In astronomy, a light curve is a graph of light intensity of a celestial object or region, as a function of time. The light is in a particular frequency interval or band. Light curves can be periodic, as in the case of eclipsing binaries, Cepheid variables, other periodic variables, transiting extrasolar planets, or aperiodic, like the light curve of a nova, a cataclysmic variable star, a supernova or a microlensing event or binary as observed during occultation events; the study of the light curve, together with other observations, can yield considerable information about the physical process that produces it or constrain the physical theories about it. Graphs of the apparent magnitude of a variable star over time are used to visualise and analyse their behaviour. Although the categorisation of variable star types is done from their spectral properties, the amplitudes and regularity of their brightness changes are still important factors; some types such as Cepheids have regular light curves with the same period and shape in each cycle.
Others such as Mira variables have somewhat less regular light curves with large amplitudes of several magnitudes, while the semiregular variables are less regular still and have smaller amplitudes. The shapes of variable star light curves give valuable information about the underlying physical processes producing the brightness changes. For eclipsing variables, the shape of the light curve indicates the degree of totality, the relative sizes of the stars, their relative surface brightnesses, it may show the eccentricity of the orbit and distortions in the shape of the two stars. For pulsating stars, the amplitude or period of the pulsations can be related to the luminosity of the star, the light curve shape can be an indicator of the pulsation mode. Light curves from supernovae can be indicative of the type of supernova. Although supernova types are defined on the basis of their spectra, each has typical light curve shapes. Type I supernovae have light curves with a sharp maximum and decline, while Type II supernovae have less sharp maxima.
Light curves are helpful for classification of faint supernovae and for the determination of sub-types. For example, the type II-P have similar spectra to the type II-L but are distinguished by a light curve where the decline flattens out for several weeks or months before resuming its fade. In planetary science, a light curve can be used to derive the rotation period of a minor planet, moon, or comet nucleus. From the Earth there is no way to resolve a small object in the Solar System in the most powerful of telescopes, since the apparent angular size of the object is smaller than one pixel in the detector. Thus, astronomers measure the amount of light produced by an object as a function of time; the time separation of peaks in the light curve gives an estimate of the rotational period of the object. The difference between the maximum and minimum brightnesses can be due to the shape of the object, or to bright and dark areas on its surface. For example, an asymmetrical asteroid's light curve has more pronounced peaks, while a more spherical object's light curve will be flatter.
This allows astronomers to infer information about the spin of asteroids. The Asteroid Lightcurve Database of the Collaborative Asteroid Lightcurve Link uses a numeric code to assess the quality of a period solution for minor planet light curves, its quality code parameter "U" ranges from 0 to 3: U = 0 → Result proven incorrect U = 1 → Result based on fragmentary light curve, may be wrong. U = 2 → Result based on less than full coverage. Period may be wrong by ambiguous. U = 3 → Secure result within the precision given. No ambiguity. U = n.a. → Not available. Incomplete or inconclusive result. A trailing plus sign or minus sign is used to indicate a better or worse quality than the unsigned value; the occultation light curve is characterised as binary, where the light from the star is terminated instantaneously, remains constant for the duration, is reinstated instantaneously. The duration is equivalent to the length of a chord across the occulting body. Circumstances where the transitions are not instantaneous are.
When the occulted body is large, e.g. a star like Antares the transitions are gradual. When the occulting body has an atmosphere, e.g. the moon TitanThe observations are recorded using video equipment and the disappearance and reappearance timed using a GPS disciplined Video Time Inserter. Occultation light curves are archived at the VizieR service. Light curve inversion is a mathematical technique used to model the surfaces of rotating objects from their brightness variations; this can be used to image starspots or asteroid surface albedos. Microlensing is a process where small and low-mass astronomical objects cause a brief small increase in the brightness of a more distant object; this is caused by the small relativistic effect as larger gravitational lenses, but allows the detection and analysis of otherwise-invisible stellar and planetary mass objects. The properties of these objects can be inferred from the shape of the lensing light curve. For example, PA-99-N2 is a microlensing event that may have been due to a star in the Andromeda galaxy that has an exoplanet.
The AAVSO online light curve generator can plot light curves for thousands of variable stars The Open Astronomy
An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. The hour was established in the ancient Near East as a variable measure of 1⁄12 of the night or daytime; such seasonal, temporal, or unequal hours varied by latitude. The hour was subsequently divided into each of 60 seconds. Equal or equinoctial hours were taken as 1⁄24 of the day. Since this unit was not constant due to long term variations in the Earth's rotation, the hour was separated from the Earth's rotation and defined in terms of the atomic or physical second. In the modern metric system, hours are an accepted unit of time defined as 3,600 atomic seconds. However, on rare occasions an hour may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of UT1, based on measurements of the mean solar day. The modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century.
