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75-508: Located relatively close at 36.7 light-years from the Sun , Arcturus is a red giant of spectral type K1.5III—an aging star around 7.1 billion years old that has used up its core hydrogen and evolved off the main sequence . It is about the same mass as the Sun , but has expanded to 25 times its size (around 35 million kilometers) and is around 170 times as luminous. The traditional name Arcturus

150-407: A star system tend to be small fractions of a light-year, and are usually expressed in astronomical units . However, smaller units of length can similarly be formed usefully by multiplying units of time by the speed of light. For example, the light-second , useful in astronomy, telecommunications and relativistic physics, is exactly 299 792 458 metres or ⁠ 1 / 31 557 600 ⁠ of

225-473: A unit of time . The light-year is most often used when expressing distances to stars and other distances on a galactic scale, especially in non-specialist contexts and popular science publications. The unit most commonly used in professional astronomy is the parsec (symbol: pc, about 3.26 light-years). As defined by the International Astronomical Union (IAU), the light-year

300-524: A B-V color index of +1.23, roughly midway between Pollux (B-V +1.00) and Aldebaran (B-V +1.54). η Boötis , or Muphrid, is only 3.3 light-years distant from Arcturus, and would have a visual magnitude −2.5, about as bright as Jupiter at its brightest from Earth, whereas an observer on the former system would find Arcturus with a magnitude -5.0, slightly brighter than Venus as seen from Earth, but with an orangish color. Based upon an annual parallax shift of 88.83  milliarcseconds , as measured by

375-420: A duration that is probably less than 14 years. A weak magnetic field has been detected in the photosphere with a strength of around half a gauss . The magnetic activity appears to lie along four latitudes and is rotationally modulated. Arcturus is estimated to be around 6 to 8.5 billion years old, but there is some uncertainty about its evolutionary status. Based upon the color characteristics of Arcturus, it

450-475: A few microhertz (μHz), the highest peak corresponding to 4.3 μHz (2.7 days) with an amplitude of 60 ms, with a frequency separation of c. 5 μHz. They suggested that the most plausible explanation for the variability of Arcturus is stellar oscillations. Asteroseismological measurements allow direct calculation of the mass and radius, giving values of 0.8 ± 0.2  M ☉ and 27.9 ± 3.4  R ☉ . This form of modelling

525-474: A given percentage approaches the extremes of 0% or 100%, its margin of error approaches ±0%. Imagine multiple-choice poll P {\displaystyle P} reports p a , p b , p c {\displaystyle p_{a},p_{b},p_{c}} as 46 % , 42 % , 12 % , n = 1013 {\displaystyle 46\%,42\%,12\%,n=1013} . As described above,

600-412: A light-year. Units such as the light-minute, light-hour and light-day are sometimes used in popular science publications. The light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures. The Hayden Planetarium specifies the light month more precisely as 30 days of light travel time. Light travels approximately one foot in a nanosecond ; the term "light-foot"

675-454: A long-period radial velocity oscillation, which could be interpreted as a substellar companion . This substellar object would be nearly 12 times the mass of Jupiter and be located roughly at the same orbital distance from Arcturus as the Earth is from the Sun, at 1.1  astronomical units . However, all three stars surveyed showed similar oscillations yielding similar companion masses, and

750-532: A normal distribution as sample size increases. If this applies, it would speak about the sampling being unbiased, but not about the inherent distribution of the data. According to the 68-95-99.7 rule , we would expect that 95% of the results p 1 , p 2 , … {\displaystyle p_{1},p_{2},\ldots } will fall within about two standard deviations ( ± 2 σ P {\displaystyle \pm 2\sigma _{P}} ) either side of

825-477: A poll P {\displaystyle P} over subsequent samples of n {\displaystyle n} respondents (newly drawn from N {\displaystyle N} ), we would expect those subsequent results p 1 , p 2 , … {\displaystyle p_{1},p_{2},\ldots } to be normally distributed about p ¯ {\displaystyle {\overline {p}}} ,

