1.
Hector
–
In Greek mythology and Roman Mythology, Hector was a Trojan prince and the greatest fighter for Troy in the Trojan War. As the first-born son of King Priam and Queen Hecuba, who was a descendant of Dardanus and Tros, the founder of Troy, he was a prince of the royal house and he was married to Andromache, with whom he had an infant son, Scamandrius. He acted as leader of the Trojans and their allies in the defense of Troy, during the European Middle Ages, Hector figures as one of the Nine Worthies noted by Jacques de Longuyon, known not only for his courage but also for his noble and courtly nature. Indeed, Homer places Hector as peace-loving, thoughtful as well as bold, a son, husband and father. James Redfield writes of Hector as a martyr to loyalties, a witness to the things of this world, in Greek, Héktōr is a derivative of the verb ἔχειν ékhein, archaic form *ἕχειν hékhein, to have or to hold from Proto-Indo-European *seǵh- to hold. Héktōr, or Éktōr as found in Aeolic poetry, is also an epithet of Zeus in his capacity as he who holds, Hectors name could thus be taken to mean holding fast. According to the Iliad, Hector does not approve of war between the Greeks and the Trojans, for ten years, the Achaeans besieged Troy and their allies in the east. Hector commanded the Trojan army, with a number of subordinates including Polydamas, and his brothers Deiphobus, Helenus, and Paris. By all accounts, Hector was the best warrior the Trojans and all their allies could field, diomedes and Odysseus, when faced with his attack, described him as what Robert Fagles translated as an incredible dynamite, and a maniac. In the Iliad, Hectors exploits in the war prior to the events of the book are recapitulated and he had fought the Greek champion Protesilaus in single combat at the start of the war and killed him. A prophecy had stated that the first Greek to land on Trojan soil would die, thus, Protesilaus, Ajax, and Odysseus would not land. Finally, Odysseus threw his shield out and landed on that, in the ensuing fight, Hector killed him, fulfilling the prophecy. The Argives were initially reluctant to accept the challenge, however, after Nestors chiding, nine Greek heroes stepped up to the challenge and drew by lot to see who was to face Hector. Ajax wins and fights Hector to a stalemate for the entire day, with neither able to achieve victory, they express admiration for each others courage, skill, and strength. Hector gave Ajax his sword, which Ajax later uses to kill himself, Ajax gives Hector his girdle, which later was used to attach Hectors corpse to Achilles chariot by which he is dragged around the walls of Troy. The Greek and the Trojans make a truce to bury the dead, in the early dawn the next day the Greeks take advantage of it to build a wall and ditch around the ships. Zeus is watching in a distance, another mention of Hectors exploits in the early years of war was given in the Iliad book 9. During the embassy to Achilles, Odysseus, Phoenix and Ajax all try to persuade Achilles to rejoin the fight and he then claims, There he stood up to me alone one day, and he barely escaped my onslaught
2.
Natural satellite
–
A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet. In the Solar System there are six planetary satellite systems containing 178 known natural satellites, four IAU-listed dwarf planets are also known to have natural satellites, Pluto, Haumea, Makemake, and Eris. As of January 2012, over 200 minor-planet moons have been discovered, the Earth–Moon system is unique in that the ratio of the mass of the Moon to the mass of Earth is much greater than that of any other natural-satellite–planet ratio in the Solar System. At 3,474 km across, Earths Moon is 0.27 times the diameter of Earth, the first known natural satellite was the Moon, but it was considered a planet until Copernicus introduction of heliocentrism in 1543. Until the discovery of the Galilean satellites in 1610, however, galileo chose to refer to his discoveries as Planetæ, but later discoverers chose other terms to distinguish them from the objects they orbited. The first to use of the satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iouis satellitibus erronibus in 1610. He derived the term from the Latin word satelles, meaning guard, attendant, or companion, the term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of moon. In 1957, however, the launching of the artificial object Sputnik created a need for new terminology, to further avoid ambiguity, the convention is to capitalize the word Moon when referring to Earths natural satellite, but not when referring to other natural satellites. A few recent authors define moon as a satellite of a planet or minor planet, there is no established lower limit on what is considered a moon. Small asteroid moons, such as Dactyl, have also been called moonlets, the upper limit is also vague. Two orbiting bodies are described as a double body rather than primary. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition of what constitutes a moon, some authors consider the Pluto–Charon system to be a double planet. In contrast, irregular satellites are thought to be captured asteroids possibly further fragmented by collisions, most of the major natural satellites of the Solar System have regular orbits, while most of the small natural satellites have irregular orbits. The Moon and possibly Charon are exceptions among large bodies in that they are thought to have originated by the collision of two large proto-planetary objects. The material that would have placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting natural satellites. As opposed to planetary-sized bodies, asteroid moons are thought to form by this process. Triton is another exception, although large and in a close, circular orbit, its motion is retrograde, most regular moons in the Solar System are tidally locked to their respective primaries, meaning that the same side of the natural satellite always faces its planet. The only known exception is Saturns natural satellite Hyperion, which rotates chaotically because of the influence of Titan
3.
