the amplitude of temperature changes during each cycle, from less than 50  K to at least 170 K, may be related to the orbit with Polaris Ab. Research reported in Science suggests that Polaris

4020-501: Is different from the more accurate relativistic result described above, in the limit of small angle and low velocity they are approximately the same, within the error of the measurements of Bradley's day. These results allowed Bradley to make one of the earliest measurements of the speed of light . In the early nineteenth century the wave theory of light was being rediscovered, and in 1804 Thomas Young adapted Bradley's explanation for corpuscular light to wavelike light traveling through

4154-403: Is distinct from parallax , which is a change in the apparent position of a relatively nearby object, as measured by a moving observer, relative to more distant objects that define a reference frame. The amount of parallax depends on the distance of the object from the observer, whereas aberration does not. Aberration is also related to light-time correction and relativistic beaming , although it

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4288-523: Is given as 1.86–2.13, but the amplitude has changed since discovery. Prior to 1963, the amplitude was over 0.1 magnitude and was very gradually decreasing. After 1966, it very rapidly decreased until it was less than 0.05 magnitude; since then, it has erratically varied near that range. It has been reported that the amplitude is now increasing again, a reversal not seen in any other Cepheid. The period, roughly 4 days, has also changed over time. It has steadily increased by around 4.5 seconds per year except for

4422-482: Is invisible in light-polluted urban skies. During the 1st millennium BC, Beta Ursae Minoris (Kochab) was the bright star closest to the celestial pole, but it was never close enough to be taken as marking the pole, and the Greek navigator Pytheas in ca. 320 BC described the celestial pole as devoid of stars. In the Roman era , the celestial pole was about equally distant between Polaris and Kochab. The precession of

4556-445: Is known as the constant of aberration , conventionally represented by κ {\displaystyle \kappa } . It may be calculated using the relation κ = θ − ϕ ≈ v / c {\displaystyle \kappa =\theta -\phi \approx v/c} substituting the Earth's average speed in the Sun's frame for v {\displaystyle v} and

4690-417: Is often considered separately from these effects. Aberration is historically significant because of its role in the development of the theories of light , electromagnetism and, ultimately, the theory of special relativity . It was first observed in the late 1600s by astronomers searching for stellar parallax in order to confirm the heliocentric model of the Solar System. However, it was not understood at

4824-457: Is only 0.32 arcseconds in the case of an observer at the Equator , where the rotational velocity is greatest. The secular component of aberration, caused by the motion of the Solar System in space, has been further subdivided into several components: aberration resulting from the motion of the solar system barycenter around the center of our Galaxy , aberration resulting from the motion of

4958-495: Is only noticeable over centuries. In Inuit astronomy , Polaris is known as Nuutuittuq ( syllabics : ᓅᑐᐃᑦᑐᖅ ). In traditional Lakota star knowledge, Polaris is named "Wičháȟpi Owáŋžila". This translates to "The Star that Sits Still". This name comes from a Lakota story in which he married Tȟapȟúŋ Šá Wíŋ, "Red Cheeked Woman". However, she fell from the heavens, and in his grief Wičháȟpi Owáŋžila stared down from "waŋkátu" (the above land) forever. The Plains Cree call

5092-405: Is only valid if the observer and source's frames are inertial frames. In practice, because the Earth is not an inertial rest frame but experiences centripetal acceleration towards the Sun, many aberrational effects such as annual aberration on Earth cannot be considered light-time corrections. However, if the time between emission and detection of the light is short compared to the orbital period of

5226-485: Is possible since the transit time of sunlight is short relative to the orbital period of the Earth, so the Earth's frame may be approximated as inertial. In the Earth's frame, the Sun moves, at a mean velocity v = 29.789 km/s, by a distance Δ x = v t {\displaystyle \Delta x=vt} ≈ 14,864.7 km in the time it takes light to reach Earth, t = R / c {\displaystyle t=R/c} ≈ 499 sec for

5360-511: Is possible to see both Polaris and the Southern Cross. The celestial south pole is moving toward the Southern Cross, which has pointed to the south pole for the last 2000 years or so. As a consequence, the constellation is no longer visible from subtropical northern latitudes, as it was in the time of the ancient Greeks . Around 200 BC, the star Beta Hydri was the nearest bright star to the celestial south pole. Around 2800 BC, Achernar

5494-471: Is the closest Cepheid variable to Earth so its physical parameters are of critical importance to the whole astronomical distance scale . It is also the only one with a dynamically measured mass. The Hipparcos spacecraft used stellar parallax to take measurements from 1989 and 1993 with the accuracy of 0.97  milliarcseconds (970 microarcseconds), and it obtained accurate measurements for stellar distances up to 1,000 pc away. The Hipparcos data