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900-607: A poll has multiple percentage results (for example, a poll measuring a single multiple-choice preference), the result closest to 50% will have the highest margin of error. Typically, it is this number that is reported as the margin of error for the entire poll. Imagine poll P {\displaystyle P} reports p a , p b , p c {\displaystyle p_{a},p_{b},p_{c}} as 71 % , 27 % , 2 % , n = 1013 {\displaystyle 71\%,27\%,2\%,n=1013} As

975-471: A population N ,  ( n ≪ N ) {\displaystyle N{\text{, }}(n\ll N)} reporting the percentage p {\displaystyle p} of yes responses. We would like to know how close p {\displaystyle p} is to the true result of a survey of the entire population N {\displaystyle N} , without having to conduct one. If, hypothetically, we were to conduct

1050-432: A population having expected standard deviation σ {\displaystyle \sigma } has a margin of error where z γ {\displaystyle z_{\gamma }} denotes the quantile (also, commonly, a z-score ), and σ 2 n {\displaystyle {\sqrt {\frac {\sigma ^{2}}{n}}}} is the standard error . We would expect

1125-433: A surrounding shell. Examination of carbon monoxide lines show the molecular component of the atmosphere extending outward to 2–3 times the radius of the star, with the chromospheric wind steeply accelerating to 35–40 km/s in this region. Astronomers term "metals" those elements with higher atomic numbers than helium . The atmosphere of Arcturus has an enrichment of alpha elements relative to iron but only about

1200-460: A table of the first two batches of names approved by the WGSN, which included Arcturus for α Boötis. With an apparent visual magnitude of −0.05, Arcturus is the brightest star in the northern celestial hemisphere and the fourth-brightest star in the night sky, after Sirius (−1.46 apparent magnitude), Canopus (−0.72) and α Centauri (combined magnitude of −0.27). However, α Centauri AB

1275-453: A third of solar metallicity . Arcturus is possibly a Population II star . As one of the brightest stars in the sky, Arcturus has been the subject of a number of studies in the emerging field of asteroseismology . Belmonte and colleagues carried out a radial velocity (Doppler shift of spectral lines) study of the star in April and May 1988, which showed variability with a frequency of the order of

1350-548: Is "ly", International standards like ISO 80000:2006 (now superseded) have used "l.y." and localized abbreviations are frequent, such as "al" in French, Spanish, and Italian (from année-lumière , año luz and anno luce , respectively), "Lj" in German (from Lichtjahr ), etc. Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in

1425-537: Is Latinised from the ancient Greek Ἀρκτοῦρος ( Arktouros ) and means "Guardian of the Bear", ultimately from ἄρκτος ( arktos ), "bear" and οὖρος ( ouros ), "watcher, guardian". The designation of Arcturus as α Boötis ( Latinised to Alpha Boötis ) was made by Johann Bayer in 1603. 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

1500-427: Is a binary star , whose components are each fainter than Arcturus. This makes Arcturus the third-brightest individual star, just ahead of α Centauri A (officially named Rigil Kentaurus ), whose apparent magnitude is −0.01 . The French mathematician and astronomer Jean-Baptiste Morin observed Arcturus in the daytime with a telescope in 1635. This was the first recorded full daylight viewing for any star other than

1575-402: Is a unit of length used to express astronomical distances and is equal to exactly 9 460 730 472 580 .8 km , which is approximately 5.88 trillion mi. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days). Despite its inclusion of the word "year", the term should not be misinterpreted as

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1650-528: Is an odd name. In 1868 an English journal labelled the light-year as a unit used by the Germans. Eddington called the light-year an inconvenient and irrelevant unit, which had sometimes crept from popular use into technical investigations. Although modern astronomers often prefer to use the parsec , light-years are also popularly used to gauge the expanses of interstellar and intergalactic space. Distances expressed in light-years include those between stars in

1725-666: Is called Da Jiao ( Chinese : 大角 ; pinyin : Dàjiǎo ; lit. 'great horn'), because it is the brightest star in the Chinese constellation called Jiao Xiu (Chinese: 角宿 ; pinyin: Jiǎo Xiǔ ; lit. 'horn star'). Later it became a part of another constellation Kang Xiu (Chinese: 亢宿 ; pinyin: Kàng Xiǔ ). The Wotjobaluk Koori people of southeastern Australia knew Arcturus as Marpean-kurrk , mother of Djuit ( Antares ) and another star in Boötes, Weet-kurrk (Muphrid). Its appearance in

