Astronomical unit

The astronomical unit (symbol: au,[1][2][3] ua,[4] or AU) is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as exactly 149597870700 metres, or about 150 million kilometres (93 million miles).[5] The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec.

Astronomical unit
Astronomical unit
The grey line indicates the Earth–Sun distance, which on average is about 1 astronomical unit.
General information
Unit systemAstronomical system of units
(Accepted for use with the SI)
Unit oflength
Symbolau, ua, or AU 
Conversions
1 au, ua, or AU in ...... is equal to ...
   metric (SI) units   149597870700 m
   imperial & US units   9.2956×107 mi
   astronomical units   4.8481×10−6 pc
   1.5813×10−5 ly

History of symbol usage

A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) used the symbol A to denote a length equal to the astronomical unit.[6] In the astronomical literature, the symbol AU was (and remains) common. In 2006, the International Bureau of Weights and Measures (BIPM) recommended ua as the symbol for the unit.[7] In the non-normative Annex C to ISO 80000-3 (2006), the symbol of the astronomical unit is "ua". In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".[1] In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au".[3][8]

Development of unit definition

Earth's orbit around the Sun is an ellipse. The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, and made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated. But all measurements are subject to some degree of error or uncertainty, and the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances. Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used.

Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of celestial mechanics, which govern the motions of objects in space. The expected positions and distances of objects at an established time are calculated (in AU) from these laws, and assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services.[9]

In 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides. It stated that "the astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time".[6][10][11] Equivalently, by this definition, one AU is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day";[12] or alternatively that length for which the heliocentric gravitational constant (the product GM) is equal to (0.01720209895)2 AU3/d2, when the length is used to describe the positions of objects in the Solar System.

Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry. As with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting. In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in the TDB scale leads to a value for the speed of light in astronomical units per day (of 86400 s). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at 173.1446326847(69) AU/d (TDB).[13]

In 1983, the International Committee for Weights and Measures (CIPM) modified the International System of Units (SI, or "modern" metric system) to make the metre defined as the distance travelled in a vacuum by light in 1/299792458 second. This replaced the previous definition, valid between 1960 and 1983, which was that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. (The reason for the change was an improved method of measuring the speed of light.) The speed of light could then be expressed exactly as c0 = 299792458 m/s, a standard also adopted by the IERS numerical standards.[14] From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be τA = 499.0047838061±0.00000001 s, which is slightly more than 8 minutes 19 seconds. By multiplication, the best IAU 2009 estimate was A = c0τA = 149597870700±3 m,[15] based on a comparison of JPL and IAA–RAS ephemerides.[16][17][18]

In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m.[7] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149597870700 m.[8] or an increase of 9 meters.

This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers. In 2012, finding that the equalization of relativity alone would make the definition overly complex, the IAU simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the metre (exactly 149597870700 m).[15][19] The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications.[15]

1 astronomical unit   = 149597870700 metres (exactly)
92.955807 million miles
499.00478384 light-seconds
4.8481368 millionths (4.8481368×10−6) of a parsec
15.812507 millionths (15.812507×10−6) of a light-year

This definition makes the speed of light, defined as exactly 299792458 m/s, equal to exactly 299792458 × 86400 ÷ 149597870700 or about 173.144632674240 AU/d, some 60 parts per trillion less than the 2009 estimate.

Usage and significance

With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass M. Neither G nor M can be measured to high accuracy separately, but the value of their product is known very precisely from observing the relative positions of planets (Kepler's Third Law expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris, so ephemerides are calculated in astronomical units and not in SI units.

The calculation of ephemerides also requires a consideration of the effects of general relativity. In particular, time intervals measured on Earth's surface (terrestrial time, TT) are not constant when compared to the motions of the planets: the terrestrial second (TT) appears to be longer during the Northern Hemisphere winter and shorter during the Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in barycentric dynamical time, TDB). This is because the distance between Earth and the Sun is not fixed (it varies between 0.9832898912 and 1.0167103335 AU) and, when Earth is closer to the Sun (perihelion), the Sun's gravitational field is stronger and Earth is moving faster along its orbital path. As the metre is defined in terms of the second and the speed of light is constant for all observers, the terrestrial metre appears to change in length compared to the "planetary metre" on a periodic basis.

