Aberration (astronomy) - Knowledge (XXG)

2644: 2697: 1706:

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, 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.

2689: 4191:, Bradley's result does not merely give the classical limit of the relativistic case, in the sense that it gives incorrect predictions even at low relative velocities. Bradley's explanation cannot account for situations such as the water telescope, nor for many other optical effects (such as interference) that might occur within the telescope. This is because in the Earth's frame it predicts that the direction of propagation of the light beam in the telescope is not normal to the wavefronts of the beam, in contradiction with 4811: 372: 46: 4167:

of a resting ether did not seem directly convincing to me, since it led to an interpretation of the Michelson-Morley experiment, which seemed unnatural to me. My direct path to the sp. th. rel. was mainly determined by the conviction that the electromotive force induced in a conductor moving in a magnetic field is nothing other than an electric field. But the result of Fizeau's experiment and the phenomenon of aberration also guided me.

2720:. 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 the calculation of the effect on any given star at a specified date. 1702:, 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, 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. 3971: 2709:. 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 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 1804: 3142: 6461: 275: 3073:(yielding an earth-moon round-trip time of only seconds), 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 2472:

The other, observable, part is an acceleration toward the galactic center of approximately 2.5 × 10 m/s, which yields 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

6597: 1784: 6621: 6573: 6609: 383:. 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. 4882:. Now, motion of the aether in the x and y directions does not affect the wavefront, but the motion in the z direction advances it (in addition to the amount it advances at speed c). If the z velocity of the aether varies over space, for example if it is slower for higher x as shown in the figure, then the wavefront becomes angled, by an angle 6585: 3631: 185:, 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 4166:

My own thought was more indirectly influenced by the famous Michelson-Morley experiment. I learned of it through Lorentz' path breaking investigation on the electrodynamics of moving bodies (1895), of which I knew before the establishment of the special theory of relativity. Lorentz' basic assumption

4061:

immobile, like the electromagnetic aethers of Cauchy, Green and Maxwell and unlike Fresnel's aether. He obtained Fresnel's dragging coefficient from modifications of Maxwell's electromagnetic theory, including a modification of the time coordinates in moving frames ("local time"). In order to explain

4013:

of the flow are such that the aether has zero velocity far from the Earth, but moves at the Earth's velocity at its surface and within it, he was able to completely account for aberration. The velocity of the aether outside of the Earth would decrease as a function of distance from the Earth so light

2732:

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 the boat relative to the wind direction. However, there is no record of this incident in

2471:

In about 200 million years, 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.

4036:

In the 1880s once electromagnetism was better understood, interest turned again to the problem of aberration. By this time flaws were known to both Fresnel's and Stokes' theories. Fresnel's theory required that the relative velocity of aether and matter to be different for light of different colors,

3966:

bringing the light along with it. This factor is known as "Fresnel's dragging coefficient". This dragging effect, along with refraction at the telescope's objective, compensates for the slower speed of light in the water telescope in Bradley's explanation. With this modification Fresnel obtained

2837:

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 a circle. Since he only observed the deviation in

4137:

Lorentz' theory matched experiment well, but it was complicated and made many unsubstantiated physical assumptions about the microscopic nature of electromagnetic media. In his 1905 theory of special relativity, Albert Einstein reinterpreted the results of Lorentz' theory in a much simpler and more

4122:

in the direction of their motion through the aether. In this way, aberration (and all related optical phenomena) can be accounted for in the context of an immobile aether. Lorentz' theory became the basis for much research in the next decade, and beyond. Its predictions for aberration are identical

3875:

developed a modified explanation to account for the water telescope and for other aberration phenomena. He explained that the aether is generally at rest in the Sun's frame of reference, but objects partially drag the aether along with them as they move. That is, the aether in an object of index of

3643:

adapted Bradley's explanation for corpuscular light to wavelike light traveling through 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

2680:, 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. 2534:

Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to 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

2704:

Bradley and Molyneux discussed several hypotheses in the hope of finding 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

1705:

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 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

2216:

is : x = 8.3167 min ≈ 8 min 19 sec = 499 sec. This 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 =

390:

In 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

3612:. While this 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 3165:

Consider 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

1713:

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 the Earth, the Earth may be approximated as an inertial frame and

2954:

Based on these calculations, Bradley was able to estimate 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

220:

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

2838:

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:

2498:

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 =

3634:

Young reasoned that aberration could only be explained if the aether were immobile in the frame of the Sun. On the left, stellar aberration occurs if an immobile aether is assumed, showing that the telescope must be tilted. On the right, the aberration disappears if the aether moves with the

1454: 2672:(1675–1751), a celebrated instrument-maker. This was fixed to a vertical chimney stack in such manner as to permit 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. 4056:

Hendrik Lorentz spent considerable effort along these lines. After working on this problem for a decade, the issues with Stokes' theory caused him to abandon it and to follow Fresnel's suggestion of a (mostly) stationary aether (1892, 1895). However, in Lorentz's model the aether was

2503:

satellite data of 1.6 million extragalactic sources indicated an acceleration of 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 =

2129:

In actuality, Earth's orbit is slightly elliptic rather than circular, and its speed varies somewhat over the course of its orbit, which means the description above is only approximate. Aberration is more accurately calculated using Earth's instantaneous velocity relative to the

4004:

proposed a 'putty-like' aether which acts as a liquid on large scales but as a solid on small scales, thus supporting both the transverse vibrations required for polarized light and the aether flow required to explain aberration. Making only the assumptions that the fluid is

2590:

had suggested that parallactic shifting of 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

836: 3064:

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.

2173:(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 the Sun appear to be behind (or retarded) from its rest-frame position on the ecliptic by a position or angle 4037:

and it was shown that the boundary conditions Stokes had assumed in his theory were inconsistent with his assumption of irrotational flow. At the same time, the modern theories of electromagnetic aether could not account for aberration at all. Many scientists such as

2663:

entered this sphere of research in 1725, there 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

3974:

Conceptual illustration of Stokes' aether drag theory. In the rest frame of the Sun the Earth moves to the right through the aether, in which it induces a local current. A ray of light (in red) coming from the vertical becomes dragged and tilted due to the flow of

2744:

and ecliptic prime meridian, of the tangent of the velocity of the Earth in its orbit for each of 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:

3161:

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.

3967:

Bradley's vacuum result even for non-vacuum telescopes, and was also able to predict many other phenomena related to the propagation of light in moving bodies. Fresnel's dragging coefficient became the dominant explanation of aberration for the next decades.

3847:

performed a similar experiment and found that the aberration was unaffected by the medium in the telescope, providing solid evidence against Young's theory. This experiment was subsequently verified by many others in the following decades, most accurately by

3521: 3996:

to believe that the aether was a totally immobile elastic solid as opposed to Fresnel's fluid aether. There was thus renewed need for an explanation of aberration consistent both with Fresnel's predictions (and Arago's observations) as well as polarization.

2675:

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 the same time,

3648:

Upon consideration of the phenomena of the aberration of the stars I am disposed to believe that 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

3116:

proposed 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

3048:

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 the relative motion of the Earth and the stars.

3039: 1770:"The apparent angular displacement of the observed position of a solar system body from its instantaneous geocentric direction as would be seen by an observer at the geocenter. This displacement is caused by the aberration of light and 2615:, 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. 386:

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.

5121: 5624:

In fact, the light source doesn't need to be stationary, consider for example eclipsing binary stars: they are rotating with high speed —and ever changing and different velocity vectors— around each other, but they appear as

5195: 3044:

Thus, 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.

4021:

Both Fresnel and Stokes' theories were popular. However, the question of aberration was put aside during much of the second half of the 19th century as focus of inquiry turned to the electromagnetic properties of aether.

2141:. If parallax is detectable, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It is this apparently anomalous motion that so mystified early astronomers. 3833: 2450:

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

4697: 1286: 5475:"A Letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr.Edmond Halley Astronom. Reg. &c. Giving an Account of a New Discovered Motion of the Fix'd Stars" 157:

of the observer. In the case of "stellar" or "annual" aberration, 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

2516:(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 2467:

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.

1709:

The relationship between these phenomena 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

1735:"The apparent angular displacement of the observed position of a celestial body resulting from the motion of the observer. Stellar aberration is divided into diurnal, annual, and secular components." 1209: 2356: 4359: 2513: 1117: 4066:(1887), which apparently contradicted both Fresnel's and Lorentz's immobile aether theories, and apparently confirmed Stokes' complete aether drag, Lorentz theorized (1892) that objects undergo " 2196:

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

81:

about their true positions based on 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

1278: 1943: 375:

Light rays striking the earth in the Sun's rest frame compared to the same rays in the Earth's rest frame according to special relativity. The effect is exaggerated for illustrative purposes.

1676: 686: 5368: 4542: 5056: 402:

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

3375: 1762:"The component of stellar aberration resulting from the essentially uniform and almost rectilinear motion of the entire solar system in space. Secular aberration is usually disregarded." 5835: 566: 1791:

appear to move in circles, stars exactly in the ecliptic plane move in lines, and stars at intermediate angles move in ellipses. Shown here are the apparent motions of stars with the

5728:

Charlot, P.; Jacobs, C. S.; Gordon, D.; Lambert, S.; et al. (2020). "The third realization of the International Celestial Reference Frame by very long baseline interferometry".

5259: 4120: 3610: 1542: 924: 4935: 5643: 3558: 2396: 1490: 872: 635: 1616: 998: 678: 49:

A diagram showing how the apparent position of a star viewed from the Earth can change depending on the Earth's velocity. The effect is typically much smaller than illustrated.

4457: 4408: 2494:

have successfully measured this small effect. The first VLBI measurement of the apparent motion, over a period of 20 years, of 555 extragalactic objects towards the center of

6341: 4967: 3964: 3145:

Figure 2: As light propagates down the telescope, the telescope moves requiring a tilt to the telescope that depends on the speed of light. The apparent angle of the star

2643: 2619:, from measurements made in 1689 and succeeding years with his mural quadrant, similarly concluded that the declination of Polaris was 40″ less in July than in September. 2247: 4228: 3100:. However, this explanation proved inaccurate once the wave nature of light was better understood, and correcting it became a major goal of the 19th century theories of 5853:

the correction of star places with secular aberration is not at all necessary and is even inconvenient, so long as the solar motion remains uniform and rectilinear.

4758: 3070: 6299: 1576: 958: 5312: 4798: 4582: 4270: 4189: 4162:

and (indirectly) the negative aether drift experiments, already mentioned by him in the introduction of his first relativity paper. Einstein wrote in a note in 1952:

3323: 3184: 3166:

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 the tube from the star at angle

2696: 2416: 2214: 2191: 2167: 2108: 2053: 2029: 1897: 506: 2961: 4880: 4848: 4778: 4609: 4290: 3367: 3347: 3303: 3085:

The phenomenon of aberration became a driving force for many physical theories during the 200 years between its observation and the explanation by Albert Einstein.

2281: 486: 459: 3283: 3689: 3232: 2535:

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.

1280:, giving 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 107: 4990: 5332: 5279: 4717: 4562: 3914: 3894: 3729: 3709: 3252: 3204: 2301: 1986: 1963: 1850: 586: 432: 151: 127: 2955:

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:

3663:

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 is given by

6108:

Bradley, James; Rigaud, Stephen Peter (1832). Miscellaneous works and correspondence of the Rev. James Bradley, D.D., F.R.S. Oxford: University Press. p. 11.

6478: 3125:

which featured an immobile aether, and he explained that objects contract in length as they move through the aether. Motivated by these previous theories,

5064: 3112:. 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. 4014:

rays from stars would be progressively dragged as they approached the surface of the Earth. The Earth's motion would be unaffected by the aether due to

181:

has historically been used to refer to a number of related phenomena concerning the propagation of light in moving bodies. Aberration is distinct from

5140: 4810: 2512:, 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 the 1687: 292: 4192: 394:

While classical reasoning gives intuition for aberration, it leads to a number of physical paradoxes observable even at the classical level (see

3737: 391:

course of the year, and causes the apparent position of the star to differ from its true position as measured in the inertial frame of the Sun.

2438:

of the observer. Its effect is much smaller than that of annual aberration, and is only 0.32 arcseconds in the case of an observer at the

588:

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

6372: 6246: 6188: 4818:

Stokes' derivation may be summarized as follows: Consider a wavefront moving in the downwards z direction. Say the aether has velocity field

4614: 2740:

The following table shows the magnitude of deviation from true declination for γ Draconis and the direction, on the planes of the solstitial

1753:"The component of stellar aberration resulting from the observer's diurnal motion about the center of the Earth due to the Earth's rotation." 6473: 6045:

Gaia Collaboration; Klioner, S. A.; et al. (2021). "Gaia Early Data Release 3: Acceleration of the Solar System from Gaia astrometry".

