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
The term apsis refers to an extreme point in the orbit of an object. It denotes either the respective distance of the bodies; the word comes via Latin from Greek, there denoting a whole orbit, is cognate with apse. Except for the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions, there are two apsides for any elliptic orbit, named with the prefixes peri- and ap-/apo-, added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, ellipses: either the two individual ellipses of both bodies, with the center of mass of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, the other body orbiting this focus. All these ellipses share a straight line, the line of apsides, that contains their major axes, the foci, the vertices, thus the periapsis and the apoapsis; the major axis of the orbital ellipse is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.
The major axes of the individual ellipses around the barycenter the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e. a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g. the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger the orbital parameters are independent of the smaller mass. For general orbits, the terms periapsis and apoapsis are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may refer to the smallest and largest distances of the orbiter and its host.
For a body orbiting the Sun, the point of least distance is the perihelion, the point of greatest distance is the aphelion. The terms become apastron when discussing orbits around other stars. For any satellite of Earth, including the Moon, the point of least distance is the perigee and greatest distance the apogee, from Ancient Greek Γῆ, "land" or "earth". For objects in lunar orbit, the point of least distance is sometimes called the pericynthion and the greatest distance the apocynthion. Perilune and apolune are used. In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are used to refer to the orbital altitude of the spacecraft above the surface of the central body; these formulae characterize the pericenter and apocenter of an orbit: Pericenter Maximum speed, v per = μ a, at minimum distance, r per = a. Apocenter Minimum speed, v ap = μ a, at maximum distance, r ap = a.
While, in accordance with Kepler's laws of planetary motion and the conservation of energy, these two quantities are constant for a given orbit: Specific relative angular momentum h = μ a Specific orbital energy ε = − μ 2 a where: a is the semi-major axis: a = r per + r ap 2 μ is the standard gravitational parameter e is the eccentricity, defined as e = r ap − r per r ap + r per = 1 − 2 r ap r per + 1 Note t
The apparent magnitude of an astronomical object is a number, a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The brighter an object appears, the lower its magnitude value, with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46. 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 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 simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object; 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 night sky were said to be of first magnitude, whereas the faintest were of sixth magnitude, the limit of human visual perception. Each grade of magnitude was considered twice the brightness of the following grade, although that ratio was subjective as no photodetectors existed; this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is believed to have originated with Hipparchus. In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star, 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today; this implies that a star of magnitude m is about 2.512 times as bright as a star of magnitude m + 1. This figure, the fifth root of 100, became known as Pogson's Ratio; the zero point of Pogson's scale was defined by assigning Polaris a magnitude of 2. Astronomers discovered that Polaris is variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.
Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution approximates that of a black body for a temperature of 11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess due to a circumstellar 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 magnitude 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, as a function of wavelength, can be computed. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.
With the modern magnitude systems, brightness over a wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30; the brightness of Vega is exceeded by four stars in the night sky at visible wavelengths as well as the bright planets Venus and Jupiter, these must be described by negative magnitudes. For example, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other bright astronomical objects can be found in the table below. Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system; the most used is the AB magnitude system, in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be equal in the V filter band.
As the amount of light received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. 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 100. Therefore, the apparent magnitude m, in the spectral band x, would be given by m x = − 5 log 100 , more expressed in terms of common logarithms as m x
An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The term is used in astronomy, but can refer to any situation in which an object in the foreground blocks from view an object in the background. In this general sense, occultation applies to the visual scene observed from low-flying aircraft when foreground objects obscure distant objects dynamically, as the scene changes over time; the term occultation is most used to describe those frequent occasions when the Moon passes in front of a star during the course of its orbital motion around the Earth. Since the Moon, with an angular speed with respect to the stars of 0.55 arcsec/s or 2.7 µrad/s, has a thin atmosphere and stars have an angular diameter of at most 0.057 arcseconds or 0.28 µrad, a star, occulted by the Moon will disappear or reappear in 0.1 seconds or less on the Moon's edge, or limb. Events that take place on the Moon's dark limb are of particular interest to observers, because the lack of glare allows these occultations to more be observed and timed.