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5628-441: Is this apparently anomalous motion that so mystified early astronomers. A special case of annual aberration is the nearly constant deflection of the Sun from its position in the Sun's rest frame by κ {\displaystyle \kappa } towards the west (as viewed from Earth), opposite to the apparent motion of the Sun along the ecliptic (which is from west to east, as seen from Earth). The deflection thus makes

5762-471: Is true north; the rest of the time it is displaced eastward or westward, and the bearing must be corrected using tables or a rule of thumb . The best approximation is made using the leading edge of the " Big Dipper " asterism in the constellation Ursa Major. The leading edge (defined by the stars Dubhe and Merak ) is referenced to a clock face, and the true azimuth of Polaris worked out for different latitudes. The apparent motion of Polaris towards and, in

5896-492: The Canadian Inuit territory of Nunavut , the flag of the U.S. states of Alaska and Minnesota , and the flag of the U.S. city of Duluth, Minnesota . Aberration of light In astronomy , aberration (also referred to as astronomical aberration , stellar aberration , or velocity aberration ) is a phenomenon where celestial objects exhibit an apparent motion about their true positions based on

6030-503: The International Celestial Reference Frame (ICRF3) adopted a recommended galactocentric aberration constant of 5.8 μas/yr and recommended a correction for secular aberration to obtain the highest positional accuracy for times other than the reference epoch 2015.0. Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to

6164-514: The aether drag theories of Augustin Fresnel (in 1818) and G. G. Stokes (in 1845), and for Hendrik Lorentz 's aether theory of electromagnetism in 1892. The aberration of light, together with Lorentz's elaboration of Maxwell's electrodynamics , the moving magnet and conductor problem , the negative aether drift experiments , as well as the Fizeau experiment , led Albert Einstein to develop

6298-523: The naked eye at night. The position of the star lies less than 1° away from the north celestial pole , making it the current northern pole star . The stable position of the star in the Northern Sky makes it useful for navigation . As the closest Cepheid variable its distance is used as part of the cosmic distance ladder . The revised Hipparcos stellar parallax gives a distance to Polaris of about 433 light-years (133 parsecs ), while

6432-414: The orbital velocity v {\displaystyle v} of Earth (in the Sun's rest frame) varies periodically during the year as the planet traverses its elliptic orbit and consequently the aberration also varies periodically, typically causing stars to appear to move in small ellipses . Approximating Earth's orbit as circular, the maximum displacement of a star due to annual aberration

6566-453: The speed of light c {\displaystyle c} . Its accepted value is 20.49552  arcseconds (sec) or 0.000099365  radians (rad) (at J2000 ). Assuming a circular orbit , annual aberration causes stars exactly on the ecliptic (the plane of Earth's orbit) to appear to move back and forth along a straight line, varying by κ {\displaystyle \kappa } on either side of their position in

6700-452: The "Star of the Sea" metaphor, saying that Mary is the "Star of the Sea" to be followed on the way to Christ, "lest we capsize amid the storm-tossed waves of the sea." In Mandaean cosmology , the Pole Star is considered to be auspicious and is associated with the World of Light ("heaven"). Mandaeans face north when praying, and temples are also oriented towards the north. On the contrary,

6834-493: The 'A' refers to what is now known to be the Aa/Ab pair. Polaris Aa is an evolved yellow supergiant of spectral type F7Ib with 5.4 solar masses ( M ☉ ). It is the first classical Cepheid to have a mass determined from its orbit. The two smaller companions are Polaris B, a 1.39  M ☉ F3 main-sequence star orbiting at a distance of 2,400  astronomical units (AU), and Polaris Ab (or P),

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6968-448: The 200 years between its observation and the explanation by Albert Einstein. The first classical explanation was provided in 1729, by James Bradley as described above, who attributed it to the finite speed of light and the motion of Earth in its orbit around the Sun . However, this explanation proved inaccurate once the wave nature of light was better understood, and correcting it became

7102-525: The 5th century, when it was still removed from the celestial pole by about 8°. It was known as scip-steorra ("ship-star") in 10th-century Anglo-Saxon England , reflecting its use in navigation. In the Vishnu Purana , it is personified under the name Dhruva ("immovable, fixed"). The name stella polaris was coined in the Renaissance, even though at that time it was well recognized that it

7236-481: The Earth is moving at velocity v {\displaystyle v} in the x direction relative to the Sun, then by velocity addition the x component of the beam's velocity in the Earth's frame of reference is u x ′ = u x + v {\displaystyle u_{x}'=u_{x}+v} , and the y velocity is unchanged, u y ′ = u y {\displaystyle u_{y}'=u_{y}} . Thus

7370-429: The Earth, the Earth may be approximated as an inertial frame and aberrational effects are equivalent to light-time corrections. The Astronomical Almanac describes several different types of aberration, arising from differing components of the Earth's and observed object's motion: Annual aberration is caused by the motion of an observer on Earth as the planet revolves around the Sun . Due to orbital eccentricity ,