2631:

2 which passes practically overhead at the latitude of London (hence its observations are largely free from the complex corrections due to

261:

to develop the theory of special relativity in 1905, which presents a general form of the equation for aberration in terms of such theory.

5281:

s represent the x component of the aether's velocity at the start and end of the ray. Far from the earth the aether has zero velocity, so

1449:{\displaystyle \tan(\phi )={\frac {u_{y}'}{u_{x}'}}={\frac {u_{y}}{\gamma (u_{x}+v)}}={\frac {\sin(\theta )}{\gamma (v/c+\cos(\theta ))}}} 4159: 2688: 246: 6641: 1690:

Aberration, light-time correction, and relativistic beaming can be considered the same phenomenon depending on the frame of reference.

6408: 6332: 6153: 5685: 5653: 5609: 5528: 5411: 2543:

The discovery of the aberration of light was totally unexpected, and it was only by considerable perseverance and perspicacity that

2484: 358: 2595:

concluded that they existed only in the minds of the observers, and were due to instrumental and personal errors. However, in 1680

339: 311: 4063: 2716:

On August 19, 1727, Bradley embarked upon a further series of observations using a telescope of his own erected at the Rectory,

1728:

describes several different types of aberration, arising from differing components of the Earth's and observed object's motion:

250: 5584: 6378: 3234:

to reach the bottom of the tube, where it is detected. Suppose observations are made from Earth, which is moving with a speed

2149:

A special case of annual aberration is the nearly constant deflection of the Sun from its position in the Sun's rest frame by

4001: 2306: 296: 6296: 4299: 3369:

changes with the time of year the observation is made. The apparent angle and true angle are related using trigonometry as:

318: 4150:

He continued to say the experimental results which had influenced him most were the observations of stellar aberration and

3088:

The first classical explanation was provided in 1729, by James Bradley as described above, who attributed it to the finite

4132: 1123: 6563: 5131: 5639: 3993: 2728:

Bradley eventually developed his explanation of aberration in about September 1728 and this theory was presented to the

831:{\displaystyle \tan(\phi )={\frac {u_{y}'}{u_{x}'}}={\frac {u_{y}}{u_{x}+v}}={\frac {\sin(\theta )}{v/c+\cos(\theta )}}} 380: 6543:

Reduction of the Observations Made by Bradley at Kew and Wansted to Determine the Quantities of Aberration and Nutation

1217: 1022: 3644:

the medium (and therefore the light) would move along with the earth and no aberration would be observed. He wrote:

3158: 2460: 1902: 325: 1621: 3630: 3516:{\displaystyle \tan(\phi )={\frac {h\sin(\theta )}{hv/c+h\cos(\theta )}}={\frac {\sin(\theta )}{v/c+\cos(\theta )}}} 5677: 5340: 4462: 4015: 2669: 2592: 2056: 4995: 3285:. Consequently, for the particles of light to reach the bottom of the tube, the tube must be inclined at an angle 285: 1009: 307: 1698:, which is due to the motion of an observed object during the time taken by its light to reach an observer, and 208:. It was first observed in the late 1600s by astronomers searching for stellar parallax in order to confirm the 3659:

However, it soon became clear Young's theory could not account for aberration when materials with a non-vacuum

3640: 511: 5790:

MacMillan, D. S.; Fey, A.; Gipson, J. M.; et al. (2019). "Galactocentric acceleration in VLBI analysis".

3731:

is the refractive index of the water. Thus, by Bradley and Young's reasoning the aberration angle is given by

5204: 4719:

is the modified path length through the water and t is the time it takes the light to travel the distance h,

4073: 3563: 1495: 877: 4233: 3074: 2547:

was able to explain it in 1727. It originated from attempts to discover whether stars possessed appreciable

2464: 1013: 4885: 4361:. Then drag must be accounted for. Without drag, the x and y components of the light in the telescope are 4050: 4049:

unsuccessfully attempted to solve these problems by incorporating either Fresnel or Stokes' theories into

4010: 3861: 3109: 3108:

proposed a correction due to the motion of a medium (the aether) through which light propagated, known as

2632: 1807:

The direction of aberration of a star at the northern ecliptic pole differs at different times of the year

242: 222: 3530: 2361: 1462: 844: 6023: 4969:(assuming the speed of the aether is negligible compared to the speed of light). Then for each distance 4218: 3989: 3113: 3105: 2706: 2700:

Hypothetical observation of γ Draconis and 35 Camelopardalis if their movements were caused by nutation.

2529: 2066:

For illustration, consider a star at the northern ecliptic pole viewed by an observer at a point on the

1771: 1695: 230: 226: 212:

of the Solar System. However, it was not understood at the time to be a different phenomenon. In 1727,

186: 2710: 1581: 963: 6180: 6171: 5962:

Titov, O.; Lambert, S. B.; Gontier, A.-M. (2011). "VLBI measurement of the secular aberration drift".

4413: 4364: 4146:

reported some conversations with Einstein, in which Einstein emphasized the importance of aberration:

2398:≈ 0.000099365 rad = 20.49559 sec, very nearly the same as the aberrational correction (here 371: 45: 6501: 6433: 6064: 6015: 5981: 5929: 5878: 5799: 5747: 5560: 5486: 5436: 4199:

between frames. However, Bradley did correctly infer that the effect was due to relative velocities.

4031: 3985: 3122: 2499:

270.2 ± 2.3° and δ = −20.2° ± 3.6°. Optical observations using only 33 months of

1826: 1724: 1699: 238: 190: 39: 35: 591: 6646: 6625: 5427:

Williams, M. E. W. (1979). "Flamsteed's Alleged Measurement of Annual Parallax for the Pole Star".

4143: 4139: 4038: 3849: 3625: 3101: 2713:, thus involving abnormal variations in the refractive index, but again obtained negative results. 2560: 2427: 4940: 3919: 640: 332: 6651: 6613: 6601: 6279: 6271: 6145: 6054: 5997: 5971: 5919: 5815: 5763: 5737: 5709: 5576: 5452: 4171:

While Einstein's result is the same as Bradley's original equation except for an extra factor of

4067: 3840: 3130: 3066: 2628: 2220: 1796: 399: 205: 196:

Aberration is historically significant because of its role in the development of the theories of

159: 31: 2011:(the plane of Earth's orbit) to appear to move back and forth along a straight line, varying by 6538: 4722: 3034:{\displaystyle \cos \left({\frac {1}{2}}\pi -0.00009793\right)=\sin(0.00009793)={\frac {v}{c}}} 680:. Thus the angle of the light in the Earth's frame in terms of the angle in the Sun's frame is 6404: 6368: 6263: 6184: 6179:. Vol. I: A-ak Bayes (15th ed.). Chicago, IL: Encyclopædia Britannica Inc. pp. 6149: 5681: 5649: 5605: 5524: 5407: 5058:, and so the total angle by which it has changed after travelling through the entire fluid is 4151: 4138:

natural conceptual framework which disposed of the idea of an aether. His derivation is given

3844: 3058: 2652: 2517: 2505: 2488: 2111: 1792: 1547: 929: 254: 217: 5284: 4783: 4567: 4255: 4174: 3639:

In the early nineteenth century the wave theory of light was being rediscovered, and in 1804

3308: 3169: 2401: 2199: 2176: 2152: 2093: 2038: 2014: 1882: 491: 241:

of electromagnetism in 1892. The aberration of light, together with Lorentz's elaboration of

6577: 6441: 6255: 6220: 6072: 6068: 5989: 5985: 5937: 5886: 5882: 5844: 5807: 5803: 5755: 5751: 5599: 5568: 5494: 5444: 4213: 4042: 3872: 3660: 2548: 2031:

on either side of their position in the Sun's frame. A star that is precisely at one of the

1872: 1861: 1812: 1686: 201: 182: 74: 4853: 4821: 4763: 4587: 4275: 3352: 3332: 3288: 2252: 2114:, the star's position is displaced to the north by an equal and opposite amount. On either 1744:"The component of stellar aberration resulting from the motion of the Earth about the Sun." 464: 437: 6322: 6303: 6016:"Gaia's measurement of the solar system acceleration with respect to the distant universe" 3839:

which predicts a medium-dependent angle of aberration. When refraction at the telescope's

3257: 3126: 3118: 2660: 2579: 2571: 2563: 2452: 2119: 258: 234: 167: 6326: 5645:

Astronomical Almanac for the Year 2015 and Its Companion, The Astronomical Almanac Online

4611:

is the velocity of the light with these velocity components, then by Bradley's reasoning

3666: 3209: 2668:. They decided to reinvestigate the motion of γ Draconis with a telescope constructed by 1875:

as circular, the maximum displacement of a star due to annual aberration is known as the

84: 6437: 6242:"Descartes' Experimental Proof of the Infinite Velocity of Light and Huygens' Rejoinder" 5933: 5564: 5490: 5440: 4972: 2086:, Earth's orbit carries the observer in a southwards direction, and the star's apparent 6528: 6511: 6397: 6138: 5317: 5264: 5127: 4702: 4547: 4293: 4208: 4046: 4006: 3899: 3879: 3714: 3694: 3613: 3237: 3189: 3089: 3061: 2648: 2624: 2616: 2286: 2004: 1971: 1966: 1948: 1857: 1835: 571: 417: 414:

In the Sun's frame, consider a beam of light with velocity equal to the speed of light

379:

Aberration may be explained as the difference in angle of a beam of light in different

136: 130: 112: 78: 2137:

Note that the displacement due to aberration is orthogonal to any displacement due to

6635: 6467: 6283: 6001: 5819: 5767: 5701: 5456: 4223: 3843:

is taken into account this result deviates even more from the vacuum result. In 1810

2760:

Direction of tangential velocity of Earth on the plane of the ecliptic prime meridian

2729: 2587: 2544: 2473: 2083: 2067: 2032: 1860:

and consequently the aberration also varies periodically, typically causing stars to

1830: 1788: 213: 209: 6357: 5580: 5548: 5116:{\displaystyle \alpha \approx {\frac {1}{c}}\int {\frac {\partial w}{\partial x}}dz} 6589: 6533:

Essays on Several Curious and Useful Subjects in Speculative and Mix'd Mathematicks

2620: 2583: 2567: 2426:

Diurnal aberration is caused by the velocity of the observer on the surface of the

2079: 1853: 1710: 403: 6076: 5993: 5848: 5811: 5759: 3970: 3141: 2430:. It is therefore dependent not only on the time of the observation, but also the 2118:, the displacement in declination is 0. Conversely, the amount of displacement in 17: 5891: 5866: 5190:{\displaystyle {\frac {\partial w}{\partial x}}={\frac {\partial u}{\partial z}}} 6555: 5648:. Washington, DC: U.S. Government Printing Office (published 2014). p. M1. 2635:), and concluded that this star was 23″ more northerly in July than in October. 2596: 2575: 2456: 2087: 2071: 1803: 274: 171: 5549:"Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905" 5448: 2754:

Direction of tangential velocity of Earth on the plane of the solstitial colure

27:

Phenomenon wherein objects appear to move about their true positions in the sky

5572: 4158:

Other important motivations for Einstein's development of relativity were the

2692:

Hypothetical observation of γ Draconis if its movement was caused by parallax.

2480: 2459:, and aberration resulting from the motion of the Local Group relative to the 2131: 6506:

Miscellaneous Works and Correspondence of the Rev. James Bradley, D.D. F.R.S.

6267: 2734: 2602: 2495: 2435: 1989: 1678:

constant in all frames of reference, unlike the classical derivation above.

163: 54: 6225: 6208: 5499: 5474: 2850:

Maximum deviation in declination of a star in the pole of the ecliptic (")

2035:(at 90° from the ecliptic plane) will appear to move in a circle of radius 3828:{\displaystyle \tan(\phi )={\frac {\sin(\theta )}{v/(c/n)+\cos(\theta )}}} 5924: 2717: 2677: 2431: 2138: 2115: 2008: 154: 30:

Not to be confused with the defects in astronomical instruments known as

6275: 6241: 2358:≈ 0.000099364 rad = 20.49539 sec, which can be solved to give 1783: 6259: 4692:{\displaystyle \tan(\phi )={\frac {h\sin(\alpha )}{vt+h\cos(\alpha )}}} 2612: 2439: 2123: 2060: 1865: 299: in this section. Unsourced material may be challenged and removed. 6445: 2303:= 1 AU = 149,597,870.7 km. This gives an angular correction 2741: 2455:, aberration resulting from the motion of the Galaxy relative to the 2075: 1993: 6584: 6059: 5942: 5907: 5742: 4154:

on the speed of light in moving water. "They were enough," he said.

