Astronomy Conversions

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Kilometer - The kilometre (American spelling: kilometer), symbol km is a unit of length in the metric system, equal to one thousand metres. It is the conventionally used measurement unit for expressing distances between geographical places in countries which use the metric system. While it is defined exactly as 1000 m, it equals roughly a ten minutes' walk. Slang terms for kilometre include click (sometimes spelled klick or klik) and kay (or k).

The United Kingdom and the United States are the only two developed countries which continue to use miles on road signs. Although the UK has officially adopted the metric system, there are currently no plans to replace the mile on road signs in the near future, owing to the British public's attachment to traditional imperial units of distance, i.e., miles, yards and inches, and the cost of changing speed signs (which could not be replaced during general maintenance, like distance signs, for safety reasons). As of 11 September 2007, the EU has not challenged Britain's use of the imperial systems. EU commissioner Gunter Verheugen said: "There is not now and never will be any requirement to drop imperial measurements."

In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. However, the Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units.

Light Year - A light-year or light year (symbol: ly) is a unit of length, equal to just under ten trillion kilometres. As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in a vacuum in one Julian year. The light-year is often used to measure distances to stars and other distances on a galactic scale, especially in non-specialist and popular science publications. The preferred unit in astrometry is the parsec, because it can be more easily derived from, and compared with, observational data. The parsec is defined as the distance at which an object will appear to move one arcsecond of parallax when the observer moves one astronomical unit perpendicular to the line of sight to the observer, and is equal to approximately 3.26 light-years. The related unit of the light-month, roughly one-twelfth of a light-year, is also used occasionally for approximate measures.

Before 1984, the tropical year (not the Julian year) and a measured (not defined) speed of light were included in 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 9.460530 x 1015 metres (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 a reputable 1973 reference which was not updated until 2000.

Other high precision values are not derived from a coherent IAU system. A value of 9.460536207 x 1015 metres found in some modern sources is the product of a mean Gregorian year of 365.2425 days (31,556,952 s) and the defined speed of light (299,792,458 m/s). The Live Search value, 9.460528405 x 1015 metres, is the product of the J1900.0 mean tropical year and the defined speed of light.

Astronomical Unit - An astronomical unit (abbreviated as AU, au, a.u., or sometimes ua) is a unit of length roughly equal to the mean distance between the Earth and the Sun. It is approximately 150 million kilometres (93 million miles). The symbol ua is recommended by the International Bureau of Weights and Measures, but au is more common in Anglosphere countries. The International Astronomical Union recommends au, while international standard ISO 31-1 uses AU. In general, capital letters are only used for the symbols of units which are named after individual scientists, while au or a.u. can also mean atomic unit or even arbitrary unit; however, the use of AU to refer to the astronomical unit is widespread. The astronomical constant whose value is one astronomical unit is referred to as unit distance and given the symbol A.

Originally, the AU was defined as the length of the semi-major axis of the Earth's elliptical orbit around the Sun. In 1976, the International Astronomical Union revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time. An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.017 202 098 95 radians per day, or that length for which the heliocentric gravitational constant (the product GM) is equal to (0.017 202 098 95)2 AU3/d2. It is approximately equal to the mean Earth-Sun distance.

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." As such, the metre is undefined for the purposes of measuring distances within the solar system. The 1976 definition of the astronomical unit is incomplete, in particular because it does not specify the frame of reference in which time is to be measured, but has proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity has been proposed.

Mile - A mile is a unit of length, usually used to measure distance, in a number of different systems. In contemporary English contexts, mile most commonly refers to the statute mile of 5,280 feet (exactly 1,609.344 meters) or the nautical mile of 1,852 meters (about 6,076.1 ft). There are many other historical miles, and similar units in other systems translated as miles in English, varying between one and fifteen kilometers. It is about a third of the old measurement, a League.

The measurement is now used almost exclusively in the United States and the United Kingdom. It has been replaced by the kilometer as a measure of distance elsewhere. It is sometimes retained as a customary unit. There have been several abbreviations for mile (with and without trailing period): mi, ml, m, M. In the United States, the National Institute of Standards and Technology now uses and recommends mi but in everyday usage (at least in the United States and in the United Kingdom) usages such as miles per hour and miles per gallon are almost always abbreviated as mph or mpg (rather than mi/h or mi/gal).

The formula "multiply by 8 and divide by 5" to convert international miles to kilometers gives a conversion of 1.6, which, at less than 1 percent high, makes a useful approximation.

The statute mile was defined by English Act of Parliament (hence the name) in 1592, during the reign of Queen Elizabeth I; it is equal to 1760 yards (5280 feet). For surveying, the statute mile is divided into eight furlongs; each furlong is ten chains; each chain is four rods (also known as poles or perches); and each rod is 25 links. This makes the rod equal to 5.5 yards or 16.5 feet in both Imperial and U.S. usage.

The exact conversion of the mile to SI units depends on which definition of the yard is in use. The different English-speaking countries maintained independent physical standards for the yard that were found to differ by small but measurable amounts, and even to slowly shorten in length. The United States redefined the U.S. yard in 1893, but this meant that U.S. and Imperial units with the same names had very slightly different values. The confusion was resolved in 1959 with the definition of the international yard in terms of the metre by Australia, Canada, New Zealand, South Africa, the United Kingdom, and the United States. The "international mile" of 1760 international yards is exactly 1609.344 metres.