The metre is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. Indeed, the International Committee for Weights and Measures (CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored".[20] As such, the metre is undefined for the purposes of measuring distances within the Solar System. The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed,[21] and "vigorous debate" ensued[22] until August 2012 when the IAU adopted the current definition of 1 astronomical unit = 149597870700 metres.

The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance of an asteroid, whereas other units are used for other distances in astronomy. The astronomical unit is too small to be convenient for interstellar distances, where the parsec and light-year are widely used. The parsec (parallax arcsecond) is defined in terms of the astronomical unit, being the distance of an object with a parallax of 1 arcsecond. The light-year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.[23]

When simulating a numerical model of the Solar System, the astronomical unit provides an appropriate scale that minimizes (overflow, underflow and truncation) errors in floating point calculations.

History

The book On the Sizes and Distances of the Sun and Moon, which has long been ascribed to Aristarchus, says that he calculated the distance to the Sun to be between 18 and 20 times the distance to the Moon, whereas the true ratio is about 389.174. The latter estimate was based on the angle between the half moon and the Sun, which he estimated as 87° (the true value being close to 89.853°). Depending on the distance that Van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between 380 and 1520 Earth radii.[24]

According to Eusebius of Caesarea in the Praeparatio Evangelica (Book XV, Chapter 53), Eratosthenes found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of stadia myriads 400 and 80000") but with the additional note that in the Greek text the grammatical agreement is between myriads (not stadia) on the one hand and both 400 and 80000 on the other, as in Greek, unlike English, all three (or all four if one were to include stadia) words are inflected. This has been translated either as 4080000 stadia (1903 translation by Edwin Hamilton Gifford), or as 804000000 stadia (edition of des Places", dated 1974–1991). Using the Greek stadium of 185 to 190 metres,[25][26] the former translation comes to 754800 km to 775200 km, which is far too low, whereas the second translation comes to 148.7 to 152.8 million kilometres (accurate within 2%).[27] Hipparchus also gave an estimate of the distance of Earth from the Sun, quoted by Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of Noel Swerdlow and G. J. Toomer, this was derived from his assumption of a "least perceptible" solar parallax of 7 arc minutes.[28]

A Chinese mathematical treatise, the Zhoubi Suanjing (c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 1000 li apart and the assumption that Earth is flat.[29]

Distance to the Sun
estimated by
Estimate In AU
Solar
parallax
Earth
radii
Archimedes (3rd century BCE)
(in The Sand Reckoner)
40″ 10000 0.426
Aristarchus (3rd century BCE)
(in On the Sizes and Distances)  
380-1520 0.016-0.065
Hipparchus (2nd century BCE) 7′ 490 0.021
Posidonius (1st century BCE)
(quoted by coeval Cleomedes)
10000 0.426
Ptolemy (2nd century) 2′ 50″ 1210 0.052
Godefroy Wendelin (1635) 15″ 14000 0.597
Jeremiah Horrocks (1639) 15″ 14000 0.597
Christiaan Huygens (1659) 8.6″ 24000 1.023
Cassini & Richer (1672) 91/2 21700 0.925
Jérôme Lalande (1771) 8.6″ 24000 1.023
Simon Newcomb (1895) 8.80″ 23440 0.9994
Arthur Hinks (1909) 8.807″ 23420 0.9985
H. Spencer Jones (1941) 8.790″ 23466 1.0005
modern astronomy 8.794143 23455 1.0000

In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1210 times Earth's radius.[30][31] To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of 64 1/6 Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct.[32][33] He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few percent can make the solar distance infinite.[32]

After Greek astronomy was transmitted to the medieval Islamic world, astronomers made some changes to Ptolemy's cosmological model, but did not greatly change his estimate of the Earth–Sun distance. For example, in his introduction to Ptolemaic astronomy, al-Farghānī gave a mean solar distance of 1170 Earth radii, whereas in his zij, al-Battānī used a mean solar distance of 1108 Earth radii. Subsequent astronomers, such as al-Bīrūnī, used similar values.[34] Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century.[35]

Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus' measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven.

A somewhat more accurate estimate can be obtained by observing the transit of Venus.[36] By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly due to the brightness of the Sun[37]). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15 arcseconds, similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by

The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15" is equivalent to an Earth–Sun distance of 13750 Earth radii.

Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii,[38] equivalent to a solar parallax of 8.6". Although Huygens' estimate is remarkably close to modern values, it is often discounted by historians of astronomy because of the many unproven (and incorrect) assumptions he had to make for his method to work; the accuracy of his value seems to be based more on luck than good measurement, with his various errors cancelling each other out.

Venustransit 2004-06-08 07-44
Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "black drop effect") and the rarity of observations.

Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 9 1/2", equivalent to an Earth–Sun distance of about 22000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3269 thousand toises. Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today.

A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley[39] and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour.[40] The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6″.

Date Method A/Gm Uncertainty
1895 aberration 149.25 0.12
1941 parallax 149.674 0.016
1964 radar 149.5981 0.001
1976 telemetry 149.597 870 0.000 001
2009 telemetry 149.597 870 700 0.000 000 003

Another method involved determining the constant of aberration. Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80″ for the solar parallax (close to the modern value of 8.794143″), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth-based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in kilometres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of astronomical constants in 1896,[41] which remained in place for the calculation of ephemerides until 1964.[42] The name "astronomical unit" appears first to have been used in 1903.[43]

The discovery of the near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement.[44] Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931.[37][45]

Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.[46]

Developments

Stellarparallax parsec1
The astronomical unit is used as the baseline of the triangle to measure stellar parallaxes (distances in the image are not to scale).

The unit distance A (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants:

where G is the Newtonian gravitational constant, M is the solar mass, k is the numerical value of Gaussian gravitational constant and D is the time period of one day. The Sun is constantly losing mass by radiating away energy,[47] so the orbits of the planets are steadily expanding outward from the Sun. This has led to calls to abandon the astronomical unit as a unit of measurement.[48]

As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant k is fixed in the astronomical system of units, measuring the light time per unit distance is exactly equivalent to measuring the product GM in SI units. Hence, it is possible to construct ephemerides entirely in SI units, which is increasingly becoming the norm.

A 2004 analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger than can be accounted for by solar radiation, +15±4 metres per century.[49][50]

The measurements of the secular variations of the astronomical unit are not confirmed by other authors and are quite controversial. Furthermore, since 2010, the astronomical unit has not been estimated by the planetary ephemerides.[51]

Examples

The following table contains some distances given in astronomical units. It includes some examples with distances that are normally not given in astronomical units, because they are either too short or far too long. Distances normally change over time. Examples are listed by increasing distance.

Object Length or distance (AU) Range Comment and reference point Refs
Light-second 0.002  distance light travels in one second
Lunar distance 0.0026 average distance from Earth (which the Apollo missions took about 3 days to travel)
Solar radius 0.005  radius of the Sun (695500 km, 432450 mi, a hundred times the radius of Earth or ten times the average radius of Jupiter)
Light-minute 0.12   distance light travels in one minute
Mercury 0.39   average distance from the Sun
Venus 0.72   average distance from the Sun
Earth 1.00   average distance of Earth's orbit from the Sun (sunlight travels for 8 minutes and 19 seconds before reaching Earth)
Mars 1.52   average distance from the Sun
Light-hour 7.2    distance light travels in one hour
Kuiper belt 30      Inner edge begins at roughly 30 AU [52]
Eris 67.8   average distance from the Sun
Light-day 173      distance light travels in one day
Light-year 63241      distance light travels in one Julian year (365.25 days)
Oort cloud 75000      ± 25000 distance of the outer limit of Oort cloud from the Sun (estimated, corresponds to 1.2 light-years)
Parsec 206265      one parsec (The parsec is defined in terms of the astronomical unit, is used to measure distances beyond the scope of the Solar System and is about 3.26 light-years.) [53]
Proxima Centauri 268000      ± 126 distance to the nearest star to the Solar System
Galactic Centre 1700000000      distance from the Sun to the centre of the Milky Way
Note: figures in this table are generally rounded, estimates, often rough estimates, and may considerably differ from other sources. Table also includes other units of length for comparison.