1008:

The reasoning in the relativistic case is the same except that the

6466:

This article incorporates text from a publication now in the

5976: 5201:

Inserting this into the previous result gives an aberration angle

4252:

More in detail, Fresnel explains that the incoming light of angle

3093: 2695: 2687: 2642: 1997: 1818: 197: 44: 2463:. Secular aberration affects the apparent positions of stars and 193:, although it is often considered separately from these effects. 5833:

Hagihara, Yusuke (1933). "On the Theory of Secular Aberration".

2733:

Bradley's own account of the discovery, and it may therefore be

2608: 6424:

Shankland, R. S. (1963). "Conversations with Albert Einstein".

4272:

is first refracted at the end of the telescope, to a new angle

1714:

aberrational effects are equivalent to light-time corrections.

3349:. As the Earth proceeds in its orbit it changes direction, so 3097: 2763:

Expected deviation from true ecliptic longitude of γ Draconis

2665: 2249:≈ 14,864.7 km in the time it takes light to reach Earth, 1945:

substituting the Earth's average speed in the Sun's frame for

1822: 1682:

Relationship to light-time correction and relativistic beaming

268: 3254:. During the transit of the light, the tube moves a distance 5314:

and at the surface of the earth it has the earth's velocity

4809: 1817:

Annual aberration is caused by the motion of an observer on

162:

around the Sun, by a maximum angle of approximately 20

6116: 6114: 6092: 6090: 6088: 6086: 6209:"An account of a new discovered motion of the fixed stars" 3133:

in 1905, which provides the modern account of aberration.

1016:

between different frames of reference. These formulas are

1856:

periodically during the year as the planet traverses its

5836:

Proceedings of the Physico-Mathematical Society of Japan

3635:

telescope, and the telescope does not need to be tilted.

1618:. This relativistic derivation keeps the speed of light 5406:. Oxford: Pergamon Press. pp. 99–117 und 255–273. 4937:. Now, say in time t the wavefront has moved by a span 3988:(discovered by Fresnel himself) led scientists such as 2351:{\displaystyle \tan(\theta )\approx \theta =\Delta x/R} 5672:

Kovalevsky, Jean & Seidelmann, P. Kenneth (2004).

4354:{\displaystyle \sin(\theta -\phi )=n\sin(\psi -\phi )} 395: 6561: 5343: 5320: 5287: 5267: 5207: 5143: 5067: 4998: 4975: 4943: 4888: 4856: 4824: 4786: 4766: 4725: 4705: 4617: 4590: 4570: 4550: 4465: 4416: 4367: 4302: 4278: 4258: 4177: 4076: 3922: 3902: 3882: 3740: 3717: 3697: 3669: 3566: 3533: 3378: 3355: 3335: 3311: 3291: 3260: 3240: 3212: 3192: 3172: 2964: 2404: 2364: 2309: 2289: 2255: 2223: 2202: 2179: 2155: 2096: 2041: 2017: 1974: 1951: 1905: 1885: 1838: 1624: 1584: 1550: 1498: 1465: 1289: 1220: 1126: 1025: 966: 932: 880: 847: 689: 643: 594: 574: 514: 494: 467: 440: 420: 139: 115: 87: 4814:

The propagating wavefront moving through the aether.

1204:{\displaystyle u_{y}'=u_{y}/\gamma (1+u_{x}v/c^{2})} 6342:

A History of the Theories of Aether and Electricity

6328:

A History of the theories of aether and electricity

4292:within the telescope. This may be accounted for by 2090:is therefore displaced to the south by an angle of 2055:about its true position, and stars at intermediate 6496:Explanatory Supplement to the Astronomical Almanac 6396: 6170: 6137: 5362: 5326: 5306: 5273: 5253: 5189: 5115: 5050: 4984: 4961: 4929: 4874: 4842: 4792: 4772: 4752: 4711: 4691: 4603: 4576: 4556: 4536: 4451: 4402: 4353: 4284: 4264: 4183: 4114: 3958: 3908: 3888: 3827: 3723: 3703: 3683: 3604: 3552: 3515: 3361: 3341: 3317: 3297: 3277: 3246: 3226: 3198: 3178: 3157:Bradley conceived of an explanation in terms of a 3033: 2410: 2390: 2350: 2295: 2275: 2241: 2208: 2185: 2161: 2102: 2047: 2023: 1980: 1957: 1937: 1891: 1844: 1670: 1610: 1570: 1536: 1484: 1448: 1272: 1203: 1111: 992: 952: 918: 866: 830: 672: 629: 580: 560: 500: 480: 453: 426: 145: 121: 101: 6358:"The Optics and Electrodynamics of Moving Bodies" 4229:Timeline of electromagnetism and classical optics 2570:had received confirmation by the observations of 1273:{\displaystyle \gamma =1/{\sqrt {1-v^{2}/c^{2}}}} 1112:{\displaystyle u_{x}'=(u_{x}+v)/(1+u_{x}v/c^{2})} 1012:formulas must be used, which can be derived from 2007:, annual aberration causes stars exactly on the 1938:{\displaystyle \kappa =\theta -\phi \approx v/c} 6498:(University Science Books, 1992), 127–135, 700. 6213:Philosophical Transactions of the Royal Society 4195:. It also does not preserve the speed of light 4164: 4148: 3646: 1671:{\displaystyle {\sqrt {u_{x}^{2}+u_{y}^{2}}}=c} 6482:. Vol. 1 (11th ed.). pp. 54–61. 6331:(1. ed.). Dublin: Longman, Green and Co. 3053:Retrodiction on Descartes' lightspeed argument 2705:celestial sphere – a phenomenon known as 1694:Aberration is related to two other phenomena, 5957: 5955: 5953: 5363:{\displaystyle \alpha \approx {\frac {v}{c}}} 4537:{\displaystyle (c/n)\cos(\psi )-(1-1/n^{2})v} 2777:← (moving toward perihelion at fast velocity) 2757:Deviation from true declination of γ Draconis 2504:−31.6° ± 4.1°. It is expected that 2442:, where the rotational velocity is greatest. 8: 6356:Janssen, Michel & Stachel, John (2010). 6317: 6315: 6313: 6311: 6202: 6200: 5785: 5783: 5781: 5779: 5777: 5667: 5665: 5051:{\displaystyle \alpha \approx (dw/dx)(dz/c)} 2283:≈ 499 sec for the orbit of mean radius 5908:"Astrometric effects of secular aberration" 5514: 5512: 5510: 5397: 5395: 5393: 5391: 2811:→ (moving toward aphelion at slow velocity) 6120: 6096: 5723: 5721: 5719: 1899:. It may be calculated using the relation 6516:Mathematical and Philosophical Dictionary 6224: 6058: 5975: 5941: 5923: 5890: 5741: 5498: 5468: 5466: 5350: 5342: 5319: 5292: 5286: 5266: 5243: 5234: 5221: 5206: 5167: 5144: 5142: 5087: 5074: 5066: 5037: 5014: 4997: 4992:the ray descends, it is bent by an angle 4974: 4942: 4916: 4887: 4855: 4823: 4785: 4765: 4744: 4735: 4724: 4704: 4636: 4616: 4595: 4589: 4569: 4549: 4522: 4513: 4472: 4464: 4423: 4415: 4374: 4366: 4301: 4277: 4257: 4176: 4104: 4095: 4089: 4077: 4075: 3944: 3935: 3921: 3901: 3881: 3793: 3782: 3759: 3739: 3716: 3696: 3673: 3668: 3594: 3565: 3544: 3532: 3484: 3461: 3426: 3397: 3377: 3354: 3334: 3310: 3290: 3267: 3259: 3239: 3216: 3211: 3191: 3171: 3021: 2976: 2963: 2623:, in 1674, published his observations of 2403: 2374: 2363: 2340: 2308: 2288: 2265: 2254: 2222: 2201: 2178: 2154: 2095: 2040: 2016: 1973: 1950: 1927: 1904: 1884: 1837: 1654: 1649: 1636: 1631: 1625: 1623: 1600: 1583: 1554: 1549: 1526: 1497: 1476: 1464: 1414: 1385: 1364: 1347: 1341: 1327: 1314: 1308: 1288: 1262: 1253: 1247: 1235: 1230: 1219: 1192: 1183: 1174: 1153: 1147: 1131: 1125: 1100: 1091: 1082: 1064: 1049: 1030: 1024: 982: 965: 936: 931: 908: 879: 858: 846: 799: 776: 758: 747: 741: 727: 714: 708: 688: 664: 648: 642: 615: 599: 593: 573: 561:{\displaystyle \tan(\theta )=u_{y}/u_{x}} 552: 543: 537: 513: 493: 472: 466: 445: 439: 419: 359:Learn how and when to remove this message 138: 114: 91: 86: 6131: 6129: 5542: 5540: 3969: 3629: 3140: 2840: 2747: 1802: 1782: 1685: 370: 6568: 6399:Electrodynamics from Ampére to Einstein 5521:Parallax:The Race to Measure the Cosmos 5387: 5373:which is the known aberration result. 5254:{\displaystyle \alpha =(u_{2}-u_{1})/c} 4459:, but drag modifies the x component to 4245: 4142:, and is now the accepted explanation. 4115:{\displaystyle {\sqrt {1-v^{2}/c^{2}}}} 3605:{\displaystyle \tan(\theta -\phi )=v/c} 2724:Development of the theory of aberration 2578:and the mathematical investigations of 2514:International Celestial Reference Frame 1795:corresponding to these cases, and with 1757: 1748: 1537:{\displaystyle \sin(\theta -\phi )=v/c} 919:{\displaystyle \tan(\theta -\phi )=v/c} 1988:. Its accepted value is 20.49552 1739: 6247:Archive for History of Exact Sciences 5604:(2nd ed.). Springer. p. 8. 5553:Archive for History of Exact Sciences 4123:to those of the relativistic theory. 3916:is partially dragged with a velocity 3136: 2655:as reduced by Busch to the year 1730. 2070:. Such an observer will see the star 568:. If the Earth is moving at velocity 7: 5429:Journal for the History of Astronomy 4930:{\displaystyle \tan(\alpha )=tdw/dx} 4800:one obtains Bradley's vacuum result. 4193:Maxwell's theory of electromagnetism 2483:of extragalactic objects using both 2418:is in radian and not in arcsecond). 2078:, once every day (strictly speaking 297:adding citations to reliable sources 5708:. Macmillan, 1906 – republished by 5706:A Compendium of Spherical Astronomy 4760:. Upon solving these equations for 4160:moving magnet and conductor problem 3553:{\displaystyle \theta =90^{\circ }} 2391:{\displaystyle \theta =v/c=\kappa } 2126:and at maximum on either solstice. 1852:of Earth (in the Sun's rest frame) 1485:{\displaystyle \theta =90^{\circ }} 867:{\displaystyle \theta =90^{\circ }} 637:, and the y velocity is unchanged, 434:, with x and y velocity components 247:moving magnet and conductor problem 5906:Kopeikin, S.; Makarov, V. (2006). 5523:. New York, New York: Henry Holt. 5404:Nineteenth-century aether theories 5178: 5170: 5155: 5147: 5098: 5090: 4051:Maxwell's new electromagnetic laws 3052: 2334: 2224: 2059:will appear to move along a small 1821:as the planet revolves around the 221:became a major motivation for the 25: 6339:Whittaker, Edmund Taylor (1953). 4544:if the Earth moves with velocity 4025: 3081:Historical theories of aberration 2485:Very Long Baseline Interferometry 1611:{\displaystyle \theta -\phi =v/c} 993:{\displaystyle \theta -\phi =v/c} 251:negative aether drift experiments 6619: 6607: 6595: 6583: 6571: 6459: 6384:from the original on 2022-10-09. 6335:from the original on 2016-02-15. 5587:from the original on 2009-01-11. 4452:{\displaystyle (c/n)\cos(\psi )} 4403:{\displaystyle (c/n)\sin(\psi )} 3984:However, the fact that light is 2539:Discovery and first observations 2217:29.789 km/s, by a distance 1879:, conventionally represented by 273: 3852:in 1871, with the same result. 3137:Bradley's classical explanation 2659:Consequently, when Bradley and 284:needs additional citations for 204:and, ultimately, the theory of 6240:Sakellariadis, Spyros (1982). 6169:Hoiberg, Dale H., ed. (2010). 5912:The Astronomical Journal (USA) 5867:"Aberration in proper motions" 5402:Schaffner, Kenneth F. (1972). 5240: 5214: 5045: 5028: 5025: 5005: 4901: 4895: 4683: 4677: 4654: 4648: 4630: 4624: 4528: 4501: 4495: 4489: 4480: 4466: 4446: 4440: 4431: 4417: 4397: 4391: 4382: 4368: 4348: 4336: 4321: 4309: 3950: 3923: 3819: 3813: 3801: 3787: 3774: 3768: 3753: 3747: 3585: 3573: 3507: 3501: 3476: 3470: 3452: 3446: 3415: 3409: 3391: 3385: 3329:position of the star at angle 3015: 3009: 2322: 2316: 1517: 1505: 1440: 1437: 1431: 1408: 1400: 1394: 1376: 1357: 1302: 1296: 1198: 1161: 1106: 1069: 1061: 1042: 1010:relativistic velocity addition 899: 887: 822: 816: 791: 785: 702: 696: 630:{\displaystyle u_{x}'=u_{x}+v} 527: 521: 1: 6494:P. Kenneth Seidelmann (Ed.), 5849:10.11429/ppmsj1919.15.3-6_155 5642:(21 March 2014). "Glossary". 4133:History of special relativity 3129:then developed the theory of 6140:A Short History of Astronomy 6047:Astronomy & Astrophysics 5640:U.S. Nautical Almanac Office 5473:Bradley, James (1727–1728). 4962:{\displaystyle dz\approx ct} 3959:{\displaystyle (1-1/n^{2})v} 3149:differs from its true angle 2822:→ (moving toward perihelion) 2814:increase of less than 20.2" 2780:decrease of more than 20.2" 2639:James Bradley's observations 2638: 1578:this may be approximated by 673:{\displaystyle u_{y}'=u_{y}} 381:inertial frames of reference 6426:American Journal of Physics 6403:. Oxford: Clarendon Press. 6077:10.1051/0004-6361/202039734 5994:10.1051/0004-6361/201015718 5812:10.1051/0004-6361/201935379 5760:10.1051/0004-6361/202038368 4064:Michelson–Morley experiment 4026:Lorentz' length contraction 3866: 3159:corpuscular theory of light 2607:stated, as a result of ten 2555:Search for stellar parallax 2461:cosmic microwave background 2242:{\displaystyle \Delta x=vt} 308:"Aberration" astronomy 6668: 6472:Eppenstein, Otto (1911). " 6395:Darrigol, Olivier (2000). 5964:Astronomy and Astrophysics 5892:10.1051/0004-6361:20030560 5871:Astronomy and Astrophysics 5792:Astronomy and Astrophysics 5730:Astronomy and Astrophysics 5678:Cambridge University Press 5674:Fundamentals of Astrometry 5449:10.1177/002182867901000203 4130: 4029: 3979: 3859: 3623: 2788:← (moving toward aphelion) 2647:Bradley's observations of 2593:Giovanni Battista Riccioli 2527: 1992:(sec) or 0.000099365 1810: 29: 6642:Electromagnetic radiation 6558:on Bradley's observations 6363:. In John Stachel (ed.). 