7504-637: The Galaxy relative to the Local Group , and aberration resulting from the motion of the Local Group relative to the cosmic microwave background . Secular aberration affects the apparent positions of stars and extragalactic objects. The large, constant part of secular aberration cannot be directly observed and "It has been standard practice to absorb this large, nearly constant effect into the reported" positions of stars. In about 200 million years,

7638-534: The Marian Polar Star"), a collection of Marian poetry published by Nicolaus Lucensis (Niccolo Barsotti de Lucca) in 1655. Its name in traditional pre-Islamic Arab astronomy was al-Judayy الجدي ("the kid", in the sense of a juvenile goat ["le Chevreau"] in Description des Etoiles fixes), and that name was used in medieval Islamic astronomy as well. In those times, it was not yet as close to

7772-584: The Polaris' smaller companion orbit using the CHARA Array . During this observation campaign they have succeeded in shooting Polaris features on its surface; large bright places and dark ones have appeared in close-up images, changing over time. Further, Polaris diameter size has been re-measured to 46  R ☉ , using the Gaia distance of 446 ± 1 light-years, and its mass was determined at 5.13  M ☉ . Because Polaris lies nearly in

7906-597: The Sun appear to be behind (or retarded) from its rest-frame position on the ecliptic by a position or angle κ {\displaystyle \kappa } . This deflection may equivalently be described as a light-time effect due to motion of the Earth during the 8.3 minutes that it takes light to travel from the Sun to Earth. The relation with κ {\displaystyle \kappa } is : [0.000099365 rad / 2 π rad] x [365.25 d x 24 h/d x 60 min/h] = 8.3167 min ≈ 8 min 19 sec = 499 sec. This

8040-414: The Sun circles the galactic center, whose measured location is near right ascension (α = 266.4°) and declination (δ = −29.0°). The constant, unobservable, effect of the solar system's motion around the galactic center has been computed variously as 150 or 165 arcseconds. The other, observable, part is an acceleration toward the galactic center of approximately 2.5 × 10  m/s , which yields

8174-415: The Sun's frame. A star that is precisely at one of the ecliptic poles (at 90° from the ecliptic plane) will appear to move in a circle of radius κ {\displaystyle \kappa } about its true position, and stars at intermediate ecliptic latitudes will appear to move along a small ellipse . For illustration, consider a star at the northern ecliptic pole viewed by an observer at

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8308-656: The angle of the light in the Earth's frame in terms of the angle in the Sun's frame is In the case of θ = 90 ∘ {\displaystyle \theta =90^{\circ }} , this result reduces to tan ⁡ ( θ − ϕ ) = v / c {\displaystyle \tan(\theta -\phi )=v/c} , which in the limit v / c ≪ 1 {\displaystyle v/c\ll 1} may be approximated by θ − ϕ = v / c {\displaystyle \theta -\phi =v/c} . The reasoning in

8442-598: The apparent motion, over a period of 20 years, of 555 extragalactic objects towards the center of our galaxy at equatorial coordinates of α = 263° and δ = −20° indicated a secular aberration drift 6.4 ±1.5 μas/yr. Later determinations using a series of VLBI measurements extending over almost 40 years determined the secular aberration drift to be 5.83 ± 0.23 μas/yr in the direction α = 270.2 ± 2.3° and δ = −20.2° ± 3.6°. Optical observations using only 33 months of Gaia satellite data of 1.6 million extragalactic sources indicated an acceleration of

8576-422: The apparent position of a star to an observer on Earth varies periodically over the course of a year as the Earth's velocity changes as it revolves around the Sun, by a maximum angle of approximately 20  arcseconds in right ascension or declination . The term aberration has historically been used to refer to a number of related phenomena concerning the propagation of light in moving bodies. Aberration

8710-401: The beam in the observer's frame at the moment of observation is tilted compared to the beam in source's frame, which can be understood as an aberrational effect. Thus, a person in the light source's frame would describe the apparent tilting of the beam in terms of aberration, while a person in the observer's frame would describe it as a light-time effect. The relationship between these phenomena

8844-472: The boat relative to the wind direction. However, there is no record of this incident in Bradley's own account of the discovery, and it may therefore be apocryphal . The following table shows the magnitude of deviation from true declination for γ Draconis and the direction, on the planes of the solstitial colure and ecliptic prime meridian, of the tangent of the velocity of the Earth in its orbit for each of

8978-534: The calculation of the effect on any given star at a specified date. Bradley eventually developed his explanation of aberration in about September 1728 and this theory was presented to the Royal Society in mid January the following year. One well-known story was that he saw the change of direction of a wind vane on a boat on the Thames, caused not by an alteration of the wind itself, but by a change of course of