The Moon's orbit is inclined to the ecliptic, any stars with an ecliptic latitude of less than about 6.5 degrees may be occulted by it. There are three first magnitude stars that are sufficiently close to the ecliptic that they may be occulted by the Moon and by planets – Regulus and Antares. Occultations of Aldebaran are presently only possible by the Moon, because the planets pass Aldebaran to the north. Neither planetary nor lunar occultations of Pollux are possible. However, in the far future, occultations of Pollux will be possible; some deep-sky objects, such as the Pleiades, can be occulted by the Moon. Within a few kilometres of the edge of an occultation's predicted path, referred to as its northern or southern limit, an observer may see the star intermittently disappearing and reappearing as the irregular limb of the Moon moves past the star, creating what is known as a grazing lunar occultation. From an observational and scientific standpoint, these "grazes" are the most dynamic and interesting of lunar occultations.
The accurate timing of lunar occultations is performed by astronomers. Lunar occultations timed to an accuracy of a few tenths of a second have various scientific uses in refining our knowledge of lunar topography. Photoelectric analysis of lunar occultations have discovered some stars to be close visual or spectroscopic binaries; some angular diameters of stars have been measured by timing of lunar occultations, useful for determining effective temperatures of those stars. Early radio astronomers found occultations of radio sources by the Moon valuable for determining their exact positions, because the long wavelength of radio waves limited the resolution available through direct observation; this was crucial for the unambiguous identification of the radio source 3C 273 with the optical quasar and its jet, a fundamental prerequisite for Maarten Schmidt's discovery of the cosmological nature of quasars. Several times during the year, someone on Earth can observe the Moon occulting a planet. Since planets, unlike stars, have significant angular sizes, lunar occultations of planets will create a narrow zone on Earth from which a partial occultation of the planet will occur.
An observer located within that narrow zone could observe the planet's disk blocked by the moving moon. The same mechanic can be seen with the Sun, where observers on Earth will view it as a solar eclipse. Therefore, a total solar eclipse is the same event as the Moon occulting the Sun. Stars may be occulted by planets. Occultations of bright stars are rare. In 1959, Venus occulted Regulus, the next occultation of a bright star will be in 2044. Uranus's rings were first discovered when that planet occulted a star in 1977. On 3 July 1989, Saturn passed in front of the 5th magnitude star 28 Sagittarii. Pluto occulted stars in 1988, 2002, 2006, allowing its tenuous atmosphere to be studied via atmospheric limb sounding. In rare cases, one planet can pass in front of another. If the nearer planet appears larger than the more distant one, the event is called a mutual planetary occultation. An occultation occurs; these occultations are useful for measuring the size and position of minor planets much more than can be done by any other means.
A cross-sectional profile of the shape of an asteroid can be determined if a number of observers at different, locations observe the occultation. Occultations have been used to estimate the diameter of trans-Neptunian objects such as 2002 TX300, Varuna. In addition, mutual occultation and eclipsing events can occur between a minor planet and its satellite. A large number of these minor-planet moons have been discovered analyzing the photometric light curves of rotating minor planets and detecting a second, superimposed brightness variation, from which an orbital period for the satellite, a secondary-to-primary diameter-ratio can be derived. On 29 May 1983, 2 Pallas occulted the naked-eye bright spectroscopic binary star 1 Vulpeculae along a track across the southern United States, northern Mexico, north parts of the Caribbean. Observations from 130 different locations defined the shape of about two-thirds of the asteroid, detected the secondary companion of the bright binary star.
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.
Lund Observatory is the official English name for the astronomy department at Lund University. As of January 2010, Lund Observatory is part of the Department of Astronomy and Theoretical Physics at Lund University, it is located in Sweden. The institution was founded in 1749, but was preceded by an observatory built by astronomy professor Anders Spole in 1672, destroyed at the Battle of Lund in 1676; the now old observatory from 1867 is located in a cultural-heritage protected observatory park just outside the medieval city boundaries. The current Lund Observatory location is in a new building on the northern campus of Lund University, inaugurated in 2001; the history of astronomy in Lund through five centuries is told in the book Lundaögon mot stjärnorna Towards the middle of the last century astronomer professor Knut Lundmark, of the Lund Observatory in Sweden, supervised the two engineers Martin Kesküla and Tatjana Kesküla who painstakingly mapped the positions of about 7000 individual stars to create an unprecedented drawing of the Milky Way.