6345:(2. ed.). T. Nelson. 6172:"aberration, constant of" 5598:Richard A. Mould (2001). 5573:10.1007/s00407-004-0085-6 5519:Hirschfeld, Alan (2001). 4753:{\displaystyle t=h/v_{l}} 2479:Recently, highly precise 1492:, this result reduces to 874:, this result reduces to 243:Maxwell's electrodynamics 6323:Whittaker, Edmund Taylor 5547:Norton, John D. (2004). 5132:Cauchy–Riemann equations 3096:in its orbit around the 2453:the center of our Galaxy 1571:{\displaystyle v/c\ll 1} 1004:Relativistic explanation 953:{\displaystyle v/c\ll 1} 73:) is a phenomenon where 6479:Encyclopædia Britannica 6297:Encyclopædia Britannica 6177:Encyclopædia Britannica 6136:Berry, Arthur (1961) . 6069:2021A&A...649A...9G 5986:2011A&A...529A..91T 5883:2003A&A...404..743K 5865:Kovalevsky, J. (2003). 5804:2019A&A...630A..93M 5752:2020A&A...644A.159C 5307:{\displaystyle u_{2}=0} 4793:{\displaystyle \theta } 4577:{\displaystyle \alpha } 4265:{\displaystyle \theta } 4234:Relativistic aberration 4184:{\displaystyle \gamma } 3318:{\displaystyle \theta } 3179:{\displaystyle \theta } 3075:principle of relativity 3071:Rømer's lightspeed data 2411:{\displaystyle \kappa } 2209:{\displaystyle \kappa } 2186:{\displaystyle \kappa } 2162:{\displaystyle \kappa } 2145:Solar annual aberration 2103:{\displaystyle \kappa } 2048:{\displaystyle \kappa } 2024:{\displaystyle \kappa } 1892:{\displaystyle \kappa } 1772:light-time displacement 1014:Lorentz transformations 960:may be approximated by 501:{\displaystyle \theta } 488:, and thus at an angle 63:astronomical aberration 6539:de:August Ludwig Busch 6523:Astronomical Discovery 6226:10.1098/rstl.1727.0064 6207:James Bradley (1729). 5500:10.1098/rstl.1727.0064 5364: 5334:. Thus we finally get 5328: 5308: 5275: 5255: 5191: 5117: 5052: 4986: 4963: 4931: 4876: 4844: 4815: 4794: 4774: 4754: 4713: 4693: 4605: 4578: 4558: 4538: 4453: 4404: 4355: 4286: 4266: 4185: 4169: 4156: 4116: 3976: 3960: 3910: 3890: 3862:Aether drag hypothesis 3829: 3725: 3705: 3685: 3657: 3636: 3606: 3554: 3517: 3363: 3343: 3319: 3299: 3279: 3248: 3228: 3200: 3180: 3154: 3057:In the prior century, 3035: 2701: 2693: 2656: 2633:atmospheric refraction 2412: 2392: 2352: 2297: 2277: 2243: 2210: 2187: 2163: 2104: 2082:). At the time of the 2049: 2025: 1982: 1959: 1939: 1893: 1877:constant of aberration 1846: 1808: 1800: 1691: 1672: 1612: 1572: 1538: 1486: 1450: 1274: 1205: 1113: 994: 954: 920: 868: 832: 674: 631: 582: 562: 502: 482: 455: 428: 404:addition of velocities 376: 147: 123: 103: 50: 6024:European Space Agency 5365: 5329: 5309: 5276: 5256: 5192: 5118: 5053: 4987: 4964: 4932: 4877: 4875:{\displaystyle x,y,z} 4845: 4843:{\displaystyle u,v,w} 4813: 4795: 4775: 4773:{\displaystyle \phi } 4755: 4714: 4694: 4606: 4604:{\displaystyle v_{l}} 4579: 4559: 4539: 4454: 4405: 4356: 4287: 4285:{\displaystyle \psi } 4267: 4219:Astronomical nutation 4186: 4152:Fizeau's measurements 4117: 3973: 3961: 3911: 3891: 3867:Fresnel's aether drag 3830: 3726: 3706: 3686: 3633: 3607: 3555: 3518: 3364: 3362:{\displaystyle \phi } 3344: 3342:{\displaystyle \phi } 3320: 3300: 3298:{\displaystyle \phi } 3280: 3249: 3229: 3201: 3186:and travels at speed 3181: 3144: 3110:"partial aether drag" 3106:Augustin-Jean Fresnel 3036: 2699: 2691: 2646: 2611:' observations, that 2530:Light-time correction 2413: 2393: 2353: 2298: 2278: 2276:{\displaystyle t=R/c} 2244: 2211: 2188: 2164: 2134:of the Solar System. 2105: 2050: 2026: 1983: 1960: 1940: 1894: 1847: 1806: 1786: 1768:Planetary aberration: 1696:light-time correction 1689: 1673: 1613: 1573: 1539: 1487: 1451: 1275: 1206: 1114: 995: 955: 926:, which in the limit 921: 869: 833: 675: 632: 583: 563: 503: 483: 481:{\displaystyle u_{y}} 456: 454:{\displaystyle u_{x}} 429: 410:Classical explanation 374: 187:light-time correction 148: 124: 104: 61:(also referred to as 48: 6502:Stephen Peter Rigaud 5341: 5318: 5285: 5265: 5205: 5141: 5130:it will satisfy the 5065: 4996: 4973: 4941: 4886: 4854: 4822: 4784: 4764: 4723: 4703: 4615: 4588: 4568: 4548: 4463: 4414: 4365: 4300: 4276: 4256: 4175: 4074: 4032:Lorentz ether theory 4016:D'Alembert's paradox 3920: 3900: 3880: 3738: 3715: 3695: 3667: 3564: 3531: 3376: 3353: 3333: 3309: 3289: 3278:{\displaystyle vh/c} 3258: 3238: 3210: 3190: 3170: 2962: 2847:Annual Variation (") 2586:. As early as 1573, 2524:Planetary aberration 2402: 2362: 2307: 2287: 2253: 2221: 2200: 2177: 2153: 2094: 2039: 2015: 1972: 1949: 1903: 1883: 1836: 1827:orbital eccentricity 1725:Astronomical Almanac 1700:relativistic beaming 1622: 1582: 1548: 1496: 1463: 1287: 1218: 1124: 1023: 964: 930: 878: 845: 687: 641: 592: 572: 512: 492: 465: 438: 418: 293:improve this article 223:aether drag theories 191:relativistic beaming 137: 113: 85: 40:chromatic aberration 36:spherical aberration 6438:1963AmJPh..31...47S 5934:2006AJ....131.1471K 5565:2004AHES...59...45N 5491:1727RSPT...35..637B 5479:Phil. Trans. R. Soc 5441:1979JHA....10..102W 4144:Robert S. Shankland 4011:boundary conditions 3980:Stokes' aether drag 3896:moving at velocity 3684:{\displaystyle c/n} 3626:Luminiferous aether 3620:Luminiferous aether 3227:{\displaystyle h/c} 3102:luminiferous aether 3069:commented that, on 1733:Stellar aberration: 1659: 1641: 1544:, and in the limit 1335: 1322: 1139: 1038: 735: 722: 656: 607: 233:(in 1845), and for 102:{\displaystyle v/c} 71:velocity aberration 6302:2013-11-11 at the 6260:10.1007/BF00348308 5629:spot all the time. 5360: 5324: 5304: 5271: 5251: 5187: 5134:, one of which is 5113: 5048: 4985:{\displaystyle dz} 4982: 4959: 4927: 4872: 4840: 4816: 4790: 4770: 4750: 4709: 4689: 4601: 4574: 4554: 4534: 4449: 4400: 4351: 4282: 4262: 4181: 4127:Special relativity 4112: 4068:length contraction 3977: 3956: 3906: 3886: 3856:Aether drag models 3825: 3721: 3701: 3681: 3654:Thomas Young, 1804 3637: 3602: 3550: 3513: 3359: 3339: 3325:, resulting in an 3315: 3295: 3275: 3244: 3224: 3196: 3176: 3155: 3131:special relativity 3092:and the motion of 3031: 2711:Earth's atmosphere 2702: 2694: 2657: 2446:Secular aberration 2422:Diurnal aberration 2408: 2388: 2348: 2293: 2273: 2239: 2206: 2183: 2159: 2100: 2057:ecliptic latitudes 2045: 2021: 1978: 1955: 1935: 1889: 1842: 1809: 1801: 1797:ecliptic longitude 1793:ecliptic latitudes 1758:Secular aberration 1749:Diurnal aberration 1692: 1668: 1645: 1627: 1608: 1568: 1534: 1482: 1446: 1323: 1310: 1270: 1201: 1127: 1109: 1026: 990: 950: 916: 864: 828: 723: 710: 670: 644: 627: 595: 578: 558: 498: 478: 451: 424: 400:special relativity 377: 210:heliocentric model 206:special relativity 143: 119: 99: 67:stellar aberration 51: 32:optical aberration 18:Stellar aberration 6556:Courtney Seligman 6446:10.1119/1.1969236 6374:978-1-4020-1308-9 6190:978-1-59339-837-8 6121:Eppenstein (1911) 6097:Eppenstein (1911) 6026:. 3 December 2020 5358: 5327:{\displaystyle v} 5274:{\displaystyle u} 5185: 5162: 5105: 5082: 4850:as a function of 4712:{\displaystyle h} 4687: 4557:{\displaystyle v} 4110: 4070:" by a factor of 3909:{\displaystyle v} 3889:{\displaystyle n} 3823: 3724:{\displaystyle n} 3704:{\displaystyle c} 3511: 3456: 3247:{\displaystyle v} 3199:{\displaystyle c} 3029: 2984: 2952: 2951: 2835: 2834: 2678:35 Camelopardalis 2653:35 Camelopardalis 2492:space observatory 2296:{\displaystyle R} 2112:September equinox 1981:{\displaystyle c} 1958:{\displaystyle v} 1845:{\displaystyle v} 1779:Annual aberration 1740:Annual aberration 1660: 1444: 1380: 1336: 1268: 826: 771: 736: 581:{\displaystyle v} 427:{\displaystyle c} 398:). The theory of 369: 368: 361: 343: 255:Fizeau experiment 253:, as well as the 146:{\displaystyle v} 122:{\displaystyle c} 75:celestial objects 16:(Redirected from 6659: 6624: 6623: 6622: 6612: 6611: 6610: 6600: 6599: 6598: 6588: 6587: 6576: 6575: 6574: 6567: 6483: 6465: 6463: 6462: 6450: 6449: 6421: 6415: 6414: 6402: 6392: 6386: 6385: 6383: 6362: 6353: 6347: 6346: 6336: 6319: 6306: 6294: 6288: 6287: 6237: 6231: 6230: 6228: 6204: 6195: 6194: 6174: 6166: 6160: 6159: 6143: 6133: 6124: 6118: 6109: 6106: 6100: 6094: 6081: 6080: 6062: 6042: 6036: 6035: 6033: 6031: 6012: 6006: 6005: 5979: 5959: 5948: 5947: 5945: 5927: 5925:astro-ph/0508505 5918:(3): 1471–1478. 5903: 5897: 5896: 5894: 5862: 5856: 5855: 5830: 5824: 5823: 5787: 5772: 5771: 5745: 5725: 5714: 5713: 5698: 5692: 5691: 5669: 5660: 5659: 5636: 5630: 5622: 5616: 5615: 5601:Basic Relativity 5595: 5589: 5588: 5544: 5535: 5534: 5516: 5505: 5504: 5502: 5485:(406): 637–661. 