It displaced the Old English "tide" and "stound". The Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was a vaguer word for any span of time, including seasons and years, its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year. The time of day is expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase o'clock, from the older of clock. Hours on a 24-hour clock are expressed as "hundred" or "hundred hours". Fifteen and thirty minutes past the hour is expressed as "a quarter past" or "after" and "half past" from their fraction of the hour. Fifteen minutes before the hour may be expressed as "a quarter to", "of", "till", or "before" the hour; the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as "diagonal calendars" or "star clocks"—attest that there were 12 of these.
Clagett writes that it is "certain" this duodecimal division of the night followed the adoption of the Egyptian civil calendar placed c. 2800 BC on the basis of analyses of the Sothic cycle, but a lunar calendar long predated this and would have had twelve months in each of its years. The coffin diagrams show that the Egyptians took note of the heliacal risings of 36 stars or constellations, one for each of the ten-day "weeks" of their civil calendar; each night, the rising of eleven of these decans were noted, separating the night into twelve divisions whose middle terms would have lasted about 40 minutes each. The original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours; these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year.
During the New Kingdom, another system of decans was used, made up of 24 stars over the course of the year and 12 within any one night. The division of the day into 12 hours was accomplished by sundials marked with ten equal divisions; the morning and evening periods when the sundials failed to note time were observed as the first and last hours. The Egyptian hours were connected both with the priesthood of the gods and with their divine services. By the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ra's solar barge travelled. Protective deities were used as the names of the hours; as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. Two fire-spitting cobras were said to guard the gates of each hour of the underworld, Wadjet and the rearing cobra were sometimes referenced as wnwt from their role protecting the dead through these gates.
The Egyptian for astronomer, used as a synonym for priest, was wnwty, "One of the Hours" or "Hour-Watcher". The earliest forms of wnwt include one or three stars, with the solar hours including the determinative hieroglyph for "sun". Ancient China divided its day into 100 "marks" running from midnight to midnight; the system is said to have been used since remote antiquity, credited to the legendary Yellow Emperor, but is first attested in Han-era water clocks and in the 2nd-century history of that dynasty. It was measured with sundials and water clocks. Into the Eastern Han, the Chinese measured their day schematically, adding the 20-ke difference between the solstices evenly throughout the year, one every nine days. During the night, time was more commonly
The ecliptic is the mean plane of the apparent path in the Earth's sky that the Sun follows over the course of one year. This plane of reference is coplanar with Earth's orbit around the Sun; the ecliptic is not noticeable from Earth's surface because the planet's rotation carries the observer through the daily cycles of sunrise and sunset, which obscure the Sun's apparent motion against the background of stars during the year. The motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, the apparent path of the Sun wobbles with a period of about one month. Due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles around a mean position in a complex fashion; the ecliptic is the apparent path of the Sun throughout the course of a year. Because Earth takes one year to orbit the Sun, the apparent position of the Sun takes one year to make a complete circuit of the ecliptic. With more than 365 days in one year, the Sun moves a little less than 1° eastward every day.
This small difference in the Sun's position against the stars causes any particular spot on Earth's surface to catch up with the Sun about four minutes each day than it would if Earth would not orbit. Again, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun; the actual speed with which Earth orbits the Sun varies during the year, so the speed with which the Sun seems to move along the ecliptic varies. For example, the Sun is north of the celestial equator for about 185 days of each year, south of it for about 180 days; the variation of orbital speed accounts for part of the equation of time. Because Earth's rotational axis is not perpendicular to its orbital plane, Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, known as the obliquity of the ecliptic. If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes.
The Sun, in its apparent motion along the ecliptic, crosses the celestial equator at these points, one from south to north, the other from north to south. The crossing from south to north is known as the vernal equinox known as the first point of Aries and the ascending node of the ecliptic on the celestial equator; the crossing from north to south is descending node. The orientation of Earth's axis and equator are not fixed in space, but rotate about the poles of the ecliptic with a period of about 26,000 years, a process known as lunisolar precession, as it is due to the gravitational effect of the Moon and Sun on Earth's equatorial bulge; the ecliptic itself is not fixed. The gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earth's orbit, hence of the ecliptic, known as planetary precession; the combined action of these two motions is called general precession, changes the position of the equinoxes by about 50 arc seconds per year.
