The density, or more the volumetric mass density, of a substance is its mass per unit volume. The symbol most used for density is ρ, although the Latin letter D can be used. Mathematically, density is defined as mass divided by volume: ρ = m V where ρ is the density, m is the mass, V is the volume. In some cases, density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials have different densities, density may be relevant to buoyancy and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material water.
Thus a relative density less than one means. The density of a material varies with pressure; this variation is small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid; this causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density. In a well-known but apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy.
Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated and compared with the mass. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!". As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment; the story first appeared in written form in Vitruvius' books of architecture, two centuries after it took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. From the equation for density, mass density has units of mass divided by volume; as there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use.
The SI unit of kilogram per cubic metre and the cgs unit of gram per cubic centimetre are the most used units for density. One g/cm3 is equal to one thousand kg/m3. One cubic centimetre is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are more practical and US customary units may be used. See below for a list of some of the most common units of density. A number of techniques as well as standards exist for the measurement of density of materials; such techniques include the use of a hydrometer, Hydrostatic balance, immersed body method, air comparison pycnometer, oscillating densitometer, as well as pour and tap. However, each individual method or technique measures different types of density, therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question; the density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is measured with a scale or balance.
To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object. If the body is not homogeneous its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ = d m / d V, where d V is an elementary volume at position r; the mass of the body t
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
A day is the period of time during which the Earth completes one rotation around its axis. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive times. In 1960, the second was redefined in terms of the orbital motion of the Earth in year 1900, was designated the SI base unit of time; the unit of measurement "day", was symbolized d. In 1967, the second and so the day were redefined by atomic electron transition. A civil day is 86,400 seconds, plus or minus a possible leap second in Coordinated Universal Time, plus or minus an hour in those locations that change from or to daylight saving time. Day can be defined as each of the twenty-four-hour periods, reckoned from one midnight to the next, into which a week, month, or year is divided, corresponding to a rotation of the earth on its axis; however its use depends on its context, for example when people say'day and night','day' will have a different meaning. It will mean the interval of light between two successive nights.
However, in order to be clear when using'day' in that sense, "daytime" should be used to distinguish it from "day" referring to a 24-hour period. The word day may refer to a day of the week or to a calendar date, as in answer to the question, "On which day?" The life patterns of humans and many other species are related to Earth's solar day and the day-night cycle. Several definitions of this universal human concept are used according to context and convenience. Besides the day of 24 hours, the word day is used for several different spans of time based on the rotation of the Earth around its axis. An important one is the solar day, defined as the time it takes for the Sun to return to its culmination point; because celestial orbits are not circular, thus objects travel at different speeds at various positions in their orbit, a solar day is not the same length of time throughout the orbital year. Because the Earth orbits the Sun elliptically as the Earth spins on an inclined axis, this period can be up to 7.9 seconds more than 24 hours.
In recent decades, the average length of a solar day on Earth has been about 86 400.002 seconds and there are about 365.2422 solar days in one mean tropical year. Ancient custom has a new day start at either the setting of the Sun on the local horizon; the exact moment of, the interval between, two sunrises or sunsets depends on the geographical position, the time of year. A more constant day can be defined by the Sun passing through the local meridian, which happens at local noon or midnight; the exact moment is dependent on the geographical longitude, to a lesser extent on the time of the year. The length of such a day is nearly constant; this is the time as indicated by modern sundials. A further improvement defines a fictitious mean Sun that moves with constant speed along the celestial equator. A day, understood as the span of time it takes for the Earth to make one entire rotation with respect to the celestial background or a distant star, is called a stellar day; this period of rotation is about 4 minutes less than 24 hours and there are about 366.2422 stellar days in one mean tropical year.
Other planets and moons have solar days of different lengths from Earth's. A day, in the sense of daytime, distinguished from night time, is defined as the period during which sunlight directly reaches the ground, assuming that there are no local obstacles; the length of daytime averages more than half of the 24-hour day. Two effects make daytime on average longer than nights; the Sun has an apparent size of about 32 minutes of arc. Additionally, the atmosphere refracts sunlight in such a way that some of it reaches the ground when the Sun is below the horizon by about 34 minutes of arc. So the first light reaches the ground when the centre of the Sun is still below the horizon by about 50 minutes of arc. Thus, daytime is on average around 7 minutes longer than 12 hours; the term comes from the Old English dæg, with its cognates such as dagur in Icelandic, Tag in German, dag in Norwegian, Danish and Dutch. All of them from the Indo-European root dyau which explains the similarity with Latin dies though the word is known to come from the Germanic branch.