9112-407: The case of annual aberration of starlight, the direction of incoming starlight as seen in the Earth's moving frame is tilted relative to the angle observed in the Sun's frame. Since the direction of motion of the Earth changes during its orbit, the direction of this tilting changes during the course of the year, and causes the apparent position of the star to differ from its true position as measured in

9246-421: The case where a distant star is motionless relative to the Sun, and the star is extremely far away, so that parallax may be ignored. In the rest frame of the Sun, this means light from the star travels in parallel paths to the Earth observer, and arrives at the same angle regardless of where the Earth is in its orbit. Suppose the star is observed on Earth with a telescope, idealized as a narrow tube. The light enters

9380-407: The celestial north pole, on 24 March 2100. Precession will next point the north celestial pole at stars in the northern constellation Cepheus . The pole will drift to space equidistant between Polaris and Gamma Cephei ("Errai") by 3000 AD, with Errai reaching its closest alignment with the northern celestial pole around 4200 AD. Iota Cephei and Beta Cephei will stand on either side of

9514-408: The classical derivation above. Aberration is related to two other phenomena, light-time correction , which is due to the motion of an observed object during the time taken by its light to reach an observer, and relativistic beaming , which is an angling of the light emitted by a moving light source. It can be considered equivalent to them but in a different inertial frame of reference. In aberration,

9648-462: The components of the light beam in the Earth's frame in terms of the components in the Sun's frame. The angle of the beam in the Earth's frame is thus In the case of θ = 90 ∘ {\displaystyle \theta =90^{\circ }} , this result reduces to sin ⁡ ( θ − ϕ ) = v / c {\displaystyle \sin(\theta -\phi )=v/c} , and in

9782-405: The constant of aberration at 20.2", which is equal to 0.00009793 radians, and with this was able to estimate the speed of light at 183,300 miles (295,000 km) per second. By projecting the little circle for a star in the pole of the ecliptic, he could simplify the calculation of the relationship between the speed of light and the speed of the Earth's annual motion in its orbit as follows: Thus,

9916-402: The constellation Ursa Minor, Cynosura (from the Greek κυνόσουρα "the dog's tail"), became associated with the pole star in particular by the early modern period. An explicit identification of Mary as stella maris with the polar star ( Stella Polaris ), as well as the use of Cynosura as a name of the star, is evident in the title Cynosura seu Mariana Stella Polaris (i.e. "Cynosure, or

10050-422: The current star, with stars that will be "near-north" indicators when no North Star exists during the cycle, including each star's average brightness and closest alignment to the north celestial pole during the cycle: Currently, there is no South Pole Star like Polaris , the so-called North Star . Sigma Octantis is the closest near naked-eye star to the south celestial pole, but at apparent magnitude 5.47 it

10184-663: The declination of Polaris was 40″ less in July than in September. Robert Hooke , in 1674, published his observations of γ Draconis , a star of magnitude 2 which passes practically overhead at the latitude of London (hence its observations are largely free from the complex corrections due to atmospheric refraction ), and concluded that this star was 23″ more northerly in July than in October. Consequently, when Bradley and Samuel Molyneux entered this sphere of research in 1725, there

10318-467: The description above is only approximate. Aberration is more accurately calculated using Earth's instantaneous velocity relative to the barycenter of the Solar System. Note that the displacement due to aberration is orthogonal to any displacement due to parallax . If parallax is detectable, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It

10452-519: The distance. The next major step in high precision parallax measurements comes from Gaia , a space astrometry mission launched in 2013 and intended to measure stellar parallax to within 25 microarcseconds (μas). Although it was originally planned to limit Gaia's observations to stars fainter than magnitude 5.7, tests carried out during the commissioning phase indicated that Gaia could autonomously identify stars as bright as magnitude 3. When Gaia entered regular scientific operations in July 2014, it

10586-466: The equinoxes takes about 25,770 years to complete a cycle. Polaris' mean position (taking account of precession and proper motion ) will reach a maximum declination of +89°32'23", which translates to 1657" (or 0.4603°) from the celestial north pole, in February 2102. Its maximum apparent declination (taking account of nutation and aberration ) will be +89°32'50.62", which is 1629" (or 0.4526°) from

10720-417: The four months where the extremes are found, as well as expected deviation from true ecliptic longitude if Bradley had measured its deviation from right ascension: Bradley proposed that the aberration of light not only affected declination, but right ascension as well, so that a star in the pole of the ecliptic would describe a little ellipse with a diameter of about 40", but for simplicity, he assumed it to be

10854-473: The future, away from the celestial pole, is due to the precession of the equinoxes . The celestial pole will move away from α UMi after the 21st century, passing close by Gamma Cephei by about the 41st century , moving towards Deneb by about the 91st century . The celestial pole was close to Thuban around 2750 BC, and during classical antiquity it was slightly closer to Kochab (β UMi) than to Polaris, although still about 10 ° from either star. It