See also

References

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  36. ^ An extended historical discussion of this method is provided by Trudy E Bell, "Quest for the astronomical unit" (PDF), The Bent of Tau Beta Pi, Summer 2004, p. 20, archived from the original (PDF) on 24 March 2012, retrieved 16 January 2012
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  48. ^ "AU may need to be redefined", New Scientist, 6 February 2008
  49. ^ Krasinsky, G.A.; Brumberg, V.A. (2004), "Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation", Celestial Mechanics and Dynamical Astronomy, 90 (3–4): 267–88, Bibcode:2004CeMDA..90..267K, doi:10.1007/s10569-004-0633-z
  50. ^ John D. Anderson & Michael Martin Nieto (2009), "Astrometric Solar-System Anomalies;§ 2: Increase in the astronomical unit", American Astronomical Society, 261: 189–97, arXiv:0907.2469, Bibcode:2009IAU...261.0702A, doi:10.1017/s1743921309990378.
  51. ^ Fienga, A.; et al. (2011), "The INPOP10a planetary ephemeris and its applications in fundamental physics", Celestial Mechanics and Dynamical Astronomy, 111 (3): 363, arXiv:1108.5546, Bibcode:2011CeMDA.111..363F, doi:10.1007/s10569-011-9377-8
  52. ^ Alan Stern; Colwell, Joshua E. (1997), "Collisional Erosion in the Primordial Edgeworth-Kuiper Belt and the Generation of the 30–50 AU Kuiper Gap", The Astrophysical Journal, 490 (2): 879–82, Bibcode:1997ApJ...490..879S, doi:10.1086/304912.
  53. ^ http://www.iau.org, Measuring the Universe – The IAU and astronomical units

Further reading

External links

2004 transit of Venus

The second most recent transit of Venus observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit since that transit occurred on December 6, 1882.

European Southern Observatory (ESO) and the European Association for Astronomy Education (EAAE) launched the VT-2004 project, together with the Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE) and the Observatoire de Paris in France, as well as the Astronomical Institute of the Academy of Sciences of the Czech Republic. This project had 2,763 participants all over the world, including nearly 1,000 school classes. The participants made a measurement of the astronomical unit (AU) of 149 608 708 km ± 11 835 km which had only a 0.007% difference to the accepted value.

70P/Kojima

70P/Kojima is a periodic comet in the Solar System with a current orbital period of 7.05 years.It was discovered at Ishiki, Aichi, Japan by Nobuhisa Kojima, who estimated its brightness at magnitude 14. Its parabolic orbit was calculated by Kiichirō Furukawa to have a perihelion date of 1 November 1970. This was revised on the basis of further observations to an elliptical orbit with a perihelion of 7 October and an orbital period of 6.16.

Hiroki Kosai and Furukawa relocated the comet on 9 December 1977 at its next predicted apparition with the 105 cm Schmidt telescope at the Kiso Station of the Tokyo Astronomical Observatory, estimating its brightness at magnitude 16. It was subsequently observed in 1985/1986 and 1992/1994 by Spacewatch with magnitudes of 20 and 22.1. The comet then passed close to Jupiter, which reduced the perihelion distance from 2.4 AU (Astronomical Unit) to 1.97 AU, increased the eccentricity from 0.39 to 0.46 and reduced the orbital period from 7.85 to 6.99.

81P/Wild

Comet 81P/Wild, also known as Wild 2 (pronounced "vilt two") ( VILT), is a comet named after Swiss astronomer Paul Wild, who discovered it on January 6, 1978, using a 40-cm Schmidt telescope at Zimmerwald, Switzerland.For most of its 4.5 billion-year lifetime, Wild 2 probably had a more distant and circular orbit. In September 1974, it passed within one million kilometers of the planet Jupiter, the strong gravitational pull of which perturbed the comet's orbit and brought it into the inner Solar System. Its orbital period changed from 43 years to about 6 years, and its perihelion is now about 1.59 astronomical unit (AU).

Astronomical system of units

The astronomical system of units, formally called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976, and has been significantly updated in 1994 and 2009 (see astronomical constant).

The system was developed because of the difficulties in measuring and expressing astronomical data in International System of Units (SI units). In particular, there is a huge quantity of very precise data relating to the positions of objects within the Solar System which cannot conveniently be expressed or processed in SI units. Through a number of modifications, the astronomical system of units now explicitly recognizes the consequences of general relativity, which is a necessary addition to the International System of Units in order to accurately treat astronomical data.

The astronomical system of units is a tridimensional system, in that it defines units of length, mass and time. The associated astronomical constants also fix the different frames of reference that are needed to report observations. The system is a conventional system, in that neither the unit of length nor the unit of mass are true physical constants, and there are at least three different measures of time.