As of October 17, 2015, day is the 205th most common word in US English, the 210th most common in UK English. A day, symbol d, defined as 86 400 seconds, is not an SI unit, but is accepted for use with SI; the Second is the base unit of time in SI units. In 1967–68, during the 13th CGPM, the International Bureau of Weights and Measures redefined a second as … the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium 133 atom; this makes the SI-based day last 794 243 384 928 000 of those periods. Due to tidal effects, the
The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process, it is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Three quarters of the Sun's mass consists of hydrogen; the Sun is a G-type main-sequence star based on its spectral class. As such, it is informally and not accurately referred to as a yellow dwarf, it formed 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System; the central mass became so hot and dense that it initiated nuclear fusion in its core. It is thought that all stars form by this process.
The Sun is middle-aged. It fuses about 600 million tons of hydrogen into helium every second, converting 4 million tons of matter into energy every second as a result; this energy, which can take between 10,000 and 170,000 years to escape from its core, is the source of the Sun's light and heat. In about 5 billion years, when hydrogen fusion in its core has diminished to the point at which the Sun is no longer in hydrostatic equilibrium, its core will undergo a marked increase in density and temperature while its outer layers expand to become a red giant, it is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury and Venus, render Earth uninhabitable. After this, it will shed its outer layers and become a dense type of cooling star known as a white dwarf, no longer produce energy by fusion, but still glow and give off heat from its previous fusion; the enormous effect of the Sun on Earth has been recognized since prehistoric times, the Sun has been regarded by some cultures as a deity.
The synodic rotation of Earth and its orbit around the Sun are the basis of solar calendars, one of, the predominant calendar in use today. The English proper name Sun may be related to south. Cognates to English sun appear in other Germanic languages, including Old Frisian sunne, Old Saxon sunna, Middle Dutch sonne, modern Dutch zon, Old High German sunna, modern German Sonne, Old Norse sunna, Gothic sunnō. All Germanic terms for the Sun stem from Proto-Germanic *sunnōn; the Latin name for the Sun, Sol, is not used in everyday English. Sol is used by planetary astronomers to refer to the duration of a solar day on another planet, such as Mars; the related word solar is the usual adjectival term used for the Sun, in terms such as solar day, solar eclipse, Solar System. A mean Earth solar day is 24 hours, whereas a mean Martian'sol' is 24 hours, 39 minutes, 35.244 seconds. The English weekday name Sunday stems from Old English and is a result of a Germanic interpretation of Latin dies solis, itself a translation of the Greek ἡμέρα ἡλίου.
The Sun is a G-type main-sequence star. The Sun has an absolute magnitude of +4.83, estimated to be brighter than about 85% of the stars in the Milky Way, most of which are red dwarfs. The Sun is heavy-element-rich, star; the formation of the Sun may have been triggered by shockwaves from more nearby supernovae. This is suggested by a high abundance of heavy elements in the Solar System, such as gold and uranium, relative to the abundances of these elements in so-called Population II, heavy-element-poor, stars; the heavy elements could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive second-generation star. The Sun is by far the brightest object in the Earth's sky, with an apparent magnitude of −26.74. This is about 13 billion times brighter than the next brightest star, which has an apparent magnitude of −1.46. The mean distance of the Sun's center to Earth's center is 1 astronomical unit, though the distance varies as Earth moves from perihelion in January to aphelion in July.
At this average distance, light travels from the Sun's horizon to Earth's horizon in about 8 minutes and 19 seconds, while light from the closest points of the Sun and Earth takes about two seconds less. The energy of this sunlight supports all life on Earth by photosynthesis, drives Earth's climate and weather; the Sun does not have a definite boundary, but its density decreases exponentially with increasing height above the photosphere. For the purpose of measurement, the Sun's radius is considered to be the distance from its center to the edge of the photosphere, the apparent visible surface of the Sun. By this measure, the Sun is a near-perfect sphere with an oblateness estimated at about 9 millionths, which means that its polar diameter differs from its equatorial diameter by only 10 kilometres; the tidal effect of the planets is weak and does not affect the shape of the Sun. The Sun rotates faster at its equator than at its poles; this differential rotation is caused by convective motion
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit; the eccentricity of this Kepler orbit is a non-negative number. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
Methods of detecting exoplanets
Any planet is an faint light source compared to its parent star. For example, a star like the Sun is about a billion times as bright as the reflected light from any of the planets orbiting it. In addition to the intrinsic difficulty of detecting such a faint light source, the light from the parent star causes a glare that washes it out. For those reasons few of the extrasolar planets reported as of April 2014 have been observed directly, with fewer being resolved from their host star. Instead, astronomers have had to resort to indirect methods to detect extrasolar planets; as of 2016, several different indirect methods have yielded success. The following methods have at least once proved successful for discovering a new planet or detecting an discovered planet: A star with a planet will move in its own small orbit in response to the planet's gravity; this leads to variations in the speed with which the star moves toward or away from Earth, i.e. the variations are in the radial velocity of the star with respect to Earth.