1800-514: Is close to constant, that is, respondents choosing either A or B would almost never choose C (making P a {\displaystyle P_{a}} and P b {\displaystyle P_{b}} close to perfectly negatively correlated ). With three or more choices in closer contention, choosing a correct formula for σ P w 2 {\displaystyle \sigma _{P_{w}}^{2}} becomes more complicated. The formulae above for

1875-449: Is currently ascending the red-giant branch and will continue to do so until it accumulates a large enough degenerate helium core to ignite the helium flash . It has likely exhausted the hydrogen from its core and is now in its active hydrogen shell burning phase. However, Charbonnel et al. (1998) placed it slightly above the horizontal branch , and suggested it has already completed the helium flash stage. Arcturus has evolved off

1950-421: Is due to a lower efficacy as the star has a lower surface temperature than the Sun. There have been suggestions that Arcturus might be a member of a binary system with a faint, cool companion, but no companion has been directly detected. In the absence of a binary companion, the mass of Arcturus cannot be measured directly, but models suggest it is slightly greater than that of the Sun. Evolutionary matching to

2025-418: Is incompletely sampled and the outcome measure has positive variance , which is to say, whenever the measure varies . The term margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities. Consider a simple yes/no poll P {\displaystyle P} as a sample of n {\displaystyle n} respondents drawn from

2100-404: Is sometimes used as an informal measure of time. Margin of error The margin of error is a statistic expressing the amount of random sampling error in the results of a survey . The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the entire population . The margin of error will be positive whenever a population

2175-525: Is specified as السماك الرامح as-simāk ar-rāmiħ "the uplifted one of the lancer". The term Al Simak Al Ramih has appeared in Al Achsasi Al Mouakket catalogue (translated into Latin as Al Simak Lanceator ). This has been variously romanized in the past, leading to obsolete variants such as Aramec and Azimech . For example, the name Alramih is used in Geoffrey Chaucer 's A Treatise on

2250-518: Is still relatively inaccurate, but a useful check on other models. Hipparcos satellite astrometry suggested that Arcturus is a binary star , with the companion about twenty times dimmer than the primary and orbiting close enough to be at the very limits of humans' current ability to make it out. Recent results remain inconclusive, but do support the marginal Hipparcos detection of a binary companion. In 1993, radial velocity measurements of Aldebaran, Arcturus and Pollux showed that Arcturus exhibited

2325-560: Is the product of the Julian year (365.25 days, as opposed to the 365.2425-day Gregorian year or the 365.24219-day Tropical year that both approximate) and the speed of light ( 299 792 458  m/s ). Both of these values are included in the IAU (1976) System of Astronomical Constants , used since 1984. From this, the following conversions can be derived: The abbreviation used by the IAU for light-year

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2400-545: Is the product of the J1900.0 mean tropical year and the defined speed of light. Abbreviations used for light-years and multiples of light-years are: The light-year unit appeared a few years after the first successful measurement of the distance to a star other than the Sun, by Friedrich Bessel in 1838. The star was 61 Cygni , and he used a 160-millimetre (6.2 in) heliometre designed by Joseph von Fraunhofer . The largest unit for expressing distances across space at that time

2475-678: Is to follow the arc of the handle of the Big Dipper (or Plough in the UK ). By continuing in this path, one can find Spica , "Arc to Arcturus, then spike (or speed on) to Spica". Together with the bright stars Spica and Regulus (or Denebola , depending on the source), Arcturus is part of the Spring Triangle asterism . With Cor Caroli , these four stars form the Great Diamond asterism. Ptolemy described Arcturus as subrufa ("slightly red"): it has

2550-509: The Hipparcos satellite, Arcturus is 36.7 light-years (11.26 parsecs ) from the Sun. The parallax margin of error is 0.54 milliarcseconds, translating to a distance margin of error of ±0.23 light-years (0.069 parsecs). Because of its proximity, Arcturus has a high proper motion , two arcseconds a year, greater than any first magnitude star other than α Centauri. Arcturus is moving rapidly (122 km/s or 270,000 mph) relative to