C/1760 A1

The Great Comet of 1760 (C/1760 A1) was first seen on 7 January 1760 by Abbe Chevalier at Lisbon. Charles Messier also spotted the comet on 8 January 1760 in Paris, by the sword of Orion. The comet was his third discovery and the comet was the 51st to have a calculated orbit. Messier observed the comet for a total of 6 days.

It approached the Earth to within approximately 0.0682 astronomical unit (AU) or 6.34 million miles. This is the 17th closest approach by a comet of all time. Messier gave the comet a magnitude rating of 2.0, making it easily visible to the unaided eye. Messier also gave the comet an elongation angle of 140 degrees.

Messier came up against opposition from Navy astronomer Joseph Nicholas Delisle, who had employed Messier from October 1751, because Delisle would not publish the discovery Messier had made. This was a continuation of the mistrust that had developed between Messier and Delisle because Delisle had been slow to publish work done by Messier in 1759; Messier had independently rediscovered Halley's Comet on 21 January 1759 but because Messier had doubted the correctness of Delisle's path, Delisle instructed Messier to continue observing the comet and refused to announce his discovery. Delisle apparently later changed his mind and announced the discovery on 1 April 1759, but other French astronomers discredited Delisle's claim, labelling the discovery an April Fools' joke. Delisle retired in 1760.

As of June 2008, the comet was about 216 AU from the Sun.

Canonical units

A canonical unit is a unit of measurement agreed upon as default in a certain context.

Gaussian gravitational constant

The Gaussian gravitational constant (symbol k) is a parameter used in the orbital mechanics of the solar system.

It relates the orbital period to the orbit's semi-major axis and the mass of the orbiting body in Solar masses.

The value of k historically expresses the mean angular velocity of the system of Earth+Moon and the Sun considered as a two body problem,

with a value of about 0.986 degrees per day, or about 0.0172 radians per day.

As a consequence of Newton's law of gravitation and Kepler's third law,

k is directly proportional to the square root of the standard gravitational parameter of the Sun,

and its value in radians per day follows by setting Earth's semi-major axis (the astronomical unit, a.u.) to unity, k:(rad/day) = (GM☉)0.5·(a.u.)-1.5A value of k = 0.01720209895 rad/day was determined by Carl Friedrich Gauss in his 1809 work Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientum ("Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections").

Gauss' value was introduced as a fixed, defined value by the IAU (adpoted in 1938, formally defined in 1964),

which detached it from its immediate representation of the (observable) mean angular velocity of the Sun-Earth system. Instead, the astronomical unit now became a measurable quantity slightly different from unity.

This was useful in 20th-century celestial mechanics to prevent the constant adaptation of orbital parameters to updated measured values, but it came at the expense of intuitiveness, as the astronomical unit, ostensibly a unit of length, was now dependent on the measurement of the strength of the gravitational force.

The IAU abandoned the defined value of k in 2012 in favour of a defined value of the astronomical unit of 1.495978707×1011 m exactly, while the strength of the gravitational force is now to be expressed in the separate standard gravitational parameter GM☉, measured in SI units of m3 s−2.

Habitability of binary star systems

Planets in binary star systems may be candidates for supporting extraterrestrial life. Habitability of binary star systems is determined by a large number of factors from a variety of sources. Typical estimates often suggest that 50% or more of all star systems are binary systems. This may be partly due to sample bias, as massive and bright stars tend to be in binaries and these are most easily observed and catalogued; a more precise analysis has suggested that the more common fainter stars are usually singular, and that up to two thirds of all stellar systems are therefore solitary.The separation between stars in a binary may range from less than one astronomical unit (au, the "average" Earth-to-Sun distance) to several hundred au. In latter instances, the gravitational effects will be negligible on a planet orbiting an otherwise suitable star, and habitability potential will not be disrupted unless the orbit is highly eccentric (see Nemesis, for example). In reality, some orbital ranges are impossible for dynamical reasons (the planet would be expelled from its orbit relatively quickly, being either ejected from the system altogether or transferred to a more inner or outer orbital range), whilst other orbits present serious challenges for eventual biospheres because of likely extreme variations in surface temperature during different parts of the orbit. If the separation is significantly close to the planet's distance, a stable orbit may be impossible.