5470: 5461: 5460: 5424: 5418: 5417: 5399: 5375: 5369: 5367: 5366: 5361: 5359: 5351: 5333: 5331: 5330: 5325: 5313: 5311: 5310: 5305: 5297: 5296: 5280: 5278: 5277: 5272: 5260: 5258: 5257: 5252: 5247: 5239: 5238: 5226: 5225: 5196: 5194: 5193: 5188: 5186: 5184: 5176: 5168: 5163: 5161: 5153: 5145: 5126:If the fluid is 5122: 5120: 5119: 5114: 5106: 5104: 5096: 5088: 5083: 5075: 5057: 5055: 5054: 5049: 5041: 5018: 4991: 4989: 4988: 4983: 4968: 4966: 4965: 4960: 4936: 4934: 4933: 4928: 4920: 4881: 4879: 4878: 4873: 4849: 4847: 4846: 4841: 4807: 4801: 4799: 4797: 4796: 4791: 4779: 4777: 4776: 4771: 4759: 4757: 4756: 4751: 4749: 4748: 4739: 4718: 4716: 4715: 4710: 4698: 4696: 4695: 4690: 4688: 4686: 4657: 4637: 4610: 4608: 4607: 4602: 4600: 4599: 4583: 4581: 4580: 4575: 4563: 4561: 4560: 4555: 4543: 4541: 4540: 4535: 4527: 4526: 4517: 4476: 4458: 4456: 4455: 4450: 4427: 4409: 4407: 4406: 4401: 4378: 4360: 4358: 4357: 4352: 4291: 4289: 4288: 4283: 4271: 4269: 4268: 4263: 4250: 4214:Stellar parallax 4190: 4188: 4187: 4182: 4121: 4119: 4118: 4113: 4111: 4109: 4108: 4099: 4094: 4093: 4078: 3965: 3963: 3962: 3957: 3949: 3948: 3939: 3915: 3913: 3912: 3907: 3895: 3893: 3892: 3887: 3873:Augustin Fresnel 3834: 3832: 3831: 3826: 3824: 3822: 3797: 3786: 3777: 3760: 3730: 3728: 3727: 3722: 3710: 3708: 3707: 3702: 3690: 3688: 3687: 3682: 3677: 3661:refractive index 3655: 3611: 3609: 3608: 3603: 3598: 3559: 3557: 3556: 3551: 3549: 3548: 3522: 3520: 3519: 3514: 3512: 3510: 3488: 3479: 3462: 3457: 3455: 3430: 3418: 3398: 3368: 3366: 3365: 3360: 3348: 3346: 3345: 3340: 3324: 3322: 3321: 3316: 3304: 3302: 3301: 3296: 3284: 3282: 3281: 3276: 3271: 3253: 3251: 3250: 3245: 3233: 3231: 3230: 3225: 3220: 3205: 3203: 3202: 3197: 3185: 3183: 3182: 3177: 3040: 3038: 3037: 3032: 3030: 3022: 2999: 2995: 2985: 2977: 2841: 2748: 2684:Early hypotheses 2417: 2415: 2414: 2409: 2397: 2395: 2394: 2389: 2378: 2357: 2355: 2354: 2349: 2344: 2302: 2300: 2299: 2294: 2282: 2280: 2279: 2274: 2269: 2248: 2246: 2245: 2240: 2215: 2213: 2212: 2207: 2192: 2190: 2189: 2184: 2168: 2166: 2165: 2160: 2109: 2107: 2106: 2101: 2054: 2052: 2051: 2046: 2030: 2028: 2027: 2022: 1987: 1985: 1984: 1979: 1964: 1962: 1961: 1956: 1944: 1942: 1941: 1936: 1931: 1898: 1896: 1895: 1890: 1851: 1849: 1848: 1843: 1831:orbital velocity 1813:Stellar parallax 1677: 1675: 1674: 1669: 1661: 1658: 1653: 1640: 1635: 1626: 1617: 1615: 1614: 1609: 1604: 1577: 1575: 1574: 1569: 1558: 1543: 1541: 1540: 1535: 1530: 1491: 1489: 1488: 1483: 1481: 1480: 1455: 1453: 1452: 1447: 1445: 1443: 1418: 1403: 1386: 1381: 1379: 1369: 1368: 1352: 1351: 1342: 1337: 1331: 1318: 1309: 1279: 1277: 1276: 1271: 1269: 1267: 1266: 1257: 1252: 1251: 1236: 1234: 1210: 1208: 1207: 1202: 1197: 1196: 1187: 1179: 1178: 1157: 1152: 1151: 1135: 1118: 1116: 1115: 1110: 1105: 1104: 1095: 1087: 1086: 1068: 1054: 1053: 1034: 999: 997: 996: 991: 986: 959: 957: 956: 951: 940: 925: 923: 922: 917: 912: 873: 871: 870: 865: 863: 862: 837: 835: 834: 829: 827: 825: 803: 794: 777: 772: 770: 763: 762: 752: 751: 742: 737: 731: 718: 709: 679: 677: 676: 671: 669: 668: 652: 636: 634: 633: 628: 620: 619: 603: 587: 585: 584: 579: 567: 565: 564: 559: 557: 556: 547: 542: 541: 507: 505: 504: 499: 487: 485: 484: 479: 477: 476: 460: 458: 457: 452: 450: 449: 433: 431: 430: 425: 364: 357: 353: 350: 344: 342: 301: 277: 269: 227:Augustin Fresnel 202:electromagnetism 152: 150: 149: 144: 128: 126: 125: 120: 108: 106: 105: 100: 95: 21: 6667: 6666: 6662: 6661: 6660: 6658: 6657: 6656: 6632: 6631: 6630: 6620: 6618: 6608: 6606: 6596: 6594: 6582: 6572: 6570: 6562: 6552: 6491: 6489:Further reading 6486: 6471: 6460: 6458: 6454: 6453: 6423: 6422: 6418: 6411: 6394: 6393: 6389: 6381: 6375: 6360: 6355: 6354: 6350: 6338: 6337: 6321: 6320: 6309: 6304:Wayback Machine 6295: 6291: 6239: 6238: 6234: 6206: 6205: 6198: 6191: 6168: 6167: 6163: 6156: 6135: 6134: 6127: 6119: 6112: 6107: 6103: 6095: 6084: 6044: 6043: 6039: 6029: 6027: 6014: 6013: 6009: 5961: 5960: 5951: 5905: 5904: 5900: 5864: 5863: 5859: 5832: 5831: 5827: 5789: 5788: 5775: 5727: 5726: 5717: 5700: 5699: 5695: 5688: 5671: 5670: 5663: 5656: 5638: 5637: 5633: 5623: 5619: 5612: 5597: 5596: 5592: 5546: 5545: 5538: 5531: 5518: 5517: 5508: 5472: 5471: 5464: 5426: 5425: 5421: 5414: 5401: 5400: 5389: 5384: 5379: 5378: 5339: 5338: 5316: 5315: 5288: 5283: 5282: 5263: 5262: 5230: 5217: 5203: 5202: 5177: 5169: 5154: 5146: 5139: 5138: 5097: 5089: 5063: 5062: 4994: 4993: 4971: 4970: 4939: 4938: 4884: 4883: 4852: 4851: 4820: 4819: 4808: 4804: 4782: 4781: 4762: 4761: 4740: 4721: 4720: 4701: 4700: 4658: 4638: 4613: 4612: 4591: 4586: 4585: 4566: 4565: 4546: 4545: 4518: 4461: 4460: 4412: 4411: 4363: 4362: 4298: 4297: 4274: 4273: 4254: 4253: 4251: 4247: 4242: 4205: 4173: 4172: 4135: 4129: 4100: 4085: 4072: 4071: 4034: 4028: 3982: 3940: 3918: 3917: 3898: 3897: 3878: 3877: 3869: 3864: 3858: 3778: 3761: 3736: 3735: 3713: 3712: 3693: 3692: 3665: 3664: 3656: 3653: 3628: 3622: 3562: 3561: 3540: 3529: 3528: 3527:In the case of 3480: 3463: 3419: 3399: 3374: 3373: 3351: 3350: 3331: 3330: 3307: 3306: 3305:different from 3287: 3286: 3256: 3255: 3236: 3235: 3208: 3207: 3188: 3187: 3168: 3167: 3139: 3127:Albert Einstein 3123:electron theory 3119:Hendrik Lorentz 3083: 3055: 2975: 2971: 2960: 2959: 2825:19.5" northward 2791:19.5" southward 2726: 2686: 2661:Samuel Molyneux 2641: 2557: 2541: 2532: 2526: 2518:reference epoch 2448: 2424: 2400: 2399: 2360: 2359: 2305: 2304: 2285: 2284: 2251: 2250: 2219: 2218: 2198: 2197: 2175: 2174: 2151: 2150: 2147: 2122:is 0 on either 2120:right ascension 2092: 2091: 2037: 2036: 2013: 2012: 1970: 1969: 1947: 1946: 1901: 1900: 1881: 1880: 1834: 1833: 1815: 1781: 1720: 1684: 1620: 1619: 1580: 1579: 1546: 1545: 1494: 1493: 1472: 1461: 1460: 1459:In the case of 1404: 1387: 1360: 1353: 1343: 1285: 1284: 1258: 1243: 1216: 1215: 1188: 1170: 1143: 1122: 1121: 1096: 1078: 1045: 1021: 1020: 1006: 962: 961: 928: 927: 876: 875: 854: 843: 842: 841:In the case of 795: 778: 754: 753: 743: 685: 684: 660: 639: 638: 611: 590: 589: 570: 569: 548: 533: 510: 509: 490: 489: 468: 463: 462: 441: 436: 435: 416: 415: 412: 365: 354: 348: 345: 302: 300: 290: 278: 267: 259:Albert Einstein 235:Hendrik Lorentz 168:right ascension 135: 134: 111: 110: 83: 82: 79:apparent motion 43: 28: 23: 22: 15: 12: 11: 5: 6665: 6663: 6655: 6654: 6649: 6644: 6634: 6633: 6629: 6628: 6616: 6604: 6592: 6580: 6560: 6559: 6551: 6550:External links 6548: 6547: 6546: 6536: 6529:Thomas Simpson 6526: 6521:H. H. Turner, 6519: 6512:Charles Hutton 6509: 6499: 6490: 6487: 6485: 6484: 6455: 6452: 6451: 6416: 6409: 6387: 6373: 6365:Going Critical 6348: 6307: 6289: 6232: 6196: 6189: 6161: 6154: 6125: 6110: 6101: 6082: 6037: 6007: 5949: 5943:10.1086/500170 5898: 5877:(2): 743–747. 5857: 5839:. 3rd Series. 5825: 5773: 5715: 5702:Newcomb, Simon 5693: 5686: 5661: 5654: 5631: 5617: 5610: 5590: 5536: 5529: 5506: 5462: 5435:(2): 102–116. 5419: 5412: 5386: 5385: 5383: 5380: 5377: 5376: 5371: 5370: 5357: 5354: 5349: 5346: 5323: 5303: 5300: 5295: 5291: 5270: 5250: 5246: 5242: 5237: 5233: 5229: 5224: 5220: 5216: 5213: 5210: 5199: 5198: 5183: 5180: 5175: 5172: 5166: 5160: 5157: 5152: 5149: 5124: 5123: 5112: 5109: 5103: 5100: 5095: 5092: 5086: 5081: 5078: 5073: 5070: 5047: 5044: 5040: 5036: 5033: 5030: 5027: 5024: 5021: 5017: 5013: 5010: 5007: 5004: 5001: 4981: 4978: 4958: 4955: 4952: 4949: 4946: 4926: 4923: 4919: 4915: 4912: 4909: 4906: 4903: 4900: 4897: 4894: 4891: 4871: 4868: 4865: 4862: 4859: 4839: 4836: 4833: 4830: 4827: 4802: 4789: 4769: 4747: 4743: 4738: 4734: 4731: 4728: 4708: 4685: 4682: 4679: 4676: 4673: 4670: 4667: 4664: 4661: 4656: 4653: 4650: 4647: 4644: 4641: 4635: 4632: 4629: 4626: 4623: 4620: 4598: 4594: 4573: 4553: 4533: 4530: 4525: 4521: 4516: 4512: 4509: 4506: 4503: 4500: 4497: 4494: 4491: 4488: 4485: 4482: 4479: 4475: 4471: 4468: 4448: 4445: 4442: 4439: 4436: 4433: 4430: 4426: 4422: 4419: 4399: 4396: 4393: 4390: 4387: 4384: 4381: 4377: 4373: 4370: 4350: 4347: 4344: 4341: 4338: 4335: 4332: 4329: 4326: 4323: 4320: 4317: 4314: 4311: 4308: 4305: 4281: 4261: 4244: 4243: 4241: 4238: 4237: 4236: 4231: 4226: 4221: 4216: 4211: 4209:Apparent place 4204: 4201: 4180: 4128: 4125: 4107: 4103: 4098: 4092: 4088: 4084: 4081: 4027: 4024: 3981: 3978: 3955: 3952: 3947: 3943: 3938: 3934: 3931: 3928: 3925: 3905: 3885: 3868: 3865: 3857: 3854: 3845:François Arago 3837: 3836: 3821: 3818: 3815: 3812: 3809: 3806: 3803: 3800: 3796: 3792: 3789: 3785: 3781: 3776: 3773: 3770: 3767: 3764: 3758: 3755: 3752: 3749: 3746: 3743: 3720: 3700: 3680: 3676: 3672: 3651: 3621: 3618: 3614:speed of light 3601: 3597: 3593: 3590: 3587: 3584: 3581: 3578: 3575: 3572: 3569: 3547: 3543: 3539: 3536: 3525: 3524: 3509: 3506: 3503: 3500: 3497: 3494: 3491: 3487: 3483: 3478: 3475: 3472: 3469: 3466: 3460: 3454: 3451: 3448: 3445: 3442: 3439: 3436: 3433: 3429: 3425: 3422: 3417: 3414: 3411: 3408: 3405: 3402: 3396: 3393: 3390: 3387: 3384: 3381: 3358: 3338: 3314: 3294: 3274: 3270: 3266: 3263: 3243: 3223: 3219: 3215: 3206:taking a time 3195: 3175: 3138: 3135: 3121:to develop an 3090:speed of light 3082: 3079: 3059:René Descartes 3054: 3051: 3042: 3041: 3028: 3025: 3020: 3017: 3014: 3011: 3008: 3005: 3002: 2998: 2994: 2991: 2988: 2983: 2980: 2974: 2970: 2967: 2950: 2949: 2946: 2944: 2940: 2939: 2936: 2933: 2929: 2928: 2925: 2922: 2918: 2917: 2914: 2911: 2907: 2906: 2903: 2900: 2896: 2895: 2892: 2889: 2885: 2884: 2881: 2878: 2874: 2873: 2870: 2867: 2863: 2862: 2859: 2856: 2852: 2851: 2848: 2845: 2833: 2832: 2829: 2826: 2823: 2820: 2816: 2815: 2812: 2809: 2806: 2803: 2799: 2798: 2795: 2792: 2789: 2786: 2782: 2781: 2778: 2775: 2772: 2769: 2765: 2764: 2761: 2758: 2755: 2752: 2725: 2722: 2685: 2682: 2640: 2637: 2617:John Flamsteed 2566:theory of the 2556: 2553: 2540: 2537: 2525: 2522: 2447: 2444: 2428:rotating Earth 2423: 2420: 2407: 2387: 2384: 2381: 2377: 2373: 2370: 2367: 2347: 2343: 2339: 2336: 2333: 2330: 2327: 2324: 2321: 2318: 2315: 2312: 2292: 2272: 2268: 2264: 2261: 2258: 2238: 2235: 2232: 2229: 2226: 2205: 2182: 2158: 2146: 2143: 2099: 2044: 2033:ecliptic poles 2020: 2005:circular orbit 1977: 1967:speed of light 1954: 1934: 1930: 1926: 1923: 1920: 1917: 1914: 1911: 1908: 1888: 1871:Approximating 1862:appear to move 1858:elliptic orbit 1841: 1789:ecliptic poles 1780: 1777: 1776: 1775: 1765: 1764: 1763: 1754: 1745: 1719: 1716: 1683: 1680: 1667: 1664: 1657: 1652: 1648: 1644: 1639: 1634: 1630: 1607: 1603: 1599: 1596: 1593: 1590: 1587: 1567: 1564: 1561: 1557: 1553: 1533: 1529: 1525: 1522: 1519: 1516: 1513: 1510: 1507: 1504: 1501: 1479: 1475: 1471: 1468: 1457: 1456: 1442: 1439: 1436: 1433: 1430: 1427: 1424: 1421: 1417: 