The map took two years to complete, measures 2 m by 1 m, is known as the Lund Panorama of the Milky Way. Today Lund Observatory enjoys a vibrant research activity focusing on observational as well as theoretical astrophysics. Areas covered include galactic archeology, exoplanet research, laboratory astrophysics, high energy astrophysics, star clusters, astrometry. Lund Observatory Lund Panorama of the Milky Way
Vesta is one of the largest objects in the asteroid belt, with a mean diameter of 525 kilometres. It was discovered by the German astronomer Heinrich Wilhelm Olbers on 29 March 1807 and is named after Vesta, the virgin goddess of home and hearth from Roman mythology. Vesta is the second-most-massive and second-largest body in the asteroid belt, after the dwarf planet Ceres, it contributes an estimated 9% of the mass of the asteroid belt, it is larger than Pallas, though more massive. Vesta is the only known remaining rocky protoplanet of the kind. Numerous fragments of Vesta were ejected by collisions one and two billion years ago that left two enormous craters occupying much of Vesta's southern hemisphere. Debris from these events has fallen to Earth as howardite–eucrite–diogenite meteorites, which have been a rich source of information about Vesta. Vesta is the brightest asteroid visible from Earth, its maximum distance from the Sun is greater than the minimum distance of Ceres from the Sun, though its orbit lies within that of Ceres.
NASA's Dawn spacecraft entered orbit around Vesta on 16 July 2011 for a one-year exploration and left orbit on 5 September 2012 en route to its final destination, Ceres. Researchers continue to examine data collected by Dawn for additional insights into the formation and history of Vesta. Heinrich Olbers discovered Pallas in the year after the discovery of Ceres, he proposed. He sent a letter with his proposal to the English astronomer William Herschel, suggesting that a search near the locations where the orbits of Ceres and Pallas intersected might reveal more fragments; these orbital intersections were located in the constellations of Virgo. Olbers commenced his search in 1802, on 29 March 1807 he discovered Vesta in the constellation Virgo—a coincidence, because Ceres and Vesta are not fragments of a larger body; because the asteroid Juno had been discovered in 1804, this made Vesta the fourth object to be identified in the region, now known as the asteroid belt. The discovery was announced in a letter addressed to German astronomer Johann H. Schröter dated 31 March.
Because Olbers had credit for discovering a planet, he gave the honor of naming his new discovery to German mathematician Carl Friedrich Gauss, whose orbital calculations had enabled astronomers to confirm the existence of Ceres, the first asteroid, who had computed the orbit of the new planet in the remarkably short time of 10 hours. Gauss decided on the Roman virgin goddess of Vesta. Vesta was the fourth asteroid to be discovered, hence the number 4 in its formal designation; the name Vesta, or national variants thereof, is in international use with two exceptions: Greece and China. In Greek, the name adopted was the Hellenic equivalent of Hestia. In Chinese, Vesta is called the'hearth-god star', 灶神星 zàoshénxīng, naming the asteroid for Vesta's role rather than transliterating her name into Chinese, as is done with other bodies discovered in modern times, including Uranus and Pluto. Upon its discovery, Vesta was, like Ceres and Juno before it, classified as a planet and given a planetary symbol.
The symbol representing the altar of Vesta with its sacred fire and was designed by Gauss. In Gauss's conception, this was drawn. After the discovery of Vesta, no further objects were discovered for 38 years, the Solar System was thought to have eleven planets. However, in 1845, new asteroids started being discovered at a rapid pace, by 1851 there were fifteen, each with its own symbol, in addition to the eight major planets, it soon became clear that it would be impractical to continue inventing new planetary symbols indefinitely, some of the existing ones proved difficult to draw quickly. That year, the problem was addressed by Benjamin Apthorp Gould, who suggested numbering asteroids in their order of discovery, placing this number in a disk as the generic symbol of an asteroid. Thus, the fourth asteroid, acquired the generic symbol ④; this was soon coupled with the name into an official number–name designation, ④ Vesta, as the number of minor planets increased. By 1858, the circle had been simplified to parentheses, which were easier to typeset.
Other punctuation, such as 4) Vesta and 4, was used, but had more or less died out by 1949. Today, either Vesta, or, more 4 Vesta, is used. Photometric observations of Vesta were made at the Harvard College Observatory in 1880–1882 and at the Observatoire de Toulouse in 1909; these and other observations allowed the rotation rate of Vesta to be determined by the 1950s. However, the early estimates of the rotation rate came into question because the light curve included variations in both shape and albedo. Early estimates of the diameter of Vesta ranged from 383 to 444 km. E. C. Pickering produced an estimated diameter of 513±17 km in 1879, close to the modern value for the mean diameter, but the subsequent estimates ranged from a low of 390 km up to a high of 602 km during the next century; the measured estimates were based on photometry. In 1989, speckle interferometry was used to measure a dimension that varied between 498 and 548 km during the rotational period. In 1991, an occultation of the star SAO 93228 by Vesta was observed from multiple locations