Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. The object's mass determines the strength of its gravitational attraction to other bodies; the basic SI unit of mass is the kilogram. In physics, mass is not the same as weight though mass is determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass; this is because weight is a force, while mass is the property that determines the strength of this force. There are several distinct phenomena. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured: Inertial mass measures an object's resistance to being accelerated by a force. Active gravitational mass measures the gravitational force exerted by an object.
Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force; the inertia and the inertial mass describe the same properties of physical bodies at the qualitative and quantitative level by other words, the mass quantitatively describes the inertia. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass determines the degree to which it generates or is affected by a gravitational field. If a first body of mass mA is placed at a distance r from a second body of mass mB, each body is subject to an attractive force Fg = GmAmB/r2, where G = 6.67×10−11 N kg−2 m2 is the "universal gravitational constant". This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical.
The standard International System of Units unit of mass is the kilogram. The kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. However, because precise measurement of a decimeter of water at the proper temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of the international prototype kilogram of cast iron, thus became independent of the meter and the properties of water. However, the mass of the international prototype and its identical national copies have been found to be drifting over time, it is expected that the re-definition of the kilogram and several other units will occur on May 20, 2019, following a final vote by the CGPM in November 2018. The new definition will use only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, the Planck constant. Other units are accepted for use in SI: the tonne is equal to 1000 kg. the electronvolt is a unit of energy, but because of the mass–energy equivalence it can be converted to a unit of mass, is used like one.
In this context, the mass has units of eV/c2. The electronvolt and its multiples, such as the MeV, are used in particle physics; the atomic mass unit is 1/12 of the mass of a carbon-12 atom 1.66×10−27 kg. The atomic mass unit is convenient for expressing the masses of molecules. Outside the SI system, other units of mass include: the slug is an Imperial unit of mass; the pound is a unit of both mass and force, used in the United States. In scientific contexts where pound and pound need to be distinguished, SI units are used instead; the Planck mass is the maximum mass of point particles. It is used in particle physics; the solar mass is defined as the mass of the Sun. It is used in astronomy to compare large masses such as stars or galaxies; the mass of a small particle may be identified by its inverse Compton wavelength. The mass of a large star or black hole may be identified with its Schwarzschild radius. In physical science, one may distinguish conceptually between at least seven different aspects of mass, or seven physical notions that involve the concept of mass.
Every experiment to date has shown these seven values to be proportional, in some cases equal, this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or operationally defined: Inertial mass is a measure of an object's resistance to acceleration when a force is applied, it is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says. Active gravitational mass is a measure of the strength of an object's gravitational flux. Gravitational field can be measured by allowing a small "test object" to fall and measuring its free-fall acceleration. For example, an object in free fall near the Moon is subject to a smaller gravitational field, hence
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
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
A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. As of February 2019, there are 352 minor planets suspected to have moons. Discoveries of minor-planet moons are important because the determination of their orbits provides estimates on the mass and density of the primary, allowing insights of their physical properties, not otherwise possible; the first modern era mention of the possibility of an asteroid satellite was in connection with an occultation of the bright star Gamma Ceti by the asteroid 6 Hebe in 1977. The observer, amateur astronomer Paul D. Maley, detected an unmistakable 0.5 second disappearance of this naked eye star from a site near Victoria, Texas. Many hours several observations were reported in Mexico attributed to the occultation by 6 Hebe itself. Although not confirmed, this documents the first formally documented case of a suspected companion of an asteroid. In addition to the terms satellite and moon, the term "binary" is sometimes used for minor planets with moons, "triple" for minor planets with two moons.
If one object is much bigger it can be referred to as the primary and its companion as secondary. The term double asteroid is sometimes used for systems in which the asteroid and its moon are the same size, while binary tends to be used independently from the relative sizes of the components; when binary minor planets are similar in size, the Minor Planet Center refers to them as "binary companions" instead of referring to the smaller body as a satellite. A good example of a true binary is the 90 Antiope system, identified in August 2000. Small satellites are referred to as moonlets. Prior to the era of the Hubble Space Telescope and space probes reaching the outer Solar System, attempts to detect satellites around asteroids were limited to optical observations from Earth. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina; however more-detailed imaging by the Hubble Telescope did not reveal a satellite, the current consensus is that Herculina does not have a significant satellite.
There were other similar reports of asteroids having companions in the following years. A letter in Sky & Telescope magazine at this time pointed to simultaneous impact craters on Earth, suggesting that these craters were caused by pairs of gravitationally bound objects. In 1993, the first asteroid moon was confirmed when the Galileo probe discovered the small Dactyl orbiting 243 Ida in the asteroid belt; the second was discovered around 45 Eugenia in 1998. In 2001, 617 Patroclus and its same-sized companion Menoetius became the first known binary asteroids in the Jupiter trojans; the first trans-Neptunian binary after Pluto–Charon, 1998 WW31, was optically resolved in 2002. Triple or trinary minor planets, are known since 2005, when the asteroid 87 Sylvia was discovered to have two satellites, making it the first known triple system; this was followed by the discovery of a second moon orbiting 45 Eugenia. In 2005, the dwarf planet Haumea was discovered to have two moons, making it the second trans-Neptunian object after Pluto known to have more than one moon.