2625-634: The Society Islands , Arcturus, called Ana-tahua-taata-metua-te-tupu-mavae ("a pillar to stand by"), was one of the ten "pillars of the sky", bright stars that represented the ten heavens of the Tahitian afterlife. In Hawaii , the pattern of Boötes was called Hoku-iwa , meaning "stars of the frigatebird". This constellation marked the path for Hawaiʻiloa on his return to Hawaii from the South Pacific Ocean. The Hawaiians called Arcturus Hoku-leʻa . It

2700-410: The Sun and supernovae . Arcturus has been seen at or just before sunset with the naked eye. Arcturus is visible from both of Earth 's hemispheres as it is located 19° north of the celestial equator . The star culminates at midnight on 27 April, and at 9 p.m. on June 10 being visible during the late northern spring or the southern autumn. From the northern hemisphere , an easy way to find Arcturus

2775-485: The maximum margin of error for P {\displaystyle P} at a given confidence level γ {\displaystyle \gamma } and sample size n {\displaystyle n} , even before having actual results.  With p = 0.5 , n = 1013 {\displaystyle p=0.5,n=1013} Also, usefully, for any reported M O E 95 {\displaystyle MOE_{95}} If

2850-1212: The quantile function of the normal distribution (which the 68–95–99.7 rule approximates). Note that z γ {\displaystyle z_{\gamma }} is undefined for | γ | ≥ 1 {\displaystyle |\gamma |\geq 1} , that is, z 1.00 {\displaystyle z_{1.00}} is undefined, as is z 1.10 {\displaystyle z_{1.10}} . Since max σ P 2 = max P ( 1 − P ) = 0.25 {\displaystyle \max \sigma _{P}^{2}=\max P(1-P)=0.25} at p = 0.5 {\displaystyle p=0.5} , we can arbitrarily set p = p ¯ = 0.5 {\displaystyle p={\overline {p}}=0.5} , calculate σ P {\displaystyle \sigma _{P}} , σ p ¯ {\displaystyle \sigma _{\overline {p}}} , and z γ σ p ¯ {\displaystyle z_{\gamma }\sigma _{\overline {p}}} to obtain

2925-458: The ranking of the results. Which is in first? If, hypothetically, we were to conduct a poll P {\displaystyle P} over subsequent samples of n {\displaystyle n} respondents (newly drawn from N {\displaystyle N} ), and report the result p w = p a − p b {\displaystyle p_{w}=p_{a}-p_{b}} , we could use

3000-403: The standard error of difference to understand how p w 1 , p w 2 , p w 3 , … {\displaystyle p_{w_{1}},p_{w_{2}},p_{w_{3}},\ldots } is expected to fall about p w ¯ {\displaystyle {\overline {p_{w}}}} . For this, we need to apply

3075-620: The sum of variances to obtain a new variance, σ P w 2 {\displaystyle \sigma _{P_{w}}^{2}} , where σ P a , P b = − P a P b {\displaystyle \sigma _{P_{a},P_{b}}=-P_{a}P_{b}} is the covariance of P a {\displaystyle P_{a}} and P b {\displaystyle P_{b}} . Thus (after simplifying), Note that this assumes that P c {\displaystyle P_{c}}

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3150-406: The ultraviolet to infrared . The spectrum shows a dramatic transition from emission lines in the ultraviolet to atomic absorption lines in the visible range and molecular absorption lines in the infrared. This is due to the optical depth of the atmosphere varying with wavelength. The spectrum shows very strong absorption in some molecular lines that are not produced in the photosphere but in

3225-587: The "Star of Joy". Arcturus is the zenith star of the Hawaiian Islands . Using Hōkūleʻa and other stars, the Polynesians launched their double-hulled canoes from Tahiti and the Marquesas Islands . Traveling east and north they eventually crossed the equator and reached the latitude at which Arcturus would appear directly overhead in the summer night sky. Knowing they had arrived at the exact latitude of