Mass
–
In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the 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, according to Newtons 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 bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. 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. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and 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 mainly in the United States
4.
Trojan War
–
In Greek mythology, the Trojan War was waged against the city of Troy by the Achaeans after Paris of Troy took Helen from her husband Menelaus, king of Sparta. The war is one of the most important events in Greek mythology and has been narrated through many works of Greek literature, most notably through Homers Iliad. The Iliad relates four days in the year of the decade-long siege of Troy. Other parts of the war are described in a cycle of epic poems, episodes from the war provided material for Greek tragedy and other works of Greek literature, and for Roman poets including Virgil and Ovid. Zeus sent the goddesses to Paris, who judged that Aphrodite, as the fairest, in exchange, Aphrodite made Helen, the most beautiful of all women and wife of Menelaus, fall in love with Paris, who took her to Troy. Agamemnon, king of Mycenae and the brother of Helens husband Menelaus, led an expedition of Achaean troops to Troy and besieged the city for ten years because of Paris insult. After the deaths of heroes, including the Achaeans Achilles and Ajax, and the Trojans Hector and Paris. The Achaeans slaughtered the Trojans and desecrated the temples, thus earning the gods wrath, few of the Achaeans returned safely to their homes and many founded colonies in distant shores. The Romans later traced their origin to Aeneas, one of the Trojans, in 1868, however, the German archaeologist Heinrich Schliemann met Frank Calvert, who convinced Schliemann that Troy was a real city at what is now Hissarlik in Turkey. On the basis of excavations conducted by Schliemann and others, this claim is now accepted by most scholars, whether there is any historical reality behind the Trojan War remains an open question. The events of the Trojan War are found in works of Greek literature. There is no single, authoritative text which tells the events of the war. Instead, the story is assembled from a variety of sources, the most important literary sources are the two epic poems traditionally credited to Homer, the Iliad and the Odyssey, composed sometime between the 9th and 6th centuries BC. Each poem narrates only a part of the war, the Iliad covers a short period in the last year of the siege of Troy, while the Odyssey concerns Odysseuss return to his home island of Ithaca, following the sack of Troy. Other parts of the Trojan War were told in the poems of the Epic Cycle, also known as the Cyclic Epics, the Cypria, Aethiopis, Little Iliad, Iliou Persis, Nostoi, and Telegony. Though these poems survive only in fragments, their content is known from an included in Proclus Chrestomathy. The authorship of the Cyclic Epics is uncertain, both the Homeric epics and the Epic Cycle take origin from oral tradition. Even after the composition of the Iliad, Odyssey, and the Cyclic Epics, events and details of the story that are only found in later authors may have been passed on through oral tradition and could be as old as the Homeric poems
5.
Jupiter trojan
–
The Jupiter trojans, commonly called Trojan asteroids or just Trojans, are a large group of asteroids that share the orbit of the planet Jupiter around the Sun. Relative to Jupiter, each Trojan librates around one of Jupiters two stable Lagrangian points, L4, lying 60° ahead of the planet in its orbit, and L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average axis of about 5.2 AU. The first Jupiter trojan discovered,588 Achilles, was spotted in 1906 by German astronomer Max Wolf, a total of 6,178 Jupiter trojans have been found as of January 2015. By convention they are named after a mythological figure from the Trojan War. The total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million, like main-belt asteroids, Jupiter trojans form families. Jupiter trojans are bodies with reddish, featureless spectra. The Jupiter trojans densities vary from 0.8 to 2.5 g·cm−3, Jupiter trojans are thought to have been captured into their orbits during the early stages of the Solar Systems formation or slightly later, during the migration of giant planets. NASA has announced the discovery of an Earth trojan, the trapped body will librate slowly around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the L4 and L5 Lagrange points, however, no asteroids trapped in Lagrange points were observed until more than a century after Lagranges hypothesis. Those associated with Jupiter were the first to be discovered, E. E. Barnard made the first recorded observation of a Trojan,1999 RM11, in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he saw the recently discovered Saturnian satellite Phoebe, which was only two away in the sky at the time, or possibly an asteroid. The objects identity was not realized until its orbit was calculated in 1999, in 1906–1907 two more Jupiter trojans were found by fellow German astronomer August Kopff. Hektor, like Achilles, belonged to the L4 swarm, whereas Patroclus was the first asteroid known to reside at the L5 Lagrangian point, by 1938,11 Jupiter trojans had been detected. This number increased to 14 only in 1961, as instruments improved, the rate of discovery grew rapidly, by January 2000, a total of 257 had been discovered, by May 2003, the number had grown to 1,600. Asteroids in the L4 group are named after Greek heroes, confusingly,617 Patroclus was named before the Greece/Troy rule was devised, and a Greek name thus appears in the Trojan node. The Greek node also has one misplaced asteroid,624 Hektor, estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky. The L4 swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km
6.