Once again, this is a simplification. Periodic motions of the Moon and apparent periodic motions of the Sun cause short-term small-amplitude periodic oscillations of Earth's axis, hence the celestial equator, known as nutation; this adds a periodic component to the position of the equinoxes. Obliquity of the ecliptic is the term used by astronomers for the inclination of Earth's equator with respect to the ecliptic, or of Earth's rotation axis to a perpendicular to the ecliptic, it is about 23.4° and is decreasing 0.013 degrees per hundred years due to planetary perturbations. The angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. Astronomers produce new fundamental ephemerides as the accuracy of observation improves and as the understanding of the dynamics increases, from these ephemerides various astronomical values, including the obliquity, are derived; until 1983 the obliquity for any date was calculated from work of Newcomb, who analyzed positions of the planets until about 1895: ε = 23° 27′ 08″.26 − 46″.845 T − 0″.0059 T2 + 0″.00181 T3 where ε is the obliquity and T is tropical centuries from B1900.0 to the date in question.
From 1984, the Jet Propulsion Laboratory's DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated: ε = 23° 26′ 21″.45 − 46″.815 T − 0″.0006 T2 + 0″.00181 T3 where hereafter T is Julian centuries from J2000.0. JPL's fundamental ephemerides have been continually updated; the Astronomical Almanac for 2010 specifies:ε = 23° 26′ 21″.406 − 46″.836769 T − 0″.0001831 T2 + 0″.00200340 T3 − 0″.576×10−6 T4 − 4″.34×10−8 T5 These expressions for the obliquity are intended for high precision over a short time span ± several centuries. J. Laskar computed an expression to order T10 good to 0″.04/1000 years over 10,000 years. All of these expressions are for the mean obliquity, that is, without the nutation of the equator included; the true or instantaneous obliquity includes the nutation. Most of the major bodies of the Solar System o
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.
S-type asteroids are asteroids with a spectral type, indicative of a siliceous mineralogical composition, hence the name. 17% of asteroids are of this type, making it the second most common after the carbonaceous C-type. S-types asteroids, with an astronomical albedo of 0.20, are moderately bright and consist of iron- and magnesium-silicates. They are dominant in the inner part of the asteroid belt within 2.2 AU, common in the central belt within about 3 AU, but become rare farther out. The largest is 15 Eunomia, with the next largest members by diameter being 3 Juno, 29 Amphitrite, 532 Herculina and 7 Iris; these largest S-types are visible in 10x50 binoculars at most oppositions. Their spectrum has a moderately steep slope at wavelengths shorter than 0.7 micrometres, has moderate to weak absorption features around 1 µm and 2 µm. The 1 µm absorption is indicative of the presence of silicates. There is a broad but shallow absorption feature centered near 0.63 µm. The composition of these asteroids is similar to a variety of stony meteorites which share similar spectral characteristics.
In the SMASS classification, several "stony" types of asteroids are brought together into a wider S-group which contains the following types: A-type K-type L-type Q-type R-type a "core" S-type for asteroids having the most typical spectra for the S-group Sa, Sk, Sl, Sq, Sr-types containing transition objects between the core S-type and the A, K, L, Q, R-types, respectively. The entire "S"-assemblage of asteroids is spectrally quite distinct from the carbonaceous C-group and the metallic X-group. In the Tholen classification, the S-type is a broad grouping which includes all the types in the SMASS S-group except for the A, Q, R, which have strong "stony" absorption features around 1 μm. Prominent stony asteroid families with their typical albedo are the: Eos family Eunomia family Flora family Koronis family Nysa family Phocaea family Asteroid spectral types X-type asteroid Bus, S. J.. "Phase II of the Small Main-belt Asteroid Spectroscopy Survey: A feature-based taxonomy". Icarus. 158: 146–177.
The astronomical unit is a unit of length the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum to a minimum and back again once a year. Conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as 149597870700 metres or about 150 million kilometres; the astronomical unit is used for measuring distances within the Solar System or around other stars. It is a fundamental component in the definition of another unit of astronomical length, the parsec. A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was common. In 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In the non-normative Annex C to ISO 80000-3, the symbol of the astronomical unit is "ua". In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".
In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". Earth's orbit around the Sun is an ellipse; the semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint; because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated, but all measurements are subject to some degree of error or uncertainty, the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances.
Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became precise and sophisticated, more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used. Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of celestial mechanics, which govern the motions of objects in space; the expected positions and distances of objects at an established time are calculated from these laws, assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System provides one of several ephemeris computation services. In 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides.
It stated that "the astronomical unit of length is that length for which the Gaussian gravitational constant takes the value 0.01720209895 when the units of measurement are the astronomical units of length and time". Equivalently, by this definition, one AU is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day". Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry; as with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting.
In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in the TDB scale leads to a value for the speed of light in astronomical units per day. By 2009, the IAU had updated its standard measures to reflect improvements, calculated the speed of light at 173.1446326847 AU/d. In 1983, the International Committee for Weights and Measures modified the International System of Units to make the metre defined as the distance travelled in a vacuum by light in 1/299792458 second; this replaced the previous definition, valid between 1960 and 1983, that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. The speed of light could be expressed as c0 = 299792458 m/s, a standard adopted by the IERS numerical standards. From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be
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