3300-604: The Astrolabe (1391). Another Arabic name is Haris-el-sema , from حارس السماء ħāris al-samā’ "the keeper of heaven". or حارس الشمال ħāris al-shamāl’ "the keeper of north". In Indian astronomy , Arcturus is called Swati or Svati (Devanagari स्वाति, Transliteration IAST svāti, svātī́), possibly 'su' + 'ati' ("great goer", in reference to its remoteness) meaning very beneficent. It has been referred to as "the real pearl" in Bhartṛhari 's kāvyas. In Chinese astronomy , Arcturus

3375-496: The IAU (1964) System of Astronomical Constants, used from 1968 to 1983. The product of Simon Newcomb 's J1900.0 mean tropical year of 31 556 925 .9747 ephemeris seconds and a speed of light of 299 792 .5 km/s produced a light-year of 9.460 530 × 10  m (rounded to the seven significant digits in the speed of light) found in several modern sources was probably derived from an old source such as C. W. Allen 's 1973 Astrophysical Quantities reference work, which

3450-555: The Sun, and is now almost at its closest point to the Sun. Closest approach will happen in about 4,000 years, when the star will be a few hundredths of a light-year closer to Earth than it is today. (In antiquity, Arcturus was closer to the centre of the constellation.) Arcturus is thought to be an old-disk star , and appears to be moving with a group of 52 other such stars, known as the Arcturus stream . With an absolute magnitude of −0.30, Arcturus is, together with Vega and Sirius, one of

3525-426: The authors concluded that the variation was likely to be intrinsic to the star rather than due to the gravitational effect of a companion. So far no substellar companion has been confirmed. One astronomical tradition associates Arcturus with the mythology around Arcas , who was about to shoot and kill his own mother Callisto who had been transformed into a bear. Zeus averted their imminent tragic fate by transforming

3600-496: The average of normally distributed values   p 1 , p 2 , … {\displaystyle p_{1},p_{2},\ldots } to have a standard deviation which somehow varies with n {\displaystyle n} . The smaller n {\displaystyle n} , the wider the margin. This is called the standard error σ p ¯ {\displaystyle \sigma _{\overline {p}}} . For

3675-559: The boy into the constellation Boötes, called Arctophylax "bear guardian" by the Greeks, and his mother into Ursa Major (Greek: Arctos "the bear"). The account is given in Hyginus 's Astronomy . Aratus in his Phaenomena said that the star Arcturus lay below the belt of Arctophylax, and according to Ptolemy in the Almagest it lay between his thighs. An alternative lore associates the name with

3750-761: The island chain, they sailed due west on the trade winds to landfall. If Hōkūleʻa could be kept directly overhead, they landed on the southeastern shores of the Big Island of Hawaii. For a return trip to Tahiti the navigators could use Sirius, the zenith star of that island. Since 1976, the Polynesian Voyaging Society 's Hōkūleʻa has crossed the Pacific Ocean many times under navigators who have incorporated this wayfinding technique in their non-instrument navigation. Arcturus had several other names that described its significance to indigenous Polynesians . In

3825-405: The legend around Icarius , who gave the gift of wine to other men, but was murdered by them, because they had had no experience with intoxication and mistook the wine for poison. It is stated that Icarius became Arcturus while his dog, Maira , became Canicula ( Procyon ), although "Arcturus" here may be used in the sense of the constellation rather than the star. As one of the brightest stars in

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3900-438: The main sequence to the red giant branch , reaching an early K-type stellar classification . It is frequently assigned the spectral type of K0III, but in 1989 was used as the spectral standard for type K1.5III Fe−0.5, with the suffix notation indicating a mild underabundance of iron compared to typical stars of its type. As the brightest K-type giant in the sky, it has been the subject of multiple atlases with coverage from

3975-411: The margin of error assume that there is an infinitely large population and thus do not depend on the size of population N {\displaystyle N} , but only on the sample size n {\displaystyle n} . According to sampling theory , this assumption is reasonable when the sampling fraction is small. The margin of error for a particular sampling method is essentially

4050-417: The margin of error reported for the poll would typically be M O E 95 ( P a ) {\displaystyle MOE_{95}(P_{a})} , as p a {\displaystyle p_{a}} is closest to 50%. The popular notion of statistical tie or statistical dead heat, however, concerns itself not with the accuracy of the individual results, but with that of