Additionally, 216 Kleopatra and 93 Minerva were discovered to be trinary asteroids in 2008 and 2009 respectively. Since the first few triple minor planets were discovered, more continue to be discovered at a rate of about one a year. Most discovered were two moons orbiting large near-earth asteroid 3122 Florence, bringing the number of known trinary systems in the Solar System up to 14; the following table lists all satellites of triple systems chronologically by their discovery date, starting with Charon, discovered in 1978. The data about the populations of binary objects are still patchy. In addition to the inevitable observational bias the frequency appears to be different among different categories of objects. Among asteroids, an estimated 2% would have satellites. Among trans-Neptunian objects, an estimated 11% are thought to be binary or multiple objects, the majority of the large TNOs have at least one satellite, including all four IAU-listed dwarf planets. More than 50 binaries are known in each of the main groupings: near-Earth asteroids, belt asteroids, trans-Neptunian objects, not including numerous claims based on light-curve variation.
Two binaries have been found so far among centaurs with semi-major axes smaller than Neptune. Both are double ring systems around 2060 Chiron and 10199 Chariklo, discovered in 1994–2011 and 2013 respectively; the origin of minor-planet moons is not known with certainty, a variety of theories exist. A accepted theory is that minor-planet moons are formed from debris knocked off of the primary by an impact. Other pairings may be formed. Formation by collision is constrained by the angular momentum of the components, i.e. by the masses and their separation. Close binaries fit this model. Distant binaries however, with components of comparable size, are unlikely to have followed this scenario, unless considerable mass has been lost in the event; the distances of the components for the known binaries vary from a few hundreds of kilometres to more than 3000 km for the asteroids. Among TNOs, the known separations vary from 3,000 to 50,000 km. What is "typical" for a binary system tends to depend on its location in the Solar System (presumably because of different modes
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
Asteroids are minor planets of the inner Solar System. Larger asteroids have been called planetoids; these terms have been applied to any astronomical object orbiting the Sun that did not resemble a planet-like disc and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered they were found to have volatile-rich surfaces similar to comets; as a result, they were distinguished from objects found in the main asteroid belt. In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There exist millions of asteroids, many thought to be the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets; the vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects.
Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, S-type. These were named after and are identified with carbon-rich and silicate compositions, respectively; the sizes of asteroids varies greatly. Asteroids are differentiated from meteoroids. In the case of comets, the difference is one of composition: while asteroids are composed of mineral and rock, comets are composed of dust and ice. Furthermore, asteroids formed closer to the sun; the difference between asteroids and meteoroids is one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter. Meteoroids can be composed of either cometary or asteroidal materials. Only one asteroid, 4 Vesta, which has a reflective surface, is visible to the naked eye, this only in dark skies when it is favorably positioned. Small asteroids passing close to Earth may be visible to the naked eye for a short time; as of October 2017, the Minor Planet Center had data on 745,000 objects in the inner and outer Solar System, of which 504,000 had enough information to be given numbered designations.
The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908. In April 2018, the B612 Foundation reported "It's 100 percent certain we'll be hit, but we're not 100 percent sure when." In 2018, physicist Stephen Hawking, in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet. In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare. According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched; the first asteroid to be discovered, was considered to be a new planet.
This was followed by the discovery of other similar bodies, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid", coined in Greek as ἀστεροειδής, or asteroeidēs, meaning'star-like, star-shaped', derived from the Ancient Greek ἀστήρ astēr'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" were still used interchangeably. Overview of discovery timeline: 10 by 1849 1 Ceres, 1801 2 Pallas – 1802 3 Juno – 1804 4 Vesta – 1807 5 Astraea – 1845 in 1846, planet Neptune was discovered 6 Hebe – July 1847 7 Iris – August 1847 8 Flora – October 1847 9 Metis – 25 April 1848 10 Hygiea – 12 April 1849 tenth asteroid discovered 100 asteroids by 1868 1,000 by 1921 10,000 by 1989 100,000 by 2005 ~700,000 by 2015 Asteroid discovery methods have improved over the past two centuries.
In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law. This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would be spotted; the expected motion of the missing planet was about 30 seconds of arc per hour discernible by observers. The first object, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily, he discovered a new star-like object in Taurus and followed the displacement of this object during several nights. That year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, found to be between the planets Mars and Jupiter.
Piazzi named it after Ceres, the Roman goddess of agriculture. Three other asteroids (2 Pallas, 3 Juno, 4 Ves
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.