1413: 1410: 1407: 1402: 1399: 1396: 1393: 1390: 1384: 1378: 1375: 1372: 1367: 1363: 1359: 1356: 1350: 1346: 1340: 1334: 1330: 1326: 1321: 1317: 1313: 1307: 1304: 1301: 1298: 1295: 1292: 1265: 1261: 1256: 1250: 1246: 1242: 1239: 1233: 1229: 1226: 1223: 1212: 1211: 1200: 1195: 1191: 1186: 1182: 1177: 1173: 1169: 1166: 1163: 1160: 1156: 1150: 1146: 1142: 1138: 1134: 1130: 1119: 1108: 1103: 1099: 1094: 1090: 1085: 1081: 1077: 1074: 1071: 1067: 1063: 1060: 1057: 1052: 1048: 1044: 1041: 1037: 1033: 1029: 1005: 1002: 989: 985: 981: 978: 975: 972: 969: 949: 946: 943: 939: 935: 915: 911: 907: 904: 901: 898: 895: 892: 889: 886: 883: 861: 857: 853: 850: 839: 838: 824: 821: 818: 815: 812: 809: 806: 802: 798: 793: 790: 787: 784: 781: 775: 769: 766: 761: 757: 750: 746: 740: 734: 730: 726: 721: 717: 713: 707: 704: 701: 698: 695: 692: 667: 663: 659: 655: 651: 647: 626: 623: 618: 614: 610: 606: 602: 598: 577: 555: 551: 546: 540: 536: 532: 529: 526: 523: 520: 517: 497: 475: 471: 448: 444: 423: 411: 408: 367: 366: 281: 279: 272: 266: 263: 229:(in 1818) and 142: 131:speed of light 118: 98: 94: 90: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 6664: 6653: 6650: 6648: 6645: 6643: 6640: 6639: 6637: 6627: 6617: 6615: 6605: 6603: 6593: 6591: 6586: 6581: 6579: 6569: 6565: 6557: 6554: 6553: 6549: 6544: 6540: 6537: 6534: 6530: 6527: 6524: 6520: 6517: 6513: 6510: 6507: 6503: 6500: 6497: 6493: 6492: 6488: 6481: 6480: 6475: 6469: 6468:public domain 6457: 6456: 6447: 6443: 6439: 6435: 6431: 6427: 6420: 6417: 6412: 6410:0-19-850594-9 6406: 6401: 6400: 6391: 6388: 6380: 6376: 6370: 6366: 6359: 6352: 6349: 6344: 6343: 6334: 6330: 6329: 6324: 6318: 6316: 6314: 6312: 6308: 6305: 6301: 6298: 6293: 6290: 6285: 6281: 6277: 6273: 6269: 6265: 6261: 6257: 6253: 6249: 6248: 6243: 6236: 6233: 6227: 6222: 6218: 6214: 6210: 6203: 6201: 6197: 6192: 6186: 6182: 6178: 6173: 6165: 6162: 6157: 6155:9780486202105 6151: 6147: 6142: 6141: 6132: 6130: 6126: 6123:, p. 55. 6122: 6117: 6115: 6111: 6105: 6102: 6099:, p. 54. 6098: 6093: 6091: 6089: 6087: 6083: 6078: 6074: 6070: 6066: 6061: 6056: 6052: 6048: 6041: 6038: 6025: 6021: 6017: 6011: 6008: 6003: 5999: 5995: 5991: 5987: 5983: 5978: 5973: 5969: 5965: 5958: 5956: 5954: 5950: 5944: 5939: 5935: 5931: 5926: 5921: 5917: 5913: 5909: 5902: 5899: 5893: 5888: 5884: 5880: 5876: 5872: 5868: 5861: 5858: 5854: 5850: 5846: 5842: 5838: 5837: 5829: 5826: 5821: 5817: 5813: 5809: 5805: 5801: 5797: 5793: 5786: 5784: 5782: 5780: 5778: 5774: 5769: 5765: 5761: 5757: 5753: 5749: 5744: 5739: 5735: 5731: 5724: 5722: 5720: 5716: 5711: 5707: 5703: 5697: 5694: 5689: 5687:0-521-64216-7 5683: 5679: 5676:. Cambridge: 5675: 5668: 5666: 5662: 5657: 5655:9780707741499 5651: 5647: 5646: 5641: 5635: 5632: 5628: 5621: 5618: 5613: 5611:0-387-95210-1 5607: 5603: 5602: 5594: 5591: 5586: 5582: 5578: 5574: 5570: 5566: 5562: 5559:(1): 45–105. 5558: 5554: 5550: 5543: 5541: 5537: 5532: 5530:0-8050-7133-4 5526: 5522: 5515: 5513: 5511: 5507: 5501: 5496: 5492: 5488: 5484: 5480: 5476: 5469: 5467: 5463: 5458: 5454: 5450: 5446: 5442: 5438: 5434: 5430: 5423: 5420: 5415: 5413:0-08-015674-6 5409: 5405: 5398: 5396: 5394: 5392: 5388: 5381: 5374: 5355: 5352: 5347: 5344: 5337: 5336: 5335: 5321: 5301: 5298: 5293: 5289: 5268: 5248: 5244: 5235: 5231: 5227: 5222: 5218: 5211: 5208: 5181: 5173: 5164: 5158: 5150: 5137: 5136: 5135: 5133: 5129: 5110: 5107: 5101: 5093: 5084: 5079: 5076: 5071: 5068: 5061: 5060: 5059: 5042: 5038: 5034: 5031: 5022: 5019: 5015: 5011: 5008: 5002: 4999: 4979: 4976: 4956: 4953: 4950: 4947: 4944: 4924: 4921: 4917: 4913: 4910: 4907: 4904: 4898: 4892: 4889: 4869: 4866: 4863: 4860: 4857: 4837: 4834: 4831: 4828: 4825: 4812: 4806: 4803: 4787: 4767: 4745: 4741: 4736: 4732: 4729: 4726: 4706: 4680: 4674: 4671: 4668: 4665: 4662: 4659: 4651: 4645: 4642: 4639: 4633: 4627: 4621: 4618: 4596: 4592: 4584:is angle and 4571: 4551: 4531: 4523: 4519: 4514: 4510: 4507: 4504: 4498: 4492: 4486: 4483: 4477: 4473: 4469: 4443: 4437: 4434: 4428: 4424: 4420: 4394: 4388: 4385: 4379: 4375: 4371: 4345: 4342: 4339: 4333: 4330: 4327: 4324: 4318: 4315: 4312: 4306: 4303: 4295: 4279: 4259: 4249: 4246: 4239: 4235: 4232: 4230: 4227: 4225: 4224:Proper motion 4222: 4220: 4217: 4215: 4212: 4210: 4207: 4206: 4202: 4200: 4198: 4194: 4178: 4168: 4163: 4161: 4155: 4153: 4147: 4145: 4141: 4134: 4126: 4124: 4105: 4101: 4096: 4090: 4086: 4082: 4079: 4069: 4065: 4060: 4054: 4052: 4048: 4044: 4040: 4033: 4023: 4019: 4017: 4012: 4009:and that the 4008: 4003: 3998: 3995: 3991: 3987: 3972: 3968: 3953: 3945: 3941: 3936: 3932: 3929: 3926: 3903: 3883: 3874: 3863: 3855: 3853: 3851: 3846: 3842: 3816: 3810: 3807: 3804: 3798: 3794: 3790: 3783: 3779: 3771: 3765: 3762: 3756: 3750: 3744: 3741: 3734: 3733: 3732: 3718: 3698: 3678: 3674: 3670: 3662: 3650: 3645: 3642: 3632: 3627: 3619: 3617: 3615: 3599: 3595: 3591: 3588: 3582: 3579: 3576: 3570: 3567: 3560:, this gives 3545: 3541: 3537: 3534: 3504: 3498: 3495: 3492: 3489: 3485: 3481: 3473: 3467: 3464: 3458: 3449: 3443: 3440: 3437: 3434: 3431: 3427: 3423: 3420: 3412: 3406: 3403: 3400: 3394: 3388: 3382: 3379: 3372: 3371: 3370: 3356: 3336: 3328: 3312: 3292: 3272: 3268: 3264: 3261: 3241: 3221: 3217: 3213: 3193: 3173: 3163: 3160: 3152: 3148: 3143: 3134: 3132: 3128: 3124: 3120: 3115: 3114:George Stokes 3111: 3107: 3103: 3099: 3095: 3091: 3086: 3080: 3078: 3076: 3072: 3068: 3063: 3060: 3050: 3046: 3026: 3023: 3018: 3012: 3006: 3003: 3000: 2996: 2992: 2989: 2986: 2981: 2978: 2972: 2968: 2965: 2958: 2957: 2956: 2947: 2945: 2942: 2941: 2937: 2934: 2931: 2930: 2926: 2923: 2920: 2919: 2915: 2912: 2909: 2908: 2904: 2901: 2898: 2897: 2893: 2890: 2887: 2886: 2882: 2879: 2876: 2875: 2871: 2868: 2865: 2864: 2860: 2857: 2854: 2853: 2849: 2846: 2843: 2842: 2839: 2830: 2827: 2824: 2821: 2818: 2817: 2813: 2810: 2807: 2804: 2801: 2800: 2796: 2793: 2790: 2787: 2784: 2783: 2779: 2776: 2773: 2770: 2767: 2766: 2762: 2759: 2756: 2753: 2750: 2749: 2746: 2743: 2738: 2736: 2731: 2730:Royal Society 2723: 2721: 2719: 2714: 2712: 2708: 2698: 2690: 2683: 2681: 2679: 2673: 2671: 2670:George Graham 2667: 2662: 2654: 2650: 2645: 2636: 2634: 2630: 2626: 2622: 2618: 2614: 2610: 2606: 2604: 2598: 2594: 2589: 2588:Thomas Digges 2585: 2581: 2577: 2573: 2569: 2565: 2562: 2554: 2552: 2550: 2546: 2538: 2536: 2531: 2523: 2521: 2519: 2515: 2511: 2510:data releases 2509: 2502: 2497: 2493: 2491: 2486: 2482: 2477: 2475: 2474:proper motion 2469: 2466: 2465:extragalactic 2462: 2458: 2454: 2445: 2443: 2441: 2437: 2433: 2429: 2421: 2419: 2405: 2385: 2382: 2379: 2375: 2371: 2368: 2365: 2345: 2341: 2337: 2331: 2328: 2325: 2319: 2313: 2310: 2290: 2270: 2266: 2262: 2259: 2256: 2236: 2233: 2230: 2227: 2203: 2194: 2180: 2172: 2156: 2144: 2142: 2140: 2135: 2133: 2127: 2125: 2121: 2117: 2113: 2097: 2089: 2085: 2084:March equinox 2081: 2077: 2073: 2069: 2068:Arctic Circle 2064: 2062: 2058: 2042: 2034: 2018: 2010: 2006: 2001: 1999: 1995: 1991: 1975: 1968: 1952: 1932: 1928: 1924: 1921: 1918: 1915: 1912: 1909: 1906: 1886: 1878: 1874: 1873:Earth's orbit 1869: 1867: 1863: 1859: 1855: 1839: 1832: 1828: 1824: 1820: 1814: 1805: 1798: 1794: 1790: 1787:Stars at the 1785: 1778: 1773: 1769: 1766: 1761: 1759: 1755: 1752: 1750: 1746: 1743: 1741: 1737: 1736: 1734: 1731: 1730: 1729: 1727: 1726: 1717: 1715: 1712: 1707: 1703: 1701: 1697: 1688: 1681: 1679: 1665: 1662: 1655: 1650: 1646: 1642: 1637: 1632: 1628: 1605: 1601: 1597: 1594: 1591: 1588: 1585: 1565: 1562: 1559: 1555: 1551: 1531: 1527: 1523: 1520: 1514: 1511: 1508: 1502: 1499: 1477: 1473: 1469: 1466: 1434: 1428: 1425: 1422: 1419: 1415: 1411: 1405: 1397: 1391: 1388: 1382: 1373: 1370: 1365: 1361: 1354: 1348: 1344: 1338: 1332: 1328: 1324: 1319: 1315: 1311: 1305: 1299: 1293: 1290: 1283: 1282: 1281: 1263: 1259: 1254: 1248: 1244: 1240: 1237: 1231: 1227: 1224: 1221: 1193: 1189: 1184: 1180: 1175: 1171: 1167: 1164: 1158: 1154: 1148: 1144: 1140: 1136: 1132: 1128: 1120: 1101: 1097: 1092: 1088: 1083: 1079: 1075: 1072: 1065: 1058: 1055: 1050: 1046: 1039: 1035: 1031: 1027: 1019: 1018: 1017: 1015: 1011: 1003: 1001: 987: 983: 979: 976: 973: 970: 967: 947: 944: 941: 937: 933: 913: 909: 905: 902: 896: 893: 890: 884: 881: 859: 855: 851: 848: 819: 813: 810: 807: 804: 800: 796: 788: 782: 779: 773: 767: 764: 759: 755: 748: 744: 738: 732: 728: 724: 719: 715: 711: 705: 699: 693: 690: 683: 682: 681: 665: 661: 657: 653: 649: 645: 624: 621: 616: 612: 608: 604: 600: 596: 575: 553: 549: 544: 538: 534: 530: 524: 518: 515: 495: 473: 469: 446: 442: 421: 409: 407: 405: 401: 397: 392: 388: 384: 382: 373: 363: 360: 352: 341: 338: 334: 331: 327: 324: 320: 317: 313: 310: – 309: 305: 304:Find sources: 298: 294: 288: 287: 282:This section 280: 276: 271: 270: 264: 262: 260: 256: 252: 248: 244: 240: 239:aether theory 236: 232: 228: 224: 219: 215: 214:James Bradley 211: 207: 203: 199: 194: 192: 188: 184: 180: 175: 173: 169: 165: 161: 156: 140: 132: 116: 96: 92: 88: 80: 76: 72: 68: 64: 60: 56: 47: 41: 37: 33: 19: 6626:Solar System 6542: 6532: 6522: 6515: 6505: 6495: 6477: 6432:(1): 47–57. 6429: 6425: 6419: 6398: 6390: 6367:. Springer. 6364: 6351: 6340: 6327: 6292: 6251: 6245: 6235: 6216: 6212: 6176: 6164: 6139: 6104: 6050: 6046: 6040: 6030:14 September 6028:. Retrieved 6019: 6010: 5967: 5963: 5915: 5911: 5901: 5874: 5870: 5860: 5852: 5843:(3–6): 175. 