10988-401: The inertial frame of the Sun. 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

11122-446: The lag angle would be imperceptible. What they both overlooked is that aberration (as understood only later) would exactly counteract the lag even if large, leaving this eclipse method completely insensitive to light speed. (Otherwise, shadow-lag methods could be made to sense absolute translational motion, contrary to a basic principle of relativity .) The phenomenon of aberration became a driving force for many physical theories during

11256-489: The limit v / c ≪ 1 {\displaystyle v/c\ll 1} this may be approximated by θ − ϕ = v / c {\displaystyle \theta -\phi =v/c} . This relativistic derivation keeps the speed of light u x 2 + u y 2 = c {\displaystyle {\sqrt {u_{x}^{2}+u_{y}^{2}}}=c} constant in all frames of reference, unlike

11390-439: The luminiferous aether pervades the substance of all material bodies with little or no resistance, as freely perhaps as the wind passes through a grove of trees. However, it soon became clear Young's theory could not account for aberration when materials with a non-vacuum refractive index were present. An important example is of a telescope filled with water. The speed of light in such a telescope will be slower than in vacuum, and

11524-431: The moment of emission, the beam in the observer's rest frame is tilted compared to the one in the source's rest frame, as understood through relativistic beaming. During the time it takes the light beam to reach the observer the light source moves in the observer's frame, and the 'true position' of the light source is displaced relative to the apparent position the observer sees, as explained by light-time correction. Finally,

11658-458: The naked eye limit needed to serve as a useful indicator of north to an Earth-based observer, resulting in periods of time during the cycle when there is no clearly defined North Star. There will also be periods during the cycle when bright stars give only an approximate guide to "north", as they may be greater than 5° of angular diameter removed from direct alignment with the north celestial pole. The 26,000 year cycle of North Stars, starting with

11792-447: The naked eye under ideal conditions) that most closely coincide with the projection of the planet's axis of rotation onto the celestial sphere. Different planets have different pole stars because their axes are oriented differently. (See Poles of astronomical bodies .) In the medieval period, Polaris was also known as stella maris ("star of the sea", from its use for navigation at sea), as in e.g. Bartholomaeus Anglicus (d. 1272), in

11926-609: The name Dhruva ("immovable, fixed"). In the later medieval period, it became associated with the Marian title of Stella Maris "Star of the Sea" (so in Bartholomaeus Anglicus , c. 1270s), due to an earlier transcription error. An older English name, attested since the 14th century, is lodestar "guiding star", cognate with the Old Norse leiðarstjarna , Middle High German leitsterne . The ancient name of

12060-434: The north celestial pole as it is now, and used to rotate around the pole. It was invoked as a symbol of steadfastness in poetry, as "steadfast star" by Spenser . Shakespeare 's sonnet 116 is an example of the symbolism of the north star as a guiding principle: "[Love] is the star to every wandering bark / Whose worth's unknown, although his height be taken." In Julius Caesar , he has Caesar explain his refusal to grant

12194-428: The northern celestial pole some time around 5200 AD, before moving to closer alignment with the brighter star Alpha Cephei ("Alderamin") around 7500 AD. Precession will then point the north celestial pole at stars in the northern constellation Cygnus . Like Beta Ursae Minoris during the 1st millennium BC, the bright star closest to the celestial pole in the 10th millennium AD, first-magnitude Deneb , will be

12328-408: The object's motion and distance), as calculated in the rest frame of the Solar System. Both are determined at the instant when the moving object's light reaches the moving observer on Earth. It is so called because it is usually applied to planets and other objects in the Solar System whose motion and distance are accurately known. The discovery of the aberration of light was totally unexpected, and it

12462-410: The observer is considered to be moving relative to a (for the sake of simplicity ) stationary light source, while in light-time correction and relativistic beaming the light source is considered to be moving relative to a stationary observer. Consider the case of an observer and a light source moving relative to each other at constant velocity, with a light beam moving from the source to the observer. At

12596-609: The observer. In 2018 Polaris was 0.66° (39.6 arcminutes) away from the pole of rotation (1.4 times the Moon disc) and so revolves around the pole in a small circle 1.3° in diameter. It will be closest to the pole (about 0.45 degree, or 27 arcminutes) soon after the year 2100. Because it is so close to the celestial north pole, its right ascension is changing rapidly due to the precession of Earth's axis , going from 2.5h in AD 2000 to 6h in AD 2100. Twice in each sidereal day Polaris's azimuth

12730-567: The orbit of mean radius R {\displaystyle R} = 1 AU = 149,597,870.7 km. This gives an angular correction tan ⁡ ( θ ) ≈ θ = Δ x / R {\displaystyle \tan(\theta )\approx \theta =\Delta x/R} ≈ 0.000099364 rad = 20.49539 sec, which can be solved to give θ = v / c = κ {\displaystyle \theta =v/c=\kappa } ≈ 0.000099365 rad = 20.49559 sec, very nearly