4125-438: The mental picture of the approximate transit time for light, but he refrained from using the light-year as a unit. He may have resisted expressing distances in light-years because it would reduce the accuracy of his parallax data due to multiplying with the uncertain parameter of the speed of light. The speed of light was not yet precisely known in 1838; the estimate of its value changed in 1849 ( Fizeau ) and 1862 ( Foucault ). It

4200-439: The most luminous stars in the Sun's neighborhood. It is about 110 times brighter than the Sun in visible light wavelengths, but this underestimates its strength as much of the light it gives off is in the infrared ; total ( bolometric ) power output is about 180 times that of the Sun. With a near-infrared J band magnitude of −2.2, only Betelgeuse (−2.9) and R Doradus (−2.6) are brighter. The lower output in visible light

4275-465: The myth of King Arthur is based was originally named for the star. In the Middle Ages , Arcturus was considered a Behenian fixed star and attributed to the stone jasper and the plantain herb. Cornelius Agrippa listed its kabbalistic sign [REDACTED] under the alternate name Alchameth . Arcturus's light was employed in the mechanism used to open the 1933 Chicago World's Fair . The star

4350-597: The north signified the arrival of the larvae of the wood ant (a food item) in spring. The beginning of summer was marked by the star's setting with the Sun in the west and the disappearance of the larvae. The people of Milingimbi Island in Arnhem Land saw Arcturus and Muphrid as man and woman, and took the appearance of Arcturus at sunrise as a sign to go and harvest rakia or spikerush . The Weilwan of northern New South Wales knew Arcturus as Guembila "red". Prehistoric Polynesian navigators knew Arcturus as Hōkūleʻa ,

4425-425: The observed physical parameters gives a mass of 1.08 ± 0.06  M ☉ , while the oxygen isotope ratio for a first dredge-up star gives a mass of 1.2  M ☉ . The star, given its evolutionary state, is expected to have undergone significant mass loss in the past. The star displays magnetic activity that is heating the coronal structures, and it undergoes a solar-type magnetic cycle with

4500-412: The prologue to Plautus ' comedy Rudens (circa 211 BC). The Kāraṇḍavyūha Sūtra , compiled at the end of the 4th century or beginning of the 5th century, names one of Avalokiteśvaras meditative absorptions as "The face of Arcturus". One of the possible etymologies offered for the name " Arthur " assumes that it is derived from "Arcturus" and that the late 5th to early 6th-century figure on whom

4575-485: The same general area, such as those belonging to the same spiral arm or globular cluster . Galaxies themselves span from a few thousand to a few hundred thousand light-years in diameter, and are separated from neighbouring galaxies and galaxy clusters by millions of light-years. Distances to objects such as quasars and the Sloan Great Wall run up into the billions of light-years. Distances between objects within

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4650-440: The same regardless of whether the population of interest is the size of a school, city, state, or country, as long as the sampling fraction is small. In cases where the sampling fraction is larger (in practice, greater than 5%), analysts might adjust the margin of error using a finite population correction to account for the added precision gained by sampling a much larger percentage of the population. FPC can be calculated using

4725-580: The single result from our survey, we assume that p = p ¯ {\displaystyle p={\overline {p}}} , and that all subsequent results p 1 , p 2 , … {\displaystyle p_{1},p_{2},\ldots } together would have a variance σ P 2 = P ( 1 − P ) {\displaystyle \sigma _{P}^{2}=P(1-P)} . Note that p ( 1 − p ) {\displaystyle p(1-p)} corresponds to

4800-559: The sky, Arcturus has been significant to observers since antiquity. In ancient Mesopotamia , it was linked to the god Enlil , and also known as Shudun, "yoke", or SHU-PA of unknown derivation in the Three Stars Each Babylonian star catalogues and later MUL.APIN around 1100 BC. In ancient Greek, the star is found in ancient astronomical literature, e.g. Hesiod's Work and Days , circa 700 BC, as well as Hipparchus's and Ptolemy's star catalogs. The folk-etymology connecting

4875-461: The star commonly referred to in Armenian folklore as Gutani astgh ( Armenian : Գութանի աստղ; lit. star of the plow) was in fact Arcturus, as the constellation of Boötes was called "Ezogh" ( Armenian : Եզող; lit. the person who is plowing) by Armenians. In Ancient Rome , the star's celestial activity was supposed to portend tempestuous weather, and a personification of the star acts as narrator of