The difference from the previous standards was about 2 ppm, or about a tenth of an inch in each mile, the old U.S. standard being slightly longer and the old Imperial standards slightly shorter than the international mile. The older standards for the yard (and hence the foot and the mile) continue in use for some surveying purposes in the United States and in India.

For most applications, the difference between the two definitions is insignificant - one international foot is exactly 0.999998 of a U.S. survey foot, for a difference of about 3 millimeters per mile - but it affects the definition of the State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles. When international measure was introduced in the English-speaking countries, the basic geodetic datum in North America was the North American Datum of 1927 (NAD27), which had been constructed by triangulation based on the definition of the foot in the Mendenhall Order of 1893, that is 1 foot = 1200/3937 meters: this definition was retained for data derived from NAD27, but renamed the U.S. survey foot to distinguish it from the international foot.

The NAD27 was replaced in the 1980s by the North American Datum of 1983 (NAD83), which is defined in meters. The SPCSs were also updated, but the National Geodetic Survey left the decision of which (if any) definition of the foot to use to the individual states. All SPCSs are defined in meters, but seven states also have SPCSs defined in U.S. survey feet and an eighth state in international feet: the other 42 states use only meter-based SPCSs. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum, which is also used by the Global Positioning System.

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). In the U.S., twenty-four states have legislated that surveying measures should be based on the U.S. survey foot, eight have legislated that they be made on the basis of the international foot, and eighteen have not specified the conversion factor from metric units.

Parsec - The parsec ("parallax of one arcsecond", symbol pc) is a unit of length, equal to just under 31 trillion kilometres (about 19 trillion miles), or about 3.26 light-years. The parsec is used in astronomy. The parsec is defined as the length of the adjacent side of an imaginary right triangle in space. The two dimensions that form this triangle are the parallax angle (defined as 1 arcsecond) and the opposite side (which is defined as 1 astronomical unit (AU), the distance from the Earth to the Sun). Given these two measurements, along with the rules of trigonometry, the length of the adjacent side (the parsec) can be found.

One of the oldest methods for astronomers to calculate the distance to a particular star was to record the difference in angle between two measurements of the position of the star in the sky. The first measurement was taken from the Earth on one side of the Sun, and the second was taken half a year later when the Earth was on the opposite side of the Sun. Thus, the distance between the two measurements was known to be twice the distance between the Earth and the Sun. The distance to the star could be found using calculations of trigonometric parallax. Since it is based on an angle and the distance between the Earth and the Sun, it is fundamentally derived from the degree and the AU. The length of a parsec is about 30.857 petametres, 3.26156 light-years or 1.9174x1013 miles. The first documented use of the term parsec was in 1913, and attributed to Herbert Hall Turner.

The parallax method is the fundamental calibration step for distance determination in astrophysics, and the obvious unit for such measurements, the parsec, has become the most commonly used unit of distance in scholarly astronomical publications. Articles aimed at a wider audience, such as in newspapers and popular science magazines, often use a more intuitive unit, the light-year. Other than the Sun, which has a parallax of 90 degrees, there is no known star whose parallax is more than one arcsecond (that is, there is no known star whose distance from Earth is less than one parsec). The next closest star is Proxima Centauri with a parallax of 0.77233 arcseconds; it is thus 1.295 pc (4.225 ly) away from the Earth.

Refraction caused by the atmosphere, also known as astronomical seeing, limits ground-based telescopes to parallax angle measurement accuracies of less than approximately 0.01 arcsec, so reliable measurements, those with errors of 10% or less, can only be achieved at stellar distances of no more than about 100 pc, or 326 ly. Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of ground-based observations. Between 1989 and 1993, the Hipparcos satellite, launched by the European Space Agency (ESA), measured parallaxes for about 100,000 stars with an astrometric precision of about 0.97 milliarcseconds, and obtained accurate measurements for stellar distances of stars up to 1,000 pc away. NASA's FAME satellite was due to be launched in 2004, to measure parallaxes for about 40 million stars with sufficient precision to measure stellar distances of up to 2,000 pc. However, the mission's funding was withdrawn by NASA in January 2002. ESA's Gaia satellite, due to be launched in December 2011, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the Galactic Center, about 8,000 pc away in the constellation of Sagittarius.

The first direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used the width of the Earth's orbit as a baseline to calculate the distance of 61 Cygni using parallax and trigonometry. The parallax of a star is half of the angular distance a star appears to move relative to the celestial sphere as Earth orbits around the Sun; or, reciprocally, it is the subtended angle, from that star's perspective, of the semi-major axis of Earth's orbit.

The use of the parsec as a unit of distance follows naturally from Bessel's method, since distance (in parsecs) is simply the reciprocal of the parallax angle (in arcseconds). That is, it is the distance at which the semi-major axis of the Earth's orbit would subtend an angle of one second of arc.

Though it had probably been used before, the term parsec was first mentioned in an astronomical publication in 1913, when Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance: he proposes the name astron, but mentions that Carl Charlier had suggested siriometer, and Herbert Hall Turner had suggested parsec (parallax second).