12864-431: The pole than it is now, while in 23,600 BC it was closer to the pole. Over the course of Earth's 26,000-year axial precession cycle, a series of bright naked eye stars (an apparent magnitude up to +6; a full moon is −12.9) in the northern hemisphere will hold the transitory title of North Star. While other stars might line up with the north celestial pole during the 26,000 year cycle, they do not necessarily meet

12998-482: The relative motion of the Earth and the stars. In the prior century, René Descartes argued that if light were not instantaneous, then shadows of moving objects would lag; and if propagation times over terrestrial distances were appreciable, then during a lunar eclipse the Sun, Earth, and Moon would be out of alignment by hours' motion, contrary to observation. Huygens commented that, on Rømer's lightspeed data (yielding an earth-moon round-trip time of only seconds),

13132-407: The relativistic case is the same except that the relativistic velocity addition formulas must be used, which can be derived from Lorentz transformations between different frames of reference. These formulas are where γ = 1 / 1 − v 2 / c 2 {\displaystyle \gamma =1/{\sqrt {1-v^{2}/c^{2}}}} , giving

13266-431: The same as the aberrational correction (here κ {\displaystyle \kappa } is in radian and not in arcsecond). Diurnal aberration is caused by the velocity of the observer on the surface of the rotating Earth . It is therefore dependent not only on the time of the observation, but also the latitude and longitude of the observer. Its effect is much smaller than that of annual aberration, and

13400-409: The same time, 35 Camelopardalis , a star with a right ascension nearly exactly opposite to that of γ Draconis, was 19" more northerly at the beginning of March than in September. The asymmetry of these results, which were expected to be mirror images of each other, were completely unexpected and inexplicable by existing theories. Bradley and Molyneux discussed several hypotheses in the hope of finding

13534-498: The sea" as a (false) Hebrew etymology of the name Maria . This stilla maris was later misread as stella maris ; the misreading is also found in the manuscript tradition of Isidore 's Etymologiae (7th century); it probably arises in the Carolingian era ; a late 9th-century manuscript of Jerome's text still has stilla , not stella , but Paschasius Radbertus , also writing in the 9th century, makes an explicit reference to

13668-425: The solar system of 2.32 ± 0.16 × 10  m/s and a corresponding secular aberration drift of 5.05 ± 0.35 μas/yr in the direction of α = 269.1° ± 5.4°, δ = −31.6° ± 4.1°. It is expected that later Gaia data releases , incorporating about 66 and 120 months of data, will reduce the random errors of these results by factors of 0.35 and 0.15. The latest edition of

13802-462: The solution. Since the apparent motion was evidently caused neither by parallax nor observational errors, Bradley first hypothesized that it could be due to oscillations in the orientation of the Earth's axis relative to the celestial sphere – a phenomenon known as nutation . 35 Camelopardalis was seen to possess an apparent motion which could be consistent with nutation, but since its declination varied only one half as much as that of γ Draconis, it

13936-475: The south is associated with the World of Darkness . Polaris Polaris is a star in the northern circumpolar constellation of Ursa Minor . It is designated α Ursae Minoris ( Latinized to Alpha Ursae Minoris ) and is commonly called the North Star or Pole Star . With an apparent magnitude that fluctuates around 1.98, it is the brightest star in the constellation and is readily visible to

14070-475: The speed of light to the speed of the Earth's annual motion in its orbit is 10,210 to one, from whence it would follow, that light moves, or is propagated as far as from the Sun to the Earth in 8 minutes 12 seconds. The original motivation of the search for stellar parallax was to test the Copernican theory that the Earth revolves around the Sun. The change of aberration in the course of the year demonstrates

14204-619: The star at angle ϕ {\displaystyle \phi } . As the Earth proceeds in its orbit it changes direction, so ϕ {\displaystyle \phi } changes with the time of year the observation is made. The apparent angle and true angle are related using trigonometry as: In the case of θ = 90 ∘ {\displaystyle \theta =90^{\circ }} , this gives tan ⁡ ( θ − ϕ ) = v / c {\displaystyle \tan(\theta -\phi )=v/c} . While this

14338-524: The star had approached the celestial pole to within a few degrees. Gemma Frisius , writing in 1547, referred to it as stella illa quae polaris dicitur ("that star which is called 'polar'"), placing it 3° 8' from the celestial pole. In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016 included

14472-469: The star in Nehiyawewin : acâhkos êkâ kâ-âhcît "the star that does not move" ( syllabics : ᐊᒑᐦᑯᐢ ᐁᑳ ᑳ ᐋᐦᒌᐟ ). In Mi'kmawi'simk the star is named Tatapn . In the ancient Finnish worldview, the North Star has also been called taivaannapa and naulatähti ("the nailstar") because it seems to be attached to the firmament or even to act as a fastener for the sky when other stars orbit it. Since