5840: 5834: 5828: 5795: 5791: 5733: 5729: 5705: 5696: 5673: 5644: 5634: 5626: 5620: 5600: 5593: 5556: 5552: 5520: 5482: 5478: 5432: 5428: 5422: 5403: 5372: 5200: 5128:irrotational 5125: 4817: 4805: 4780:in terms of 4248: 4196: 4170: 4165: 4157: 4149: 4136: 4058: 4055: 4035: 4020: 4007:irrotational 3999: 3983: 3870: 3838: 3691:rather than 3658: 3647: 3641:Thomas Young 3638: 3526: 3326: 3164: 3156: 3150: 3146: 3087: 3084: 3056: 3047: 3043: 2953: 2836: 2739: 2727: 2715: 2703: 2674: 2658: 2627:, a star of 2621:Robert Hooke 2600: 2568:Solar System 2564:heliocentric 2558: 2542: 2533: 2507: 2500: 2489: 2478: 2470: 2449: 2425: 2195: 2170: 2169:towards the 2148: 2136: 2128: 2080:sidereal day 2065: 2002: 1876: 1870: 1816: 1767: 1756: 1747: 1738: 1732: 1723: 1721: 1711:acceleration 1708: 1704: 1693: 1458: 1213: 1007: 840: 413: 393: 389: 385: 378: 355: 346: 336: 329: 322: 315: 303: 291:Please help 286:verification 283: 231:G. G. Stokes 195: 178: 176: 70: 66: 62: 58: 52: 6614:Outer space 6602:Spaceflight 6254:(1): 1–12. 6219:: 637–661. 4294:Snell's law 3876:refraction 2877:η Ursa Maj. 2597:Jean Picard 2576:Tycho Brahe 2457:Local Group 2088:declination 2003:Assuming a 265:Explanation 216:provided a 172:declination 77:exhibit an 6647:Astrometry 6636:Categories 6474:Aberration 6060:2012.02036 5743:2010.13625 5382:References 5261:where the 4131:See also: 4059:completely 4030:See also: 3860:See also: 3624:See also: 3013:0.00009793 2993:0.00009793 2866:β Draconis 2855:γ Draconis 2735:apocryphal 2649:γ Draconis 2625:γ Draconis 2603:Uranibourg 2561:Copernican 2549:parallaxes 2528:See also: 2496:our galaxy 2481:astrometry 2132:barycenter 1996:(rad) (at 1990:arcseconds 1811:See also: 508:such that 319:newspapers 179:aberration 164:arcseconds 59:aberration 6652:Radiation 6578:Astronomy 6284:118187860 6268:0003-9519 6002:119305429 5977:1009.3698 5820:198471325 5768:225068756 5457:118565124 5348:≈ 5345:α 5228:− 5209:α 5179:∂ 5171:∂ 5156:∂ 5148:∂ 5099:∂ 5091:∂ 5085:∫ 5072:≈ 5069:α 5003:≈ 5000:α 4951:≈ 4899:α 4893:⁡ 4788:θ 4768:ϕ 4681:α 4675:⁡ 4652:α 4646:⁡ 4628:ϕ 4622:⁡ 4572:α 4508:− 4499:− 4493:ψ 4487:⁡ 4444:ψ 4438:⁡ 4395:ψ 4389:⁡ 4346:ϕ 4343:− 4340:ψ 4334:⁡ 4319:ϕ 4316:− 4313:θ 4307:⁡ 4296:, giving 4280:ψ 4260:θ 4179:γ 4083:− 4043:Heaviside 4000:In 1845, 3986:polarized 3930:− 3871:In 1818, 3841:objective 3817:θ 3811:⁡ 3772:θ 3766:⁡ 3751:ϕ 3745:⁡ 3583:ϕ 3580:− 3577:θ 3571:⁡ 3546:∘ 3535:θ 3505:θ 3499:⁡ 3474:θ 3468:⁡ 3450:θ 3444:⁡ 3413:θ 3407:⁡ 3389:ϕ 3383:⁡ 3357:ϕ 3337:ϕ 3313:θ 3293:ϕ 3174:θ 3007:⁡ 2990:− 2987:π 2969:⁡ 2921:35 Camel. 2819:September 2629:magnitude 2601:Voyage d' 2599:, in his 2436:longitude 2406:κ 2386:κ 2366:θ 2335:Δ 2329:θ 2326:≈ 2320:θ 2314:⁡ 2225:Δ 2204:κ 2181:κ 2157:κ 2110:. On the 2098:κ 2043:κ 2019:κ 1922:≈ 1919:ϕ 1916:− 1913:θ 1907:κ 1887:κ 1864:in small 1825:. Due to 1592:ϕ 1589:− 1586:θ 1563:≪ 1515:ϕ 1512:− 1509:θ 1503:⁡ 1478:∘ 1467:θ 1435:θ 1429:⁡ 1406:γ 1398:θ 1392:⁡ 1355:γ 1300:ϕ 1294:⁡ 1241:− 1222:γ 1159:γ 974:ϕ 971:− 968:θ 945:≪ 897:ϕ 894:− 891:θ 885:⁡ 860:∘ 849:θ 820:θ 814:⁡ 789:θ 783:⁡ 700:ϕ 694:⁡ 525:θ 519:⁡ 496:θ 349:July 2019 218:classical 177:The term 55:astronomy 6379:Archived 6333:Archived 6325:(1910). 6300:Archived 6276:41133639 5736:: A159. 5704:(1960). 5585:Archived 5581:17459755 4203:See also 3652:— 3327:apparent 2910:α Persei 2899:τ Persei 2768:December 2718:Wanstead 2707:nutation 2520:2015.0. 2487:and the 2432:latitude 2139:parallax 2116:solstice 2009:ecliptic 1965:and the 1866:ellipses 1799:of 270°. 1333:′ 1320:′ 1137:′ 1036:′ 733:′ 720:′ 654:′ 605:′ 183:parallax 160:revolves 155:velocity 6564:Portals 6545:(1838). 6535:(1740). 6525:(1904). 6518:(1795). 6508:(1832). 6470:: 6434:Bibcode 6065:Bibcode 6020:esa.int 5982:Bibcode 5970:: A91. 5930:Bibcode 5879:Bibcode 5800:Bibcode 5798:: A93. 5748:Bibcode 5561:Bibcode 5487:Bibcode 5437:Bibcode 4039:Maxwell 3975:aether. 3067:Huygens 2932:Capella 2888:α Cass. 2613:Polaris 2572:Galileo 2545:Bradley 2440:Equator 2124:equinox 2074:at the 2072:transit 2061:ellipse 1994:radians 396:history 333:scholar 129:is the 6464: 6407: 6371: 6282: 6274: 6266: 6187: 6152: 6053:: A9. 6000: 5818: 5766: 5684: 5652: 5608: 5579: 5527: 5455: 5410: 4699:where 4002:Stokes 3990:Cauchy 3711:where 3649:trees. 3062:argued 2742:colure 2584:Newton 2580:Kepler 2506:later 2076:zenith 1854:varies 1829:, the 1214:where 335: 328: 321: 314: 306: 257:, led 249:, the 245:, the 109:where 6590:Stars 6382:(PDF) 6361:(PDF) 6280:S2CID 6272:JSTOR 6146:Dover 6055:arXiv 5998:S2CID 5972:arXiv 5920:arXiv 5816:S2CID 5764:S2CID 5738:arXiv 5710:Dover 5577:S2CID 5453:S2CID 4564:. If 4240:Notes 4140:above 4047:Hertz 3994:Green 3094:Earth 2948:40.4 2938:40.0 2927:40.2 2916:40.2 2905:41.0 2894:40.8 2883:40.4 2872:40.2 2861:40.4 2831:none 2797:none 2785:March 2751:Month 2609:years 1998:J2000 1819:Earth 1718:Types 340:JSTOR 326:books 198:light 69:, or 38:, or 6405:ISBN 6369:ISBN 6264:ISSN 6185:ISBN 6150:ISBN 6032:2022 5682:ISBN 5650:ISBN 5606:ISBN 5525:ISBN 5408:ISBN 4410:and 4062:the 4045:and 3992:and 3850:Airy 2943:MEAN 2844:Star 2828:zero 2808:none 2805:zero 2802:June 2794:zero 2774:none 2771:zero 2651:and 2582:and 2574:and 2559:The 2508:Gaia 2501:Gaia 2490:Gaia 2434:and 2171:west 1722:The 461:and 312:news 189:and 153:the 133:and 6476:". 6442:doi 6256:doi 6221:doi 6073:doi 6051:649 5990:doi 5968:529 5938:doi 5916:131 5887:doi 5875:404 5845:doi 5808:doi 5796:630 5756:doi 5734:644 5627:one 5569:doi 5495:doi 5445:doi 4890:tan 4672:cos 4643:sin 4619:tan 4484:cos 4435:cos 4386:sin 4331:sin 4304:sin 3808:cos 3763:sin 3742:tan 3568:tan 3496:cos 3465:sin 3441:cos 3404:sin 3380:tan 3098:Sun 3077:.) 3004:sin 2966:cos 2666:Kew 2311:tan 2000:). 1823:Sun 1500:sin 1426:cos 1389:sin 1291:tan 882:tan 811:cos 780:sin 691:tan 516:tan 295:by 237:'s 225:of 170:or 166:in 53:In 6638:: 6541:, 6531:, 6514:, 6504:, 6440:. 6430:31 6428:. 6377:. 6310:^ 6278:. 6270:. 6262:. 6252:26 6250:. 6244:. 6217:35 6215:. 6211:. 6199:^ 6183:. 6181:30 6175:. 6148:. 6144:. 6128:^ 6113:^ 6085:^ 6071:. 6063:. 6049:. 6022:. 6018:. 5996:. 5988:. 5980:. 5966:. 5952:^ 5936:. 5928:. 5914:. 5910:. 5885:. 5873:. 5869:. 5851:. 5841:15 5814:. 5806:. 5794:. 5776:^ 5762:. 5754:. 5746:. 5732:. 5718:^ 5680:. 5664:^ 5583:. 5575:. 5567:. 5557:59 5555:. 5551:. 5539:^ 5509:^ 5493:. 5483:35 5481:. 5477:. 5465:^ 5451:. 5443:. 5433:10 5431:. 5390:^ 4053:. 4041:, 4018:. 3616:. 3542:90 3104:. 2935:16 2924:19 2913:23 2902:25 2891:34 2880:36 2869:39 2858:39 2737:. 2551:. 2476:. 2193:. 2063:. 1868:. 1774:." 1474:90 1000:. 856:90 406:. 200:, 174:. 65:, 57:, 34:, 6566:: 6448:. 6444:: 6436:: 6413:. 6286:. 6258:: 6229:. 6223:: 6193:. 6158:. 6079:. 6075:: 6067:: 6057:: 6034:. 6004:. 5992:: 5984:: 5974:: 5946:. 5940:: 5932:: 5922:: 5895:. 5889:: 5881:: 5847:: 5822:. 5810:: 5802:: 5770:. 5758:: 5750:: 5740:: 5712:. 5690:. 5658:. 5614:. 5571:: 5563:: 5533:. 5503:. 5497:: 5489:: 5459:. 5447:: 5439:: 5416:. 5356:c 5353:v 5322:v 5302:0 5299:= 5294:2 5290:u 5269:u 5249:c 5245:/ 5241:) 5236:1 5232:u 5223:2 5219:u 5215:( 5212:= 5197:. 5182:z 5174:u 5165:= 5159:x 5151:w 5111:z 5108:d 5102:x 5094:w 5080:c 5077:1 5046:) 5043:c 5039:/ 5035:z 5032:d 5029:( 5026:) 5023:x 5020:d 5016:/ 5012:w 5009:d 5006:( 4980:z 4977:d 4957:t 4954:c 4948:z 4945:d 4925:x 4922:d 4918:/ 4914:w 4911:d 4908:t 4905:= 4902:) 4896:( 4870:z 4867:, 4864:y 4861:, 4858:x 4838:w 4835:, 4832:v 4829:, 4826:u 4746:l 4742:v 4737:/ 4733:h 4730:= 4727:t 4707:h 4684:) 4678:( 4669:h 4666:+ 4663:t 4660:v 4655:) 4649:( 4640:h 4634:= 4631:) 4625:( 4597:l 4593:v 4552:v 4532:v 4529:) 4524:2 4520:n 4515:/ 4511:1 4505:1 4502:( 4496:) 4490:( 4481:) 4478:n 4474:/ 4470:c 4467:( 4447:) 4441:( 4432:) 4429:n 4425:/ 4421:c 4418:( 4398:) 4392:( 4383:) 4380:n 4376:/ 4372:c 4369:( 4349:) 4337:( 4328:n 4325:= 4322:) 4310:( 4197:c 4106:2 4102:c 4097:/ 4091:2 4087:v 4080:1 3954:v 3951:) 3946:2 3942:n 3937:/ 3933:1 3927:1 3924:( 3904:v 3884:n 3835:. 3820:) 3814:( 3805:+ 3802:) 3799:n 3795:/ 3791:c 3788:( 3784:/ 3780:v 3775:) 3769:( 3757:= 3754:) 3748:( 3719:n 3699:c 3679:n 3675:/ 3671:c 3600:c 3596:/ 3592:v 3589:= 3586:) 3574:( 3538:= 3523:. 3508:) 3502:( 3493:+ 3490:c 3486:/ 3482:v 3477:) 3471:( 3459:= 3453:) 3447:( 3438:h 3435:+ 3432:c 3428:/ 3424:v 3421:h 3416:) 3410:( 3401:h 3395:= 3392:) 3386:( 3273:c 3269:/ 3265:h 3262:v 3242:v 3222:c 3218:/ 3214:h 3194:c 3153:. 3151:θ 3147:φ 3027:c 3024:v 3019:= 3016:) 3010:( 3001:= 2997:) 2982:2 2979:1 2973:( 2605:, 2383:= 2380:c 2376:/ 2372:v 2369:= 2346:R 2342:/ 2338:x 2332:= 2323:) 2317:( 2291:R 2271:c 2267:/ 2263:R 2260:= 2257:t 2237:t 2234:v 2231:= 2228:x 1976:c 1953:v 1933:c 1929:/ 1925:v 1910:= 1840:v 1760:: 1751:: 1742:: 1666:c 1663:= 1656:2 1651:y 1647:u 1643:+ 1638:2 1633:x 1629:u 1606:c 1602:/ 1598:v 1595:= 1566:1 1560:c 1556:/ 1552:v 1532:c 1528:/ 1524:v 1521:= 1518:) 1506:( 1470:= 1441:) 1438:) 1432:( 1423:+ 1420:c 1416:/ 1412:v 1409:( 1401:) 1395:( 1383:= 1377:) 1374:v 1371:+ 1366:x 1362:u 1358:( 1349:y 1345:u 1339:= 1329:x 1325:u 1316:y 1312:u 1306:= 1303:) 1297:( 1264:2 1260:c 1255:/ 1249:2 1245:v 1238:1 1232:/ 1228:1 1225:= 1199:) 1194:2 1190:c 1185:/ 1181:v 1176:x 1172:u 1168:+ 1165:1 1162:( 1155:/ 1149:y 1145:u 1141:= 1133:y 1129:u 1107:) 1102:2 1098:c 1093:/ 1089:v 1084:x 1080:u 1076:+ 1073:1 1070:( 1066:/ 1062:) 1059:v 1056:+ 1051:x 1047:u 1043:( 1040:= 1032:x 1028:u 988:c 984:/ 980:v 977:= 948:1 942:c 938:/ 934:v 914:c 910:/ 906:v 903:= 900:) 888:( 852:= 823:) 817:( 808:+ 805:c 801:/ 797:v 792:) 786:( 774:= 768:v 765:+ 760:x 756:u 749:y 745:u 739:= 729:x 725:u 716:y 712:u 706:= 703:) 697:( 666:y 662:u 658:= 650:y 646:u 625:v 622:+ 617:x 613:u 609:= 601:x 597:u 576:v 554:x 550:u 545:/ 539:y 535:u 531:= 528:) 522:( 474:y 470:u 447:x 443:u 422:c 362:) 356:( 351:) 347:( 337:· 330:· 323:· 316:· 289:. 141:v 117:c 97:c 93:/ 89:v 42:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index