The radial velocity can be deduced from the displacement in the parent star's spectral lines due to the Doppler effect. The radial-velocity method measures these variations in order to confirm the presence of the planet using the binary mass function; the speed of the star around the system's center of mass is much smaller than that of the planet, because the radius of its orbit around the center of mass is so small.. However, velocity variations down to 3 m/s or somewhat less can be detected with modern spectrometers, such as the HARPS spectrometer at the ESO 3.6 meter telescope in La Silla Observatory, Chile, or the HIRES spectrometer at the Keck telescopes. An simple and inexpensive method for measuring radial velocity is "externally dispersed interferometry"; until around 2012, the radial-velocity method was by far the most productive technique used by planet hunters. The radial velocity signal is distance independent, but requires high signal-to-noise ratio spectra to achieve high precision, so is used only for nearby stars, out to about 160 light-years from Earth, to find lower-mass planets.
It is not possible to observe many target stars at a time with a single telescope. Planets of Jovian mass can be detectable around stars up to a few thousand light years away; this method finds massive planets that are close to stars. Modern spectrographs can easily detect Jupiter-mass planets orbiting 10 astronomical units away from the parent star, but detection of those planets requires many years of observation. Earth-mass planets are detectable only in small orbits around low-mass stars, e.g. Proxima b, it is easier to detect planets around low-mass stars, for two reasons: First, these stars are more affected by gravitational tug from planets. The second reason is that low-mass main-sequence stars rotate slowly. Fast rotation makes spectral-line data less clear because half of the star rotates away from observer's viewpoint while the other half approaches. Detecting planets around more massive stars is easier if the star has left the main sequence, because leaving the main sequence slows down the star's rotation.
Sometimes Doppler spectrography produces false signals in multi-planet and multi-star systems. Magnetic fields and certain types of stellar activity can give false signals; when the host star has multiple planets, false signals can arise from having insufficient data, so that multiple solutions can fit the data, as stars are not observed continuously. Some of the false signals can be eliminated by analyzing the stability of the planetary system, conducting photometry analysis on the host star and knowing its rotation period and stellar activity cycle periods. Planets with orbits inclined to the line of sight from Earth produce smaller visible wobbles, are thus more difficult to detect. One of the advantages of the radial velocity method is that eccentricity of the planet's orbit can be measured directly. One of the main disadvantages of the radial-velocity method is that it can only estimate a planet's minimum mass; the posterior distribution of the inclination angle i depends on the true mass distribution of the planets.
However, when there are multiple planets in the system that orbit close to each other and have sufficient mass, orbital stability analysis allows one to constrain the maximum mass of these planets. The radial-velocity method can be used to confirm findings made by the transit method; when both methods are used in combination the planet's true mass can be estimated. Although radial velocity of the star only gives a planet's minimum mass, if the planet's spectral lines can be distinguished from the star's spectral lines the radial velocity of the planet itself can be found, this gives the inclination of the planet's orbit; this enables measurement of the planet's actual mass. This rules out false positives, provides data about the composition of the planet; the main issue is that such detection is possible only if the planet orbits around a bright star and if the planet reflects or emits a lot of light. While the radial velocity method provides information about a planet's mass, the photometric method can determine the planet's radius.
If a planet crosses in front of its parent star's disk the observed
The astronomical unit is a unit of length the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum to a minimum and back again once a year. Conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as 149597870700 metres or about 150 million kilometres; the astronomical unit is used for measuring distances within the Solar System or around other stars. It is a fundamental component in the definition of another unit of astronomical length, the parsec. A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was common. In 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In the non-normative Annex C to ISO 80000-3, 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".
In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". 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, made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax 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, 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 precise and sophisticated, 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 from these laws, assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services. 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 for which the Gaussian gravitational constant takes the value 0.01720209895 when the units of measurement are the astronomical units of length and time". 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". 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. By 2009, the IAU had updated its standard measures to reflect improvements, calculated the speed of light at 173.1446326847 AU/d. In 1983, the International Committee for Weights and Measures modified the International System of Units 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, that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. The speed of light could be expressed as c0 = 299792458 m/s, a standard adopted by the IERS numerical standards. From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be