14606-403: The star's position is displaced to the north by an equal and opposite amount. On either solstice , the displacement in declination is 0. Conversely, the amount of displacement in right ascension is 0 on either equinox and at maximum on either solstice. In actuality, Earth's orbit is slightly elliptic rather than circular, and its speed varies somewhat over the course of its orbit, which means

14740-589: The starry sky seemed to rotate around it, the firmament is thought of as a wheel, with the star as the pivot on its axis. The names derived from it were sky pin and world pin . Many recent papers calculate the distance to Polaris at about 433 light-years (133 parsecs), based on parallax measurements from the Hipparcos astrometry satellite. Older distance estimates were often slightly less, and research based on high resolution spectral analysis suggests it may be up to 110 light years closer (323 ly/99 pc). Polaris

14874-447: The stars should occur according to the heliocentric model, and consequently if stellar parallax could be observed it would help confirm this theory. Many observers claimed to have determined such parallaxes, but Tycho Brahe and Giovanni Battista Riccioli concluded that they existed only in the minds of the observers, and were due to instrumental and personal errors. However, in 1680 Jean Picard , in his Voyage d' Uranibourg , stated, as

15008-439: The stars' proper motions), the role of North Star has passed from one star to another in the remote past, and will pass in the remote future. In 3000 BC, the faint star Thuban in the constellation Draco was the North Star, aligning within 0.1° distance from the celestial pole, the closest of any of the visible pole stars. However, at magnitude 3.67 (fourth magnitude) it is only one-fifth as bright as Polaris, and today it

15142-475: The successor mission Gaia gives a distance of about 448 light-years (137 parsecs ). Calculations by other methods vary widely. Although appearing to the naked eye as a single point of light, Polaris is a triple star system , composed of the primary, a yellow supergiant designated Polaris Aa, in orbit with a smaller companion, Polaris Ab; the pair is in a wider orbit with Polaris B. The outer pair AB were discovered in August 1779 by William Herschel , where

15276-427: The system in 1929, giving an orbital period of about 29.7 years with an eccentricity of 0.63. This period was confirmed by proper motion studies performed by B. P. Gerasimovič in 1939. As part of her doctoral thesis, in 1955 E. Roemer used radial velocity data to derive an orbital period of 30.46 y for the Polaris A system, with an eccentricity of 0.64. K. W. Kamper in 1996 produced refined elements with

15410-446: The theory of special relativity in 1905, which provides the modern account of aberration. Bradley conceived of an explanation in terms of a corpuscular theory of light in which light is made of particles. His classical explanation appeals to the motion of the earth relative to a beam of light-particles moving at a finite velocity, and is developed in the Sun's frame of reference, unlike the classical derivation given above. Consider

15544-413: The theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory. 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

15678-415: The time to be a different phenomenon. In 1727, James Bradley provided a classical explanation for it in terms of the finite speed of light relative to the motion of the Earth in its orbit around the Sun, which he used to make one of the earliest measurements of the speed of light. However, Bradley's theory was incompatible with 19th-century theories of light, and aberration became a major motivation for

15812-405: The transit of the light, the tube moves a distance v h / c {\displaystyle vh/c} . Consequently, for the particles of light to reach the bottom of the tube, the tube must be inclined at an angle ϕ {\displaystyle \phi } different from θ {\displaystyle \theta } , resulting in an apparent position of

15946-473: The translation of John Trevisa (1397): by the place of this sterre place and stedes and boundes of the other sterres and of cercles of heven ben knowen: therefore astronomers beholde mooste this sterre. Then this ster is dyscryved of the moste shorte cercle; for he is ferre from the place that we ben in; he hydeth the hugenesse of his quantite for unmevablenes of his place, and he doth cerfifie men moste certenly, that beholde and take hede therof; and therfore he

16080-414: The tube from the star at angle θ {\displaystyle \theta } and travels at speed c {\displaystyle c} taking a time h / c {\displaystyle h/c} to reach the bottom of the tube, where it is detected. Suppose observations are made from Earth, which is moving with a speed v {\displaystyle v} . During

16214-425: The velocity of the observer: It causes objects to appear to be displaced towards the observer's direction of motion. The change in angle is of the order of v / c {\displaystyle v/c} where c {\displaystyle c} is the speed of light and v {\displaystyle v} the velocity of the observer. In the case of "stellar" or "annual" aberration,

16348-409: Was 89.35 degrees North; (at epoch J2000 it was 89.26 degrees N). So it appears due north in the sky to a precision better than one degree, and the angle it makes with respect to the true horizon (after correcting for refraction and other factors) is within a degree of the latitude of the observer. The celestial pole will be nearest Polaris in 2100. Due to the precession of the equinoxes (as well as