Planets that orbit just one star in a binary pair are said to have "S-type" orbits, whereas those that orbit around both stars have "P-type" or "circumbinary" orbits. It is estimated that 50–60% of binary stars are capable of supporting habitable terrestrial planets within stable orbital ranges.

Light-year

The light-year is a unit of length used to express astronomical distances and measures about 9.46 trillion kilometres (9.46 x 1012 km) or 5.88 trillion miles (5.88 x 1012 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). Because it includes the word "year", the term light-year is sometimes misinterpreted as 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 nonspecialist and popular science publications. The unit most commonly used in professional astrometry is the parsec (symbol: pc, about 3.26 light-years; the distance at which one astronomical unit subtends an angle of one second of arc).

Parsec

The parsec (symbol: pc) is a unit of length used to measure large distances to astronomical objects outside the Solar System. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to 648000/π astronomical units. One parsec is equal to about 3.26 light-years or 31 trillion kilometres (31×1012 km) or 19 trillion miles (19×1012 mi). The nearest star, Proxima Centauri, is about 1.3 parsecs (4.2 light-years) from the Sun. Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun.The parsec unit was probably first suggested in 1913 by the British astronomer Herbert Hall Turner. Named as a portmanteau of the parallax of one arcsecond, it was defined to make calculations of astronomical distances from only their raw observational data quick and easy for astronomers. Partly for this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs (kpc) for the more distant objects within and around the Milky Way, megaparsecs (Mpc) for mid-distance galaxies, and gigaparsecs (Gpc) for many quasars and the most distant galaxies.

In August 2015, the IAU passed Resolution B2, which, as part of the definition of a standardized absolute and apparent bolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly 648000/π astronomical units, or approximately 3.08567758149137×1016 metres (based on the IAU 2012 exact SI definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many contemporary astronomical references.

Radar astronomy

Radar astronomy is a technique of observing nearby astronomical objects by reflecting microwaves off target objects and analyzing the reflections. This research has been conducted for six decades. Radar astronomy differs from radio astronomy in that the latter is a passive observation and the former an active one. Radar systems have been used for a wide range of solar system studies. The radar transmission may either be pulsed or continuous.

The strength of the radar return signal is proportional to the inverse fourth-power of the distance. Upgraded facilities, increased transceiver power, and improved apparatus have increased observational opportunities.

Radar techniques provide information unavailable by other means, such as testing general relativity by observing Mercury and providing a refined value for the astronomical unit. Radar images provide information about the shapes and surface properties of solid bodies, which cannot be obtained by other ground-based techniques.

Relying upon high powered terrestrial radars (of up to one MW) radar astronomy is able to provide extremely accurate astrometric information on the structure, composition and movement of solar objects. This aids in forming long-term predictions of asteroid-Earth impacts, as illustrated by the object 99942 Apophis. In particular, optical observations measure where an object appears in the sky, but cannot measure the distance with great accuracy (relying on Parallax becomes more difficult when objects are small or poorly illuminated). Radar, on the other hand, directly measures the distance to the object (and how fast it is changing). The combination of optical and radar observations normally allows the prediction of orbits at least decades, and sometimes centuries, into the future.

There are two radar astronomy facilities that are in regular use, the Arecibo Planetary Radar and the Goldstone Solar System Radar.

SI base unit

The SI base units are seven units of measure defined by the International System of Units (SI = Systeme Internationale) as a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for measurement of length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity.

The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology.

The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with an initial capital letter. For example, the metre (US English: meter) has the symbol m, but the kelvin has symbol K, because it is named after Lord Kelvin and the ampere with symbol A is named after André-Marie Ampère.

A number of other units, such as the litre (US English: liter), astronomical unit and electronvolt, are not formally part of the SI, but are accepted for use with SI.

Solar constant

The solar constant (GSC) is a flux density measuring mean solar electromagnetic radiation (solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (AU) from the Sun (roughly the distance from the Sun to the Earth).

The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite as being 1.361 kilowatts per square meter (kW/m²) at solar minimum and approximately 0.1% greater (roughly 1.362 kW/m²) at solar maximum.The solar "constant" is not a physical constant in the modern CODATA scientific sense; that is, it is not like the Planck constant or the speed of light which are absolutely constant in physics. The solar constant is an average of a varying value. In the past 400 years it has varied less than 0.2 percent. Billions of years ago, it was significantly lower.