4950-511: The star name with the bears (Greek: ἄρκτος, arktos) was probably invented much later. It fell out of use in favour of Arabic names until it was revived in the Renaissance . Arcturus is also mentioned in Plato's "Laws" (844e) as a herald for the season of vintage, specifically figs and grapes. In Arabic , Arcturus is one of two stars called al-simāk "the uplifted ones" (the other is Spica ). Arcturus

5025-472: The true but unknown percentage of the population. The margin of error describes the distance within which a specified percentage of these results is expected to vary from p ¯ {\displaystyle {\overline {p}}} . Going by the Central limit theorem , the margin of error helps to explain how the distribution of sample means (or percentage of yes, in this case) will approximate

5100-425: The true mean p ¯ {\displaystyle {\overline {p}}} .  This interval is called the confidence interval , and the radius (half the interval) is called the margin of error , corresponding to a 95% confidence level . Generally, at a confidence level γ {\displaystyle \gamma } , a sample sized n {\displaystyle n} of

5175-840: The variance of a Bernoulli distribution . For a confidence level γ {\displaystyle \gamma } , there is a corresponding confidence interval about the mean μ ± z γ σ {\displaystyle \mu \pm z_{\gamma }\sigma } , that is, the interval [ μ − z γ σ , μ + z γ σ ] {\displaystyle [\mu -z_{\gamma }\sigma ,\mu +z_{\gamma }\sigma ]} within which values of P {\displaystyle P} should fall with probability γ {\displaystyle \gamma } . Precise values of z γ {\displaystyle z_{\gamma }} are given by

5250-735: Was chosen as it was thought that light from Arcturus had started its journey at about the time of the previous Chicago World's Fair in 1893 (at 36.7 light-years away, the light actually started in 1896). At the height of the American Civil War, President Abraham Lincoln observed Arcturus through a 9.6-inch refractor telescope when he visited the Naval Observatory in Washington, D.C., in August 1863. Light-year A light-year , alternatively spelled light year ( ly or lyr ),

5325-510: Was equated to the Tuamotuan constellation Te Kiva , meaning " frigatebird ", which could either represent the figure of Boötes or just Arcturus. However, Arcturus may instead be the Tuamotuan star called Turu . The Hawaiian name for Arcturus as a single star was likely Hoku-leʻa , which means "star of gladness", or "clear star". In the Marquesas Islands , Arcturus was probably called Tau-tou and

5400-432: Was not yet considered to be a fundamental constant of nature, and the propagation of light through the aether or space was still enigmatic. The light-year unit appeared in 1851 in a German popular astronomical article by Otto Ule . Ule explained the oddity of a distance unit name ending in "year" by comparing it to a walking hour ( Wegstunde ). A contemporary German popular astronomical book also noticed that light-year

5475-440: Was the astronomical unit , equal to the radius of the Earth's orbit at 150 million kilometres (93 million miles). In those terms, trigonometric calculations based on 61 Cygni's parallax of 0.314 arcseconds, showed the distance to the star to be 660 000 astronomical units (9.9 × 10  km; 6.1 × 10  mi). Bessel added that light takes 10.3 years to traverse this distance. He recognized that his readers would enjoy

5550-668: Was the star that ruled the month approximating January. The Māori and Moriori called it Tautoru , a variant of the Marquesan name and a name shared with Orion's Belt . In Inuit astronomy , Arcturus is called the Old Man ( Uttuqalualuk in Inuit languages ) and The First Ones ( Sivulliik in Inuit languages). The Miꞌkmaq of eastern Canada saw Arcturus as Kookoogwéss , the owl. Early-20th-century Armenian scientist Nazaret Daghavarian theorized that

5625-438: Was updated in 2000, including the IAU (1976) value cited above (truncated to 10 significant digits). Other high-precision values are not derived from a coherent IAU system. A value of 9.460 536 207 × 10  m found in some modern sources is the product of a mean Gregorian year (365.2425 days or 31 556 952  s ) and the defined speed of light ( 299 792 458  m/s ). Another value, 9.460 528 405 × 10  m ,

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