16482-439: Was about the same angular distance from β UMi as to α UMi by the end of late antiquity . The Greek navigator Pytheas in ca. 320 BC described the celestial pole as devoid of stars. However, as one of the brighter stars close to the celestial pole, Polaris was used for navigation at least from late antiquity, and described as ἀεί φανής ( aei phanēs ) "always visible" by Stobaeus (5th century), also termed Λύχνος ( Lychnos ) akin to

16616-433: Was as close to the pole as Polaris is now. In classical antiquity , Beta Ursae Minoris (Kochab) was closer to the celestial north pole than Alpha Ursae Minoris. While there was no naked-eye star close to the pole, the midpoint between Alpha and Beta Ursae Minoris was reasonably close to the pole, and it appears that the entire constellation of Ursa Minor , in antiquity known as Cynosura (Greek Κυνόσουρα "dog's tail"),

16750-430: Was configured to routinely process stars in the magnitude range 3 – 20. Beyond that limit, special procedures are used to download raw scanning data for the remaining 230 stars brighter than magnitude 3; methods to reduce and analyse these data are being developed; and it is expected that there will be "complete sky coverage at the bright end" with standard errors of "a few dozen μas". Gaia Data Release 2 does not include

16884-434: Was examined again with more advanced error correction and statistical techniques. Despite the advantages of Hipparcos astrometry , the uncertainty in its Polaris data has been pointed out and some researchers have questioned the accuracy of Hipparcos when measuring binary Cepheids like Polaris. The Hipparcos reduction specifically for Polaris has been re-examined and reaffirmed but there is still not widespread agreement about

17018-475: Was no constant northern star. Despite its relative brightness, it is not, as is popularly believed, the brightest star in the sky. Polaris was referenced in Nathaniel Bowditch 's 1802 book, American Practical Navigator , where it is listed as one of the navigational stars . The modern name Polaris is shortened from Neo-Latin stella polaris " polar star ", coined in the Renaissance when

17152-433: Was obvious that nutation did not supply the answer (however, Bradley later went on to discover that the Earth does indeed nutate). He also investigated the possibility that the motion was due to an irregular distribution of the Earth's atmosphere , thus involving abnormal variations in the refractive index, but again obtained negative results. On August 19, 1727, Bradley embarked upon a further series of observations using

17286-501: Was only 8 degrees from the south pole. In the next 7500 years, the south celestial pole will pass close to the stars Gamma Chamaeleontis (4200 AD), I Carinae , Omega Carinae (5800 AD), Upsilon Carinae , Iota Carinae (Aspidiske, 8100 AD) and Delta Velorum (Alsephina, 9200 AD). From the eightieth to the ninetieth centuries, the south celestial pole will travel through the False Cross . Around 14,000 AD Canopus will have

17420-531: Was only by considerable perseverance and perspicacity that Bradley was able to explain it in 1727. It originated from attempts to discover whether stars possessed appreciable parallaxes . The Copernican heliocentric theory of the Solar System had received confirmation by the observations of Galileo and Tycho Brahe and the mathematical investigations of Kepler and Newton . As early as 1573, Thomas Digges had suggested that parallactic shifting of

17554-420: Was reported by W. W. Campbell in 1899, which suggested this star is a binary system. Since Polaris A is a known cepheid variable, J. H. Moore in 1927 demonstrated that the changes in velocity along the line of sight were due to a combination of the four-day pulsation period combined with a much longer orbital period and a large eccentricity of around 0.6. Moore published preliminary orbital elements of

17688-448: Was several degrees away from the celestial pole; Gemma Frisius in the year 1547 determined this distance as 3°8'. An explicit identification of Mary as stella maris with the North Star ( Polaris ) becomes evident in the title Cynosura seu Mariana Stella Polaris (i.e. "Cynosure, or the Marian Polar Star"), a collection of Marian poetry published by Nicolaus Lucensis (Niccolo Barsotti de Lucca) in 1655. In 2022 Polaris' mean declination

17822-446: Was still considerable uncertainty as to whether stellar parallaxes had been observed or not, and it was with the intention of definitely answering this question that they erected a large telescope at Molyneux's house at Kew . They decided to reinvestigate the motion of γ Draconis with a telescope constructed by George Graham (1675–1751), a celebrated instrument-maker. This was fixed to a vertical chimney stack in such manner as to permit

17956-475: Was used as indicating the northern direction for the purposes of navigation by the Phoenicians . The ancient name of Ursa Minor, anglicized as cynosure , has since itself become a term for "guiding principle" after the constellation's use in navigation. Alpha Ursae Minoris (Polaris) was described as ἀειφανής (transliterated as aeiphanes ) meaning "always above the horizon", "ever-shining" by Stobaeus in

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