This constant is used in the calculation of radiation pressure, which aids in the calculation of a force on a solar sail.

Solar luminosity

The solar luminosity, L☉, is a unit of radiant flux (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars, galaxies and other celestial objects in terms of the output of the Sun. One nominal solar luminosity is defined by the International Astronomical Union to be 3.828×1026 W. This does not include the solar neutrino luminosity, which would add 0.023 L☉. The Sun is a weakly variable star, and its actual luminosity therefore fluctuates. The major fluctuation is the eleven-year solar cycle (sunspot cycle) that causes a periodic variation of about ±0.1%. Other variations over the last 200–300 years are thought to be much smaller than this.

Solar mass

The solar mass (M) is a standard unit of mass in astronomy, equal to approximately 2×1030 kg. It is used to indicate the masses of other stars, as well as clusters, nebulae, and galaxies. It is equal to the mass of the Sun (denoted by the solar symbol ⊙︎). This equates to about two nonillion (two quintillion in the long scale) kilograms:

M = (1.98847±0.00007)×1030 kg

The above mass is about 332946 times the mass of Earth (M), or 1047 times the mass of Jupiter (MJ).

Because Earth follows an elliptical orbit around the Sun, the solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. Based upon the length of the year, the distance from Earth to the Sun (an astronomical unit or AU), and the gravitational constant (G), the mass of the Sun is given by:

The value of G is difficult to measure and is only known with limited accuracy in SI units (see Cavendish experiment). The value of G times the mass of an object, called the standard gravitational parameter, is known for the Sun and several planets to much higher accuracy than G alone. As a result, the solar mass is used as the standard mass in the astronomical system of units.

Solar radius

Solar radius is a unit of distance used to express the size of stars in astronomy relative to the Sun. The solar radius is usually defined as the radius to the layer in the Sun's photosphere where the optical depth equals 2/3:

695,700 kilometres (432,300 miles) is approximately 10 times the average radius of Jupiter, about 109 times the radius of the Earth, and 1/215th of an astronomical unit, the distance of the Earth from the Sun. It varies slightly from pole to equator due to its rotation, which induces an oblateness in the order of 10 parts per million.

Stellar parallax

Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at exactly opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU).

Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years. It was first observed in 1806 by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work "Osservazione e riflessione sulla parallasse annua dall’alfa della Lira". Then in 1838 Friedrich Bessel made the first successful parallax measurement, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.

Once a star's parallax is known, its distance from Earth can be computed trigonometrically. But the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs (or roughly 300 light years) too approximate to be useful when obtained by this technique. This limits the applicability of parallax as a measurement of distance to objects that are relatively close on a galactic scale. Other techniques, such as spectral red-shift, are required to measure the distance of more remote objects.

Stellar parallax measures are given in the tiny units of arcseconds, or even in thousandths of arcseconds (milliarcseconds). The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, where the other leg is 1 AU long. Because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes (in arcseconds) to distance (in parsecs). The approximate distance is simply the reciprocal of the parallax: For example, Proxima Centauri (the nearest star to Earth other than the Sun), whose parallax is 0.7687, is 1 / 0.7687 parsecs = 1.3009 parsecs (4.243 ly) distant.

Theta Andromedae

Theta Andromedae (θ And, θ Andromedae) is the Bayer designation for a binary star in the constellation Andromeda. It is approximately 310 light-years (95 parsecs) from Earth, with a visual magnitude of 4.6. On the Bortle Dark-Sky Scale, this makes it visible to the naked eye from outside urban regions.

Theta Andromedae is a white A-type main sequence dwarf with an apparent magnitude of +4.61. It appears to be a binary star with a massive, possibly A-type secondary orbiting at a distance of around 1 astronomical unit. A fainter companion is separated from Theta Andromedae by 0.06 arcseconds.

WISE 0535−7500

WISE J053516.80−750024.9 (designation abbreviated to WISE 0535−7500) is either a sub-brown dwarf or a free planet. It has spectral class ≥Y1 and is located in constellation Mensa. It is estimated to be 47 light-years from Earth. In 2017, more accurate analysis found it to be a binary system made up of two substellar objects of spectral class≥Y1 in orbit less than one astronomical unit from each other.

Base units
Derived units
with special names
Other accepted units
See also

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