Angular diameter
–
The angular diameter or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view. In the vision sciences it is called the angle and in optics it is the angular aperture. The angular diameter can alternatively be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side, Angular radius equals half the angular diameter. When D ≫ d, we have δ ≈ d / D, for practical use, the distinction is only significant for spherical objects that are relatively close, since the small-angle approximation holds for x ≪1, arcsin x ≈ arctan x ≈ x. Estimates of angular diameter may be obtained by holding the hand at right angles to an extended arm. In astronomy the sizes of objects in the sky are given in terms of their angular diameter as seen from Earth. Since these angular diameters are typically small, it is common to present them in arcseconds, an arcsecond is 1/3600th of one degree, and a radian is 180/ π degrees, so one radian equals 3600*180/ π arcseconds, which is about 206265 arcseconds. Therefore, the diameter of an object with physical diameter d at a distance D, expressed in arcseconds, is given by. These objects have a diameter of one arcsecond, an object of diameter 725. The angular diameter of the Sun, from a distance of one light-year, is 0. 03″, the angular diameter 0. 03″ of the Sun given above is approximately the same as that of a person at a distance of the diameter of the Earth. Thus the angular diameter of the Sun is about 250,000 times that of Sirius, the angular diameter of the Sun is also about 250,000 times that of Alpha Centauri A. The angular diameter of the Sun is about the same as that of the Moon, even though Pluto is physically larger than Ceres, when viewed from Earth Ceres has a much larger apparent size. While angular sizes measured in degrees are useful for larger patches of sky, we need much finer units when talking about the size of galaxies. The Moons motion across the sky can be measured in size, approximately 15 degrees every hour. A one-mile-long line painted on the face of the Moon would appear to us to be about one arc-second in length, in astronomy, it is typically difficult to directly measure the distance to an object. But the object may have a physical size and a measurable angular diameter. In that case, the angular diameter formula can be inverted to yield the Angular diameter distance to distant objects as d ≡2 D tan . In non-Euclidean space, such as our universe, the angular diameter distance is only one of several definitions of distance
7.
Lagrangian point
–
The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centrifugal force required to orbit with them. There are five points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two bodies, the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a coordinate system tied to the two large bodies. Several planets have satellites near their L4 and L5 points with respect to the Sun, the three collinear Lagrange points were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two. In 1772, Joseph-Louis Lagrange published an Essay on the three-body problem, in the first chapter he considered the general three-body problem. From that, in the chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits. The five Lagrangian points are labeled and defined as follows, The L1 point lies on the line defined by the two large masses M1 and M2, and between them. It is the most intuitively understood of the Lagrangian points, the one where the attraction of M2 partially cancels M1s gravitational attraction. Explanation An object that orbits the Sun more closely than Earth would normally have an orbital period than Earth. If the object is directly between Earth and the Sun, then Earths gravity counteracts some of the Suns pull on the object, the closer to Earth the object is, the greater this effect is. At the L1 point, the period of the object becomes exactly equal to Earths orbital period. L1 is about 1.5 million kilometers from Earth, the L2 point lies on the line through the two large masses, beyond the smaller of the two. Here, the forces of the two large masses balance the centrifugal effect on a body at L2. Explanation On the opposite side of Earth from the Sun, the period of an object would normally be greater than that of Earth. The extra pull of Earths gravity decreases the orbital period of the object, like L1, L2 is about 1.5 million kilometers from Earth. The L3 point lies on the line defined by the two masses, beyond the larger of the two. Explanation L3 in the Sun–Earth system exists on the side of the Sun
8.
Apparent magnitude
–
The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, furthermore, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512. Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
9.
Minor-planet moon
–
A minor-planet moon is an astronomical object that orbits a minor planet as its natural satellite. It is thought that many asteroids and Kuiper belt objects may possess moons, 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 minor planet 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, many hours later, several observations were reported in Mexico attributed to the occultation by Hebe itself. Although not confirmed this documents the first formally documented case of a companion of an asteroid. As of October 2016, there are over 300 minor planets known to have moons, in addition to the terms satellite and moon, the term binary is sometimes used for minor planets with moons, and triple for minor planets with two moons. If one object is much bigger it can be referred to as the primary, 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, small satellites are often referred to as moonlets. As of February 2017, over 330 moons of planets have been discovered. For example, in 1978, stellar occultation observations were claimed as evidence of a satellite for the asteroid 532 Herculina, however, later more-detailed imaging by the Hubble Telescope did not reveal a satellite, and the current consensus is that Herculina does not have a significant satellite. There were other reports of asteroids having companions in the following years. 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 asteroids in the Jupiter trojans. The first trans-Neptunian binary after Pluto–Charon,1998 WW31, was resolved in 2002. Triple asteroids, or trinary asteroids, are known since 2005 and this was followed by the discovery of a second moon orbiting 45 Eugenia. Also in 2005, the Kuiper belt object Haumea was discovered to have two moons, making it the second KBO 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 trinary asteroids were discovered, more continue to be discovered at a rate of one a year. Most recently discovered was a moon orbiting the belt asteroid 130 Elektra. List of multiple planets, The data about the populations of binary objects are still patchy
10.
Astronomical unit
–
The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory 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. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
11.
Density
–
The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, 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 supposedly 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 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 metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
12.
Orbital eccentricity
–
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 an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a 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 that defines its shape. 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 have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can also 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, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular. Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit
