1.
Minor planet
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A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, asteroids, trojans, centaurs, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has also used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies. Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, Asteroids, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance. Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
2.
Martian L5 asteroid
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The Mars trojans are a group of objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars, the origin of the Mars trojans is not well understood. One theory suggests that they were captured in its Lagrangian points as the Solar System was forming, however, spectral studies of the Mars trojans indicate this may not be the case. One explanation for this involves asteroids wandering into the Mars Lagrangian points later in the Solar Systems formation and this is also questionable considering the very low mass of Mars
3.
Perihelion and aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
4.
Astronomical unit
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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
5.
Gigametre
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The gigametre or gigameter is a unit of length in the metric system, equal to one billion metres, the SI base unit of length. This is equivalent to 1,000,000 km or approximately 621,370 mi, gigametres are composed exactly of 1,000 megametres. Although fit for distances in astronomy this professional field usually uses the unit or millions and billions of kilometres. Earths average distance from the Sun is 149.6 Gm, jupiters average distance from the Sun is 778.5 Gm. Osiris average distance from the parent star HD209458 is 6.7 Gm, PSR J1719-1438 bs average distance from the pulsar PSR J1719-1438 is 0.666 Gm, which is the smallest orbit of any known exoplanet. The mean diameter of the Sun is 1.393 Gm, the mean diameter of red supergiant star Betelgeuse is 1,302 Gm. Conversion of units, for comparison with other units of length Light year Metric system Orders of magnitude Parsec SI SI prefix
6.
Orbital eccentricity
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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
7.
Mean anomaly
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In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. Define T as the time required for a body to complete one orbit. In time T, the radius vector sweeps out 2π radians or 360°. The average rate of sweep, n, is then n =2 π T or n =360 ∘ T, define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M, the mean anomaly can be defined M = n, because the rate of increase, n, is a constant average, the mean anomaly increases uniformly from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians at the apocenter, if the mean anomaly is known at any given instant, it can be calculated at any later instant by simply adding n δt where δt represents the time difference. Mean anomaly does not measure an angle between any physical objects and it is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three parameters that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Define l as the longitude, the angular distance of the body from the same reference direction. Thus mean anomaly is also M = l − ϖ, mean angular motion can also be expressed, n = μ a 3, where μ is a gravitational parameter which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, M = μ a 3, and here mean anomaly represents uniform angular motion on a circle of radius a
8.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
9.
Orbital inclination
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Orbital inclination measures the tilt of an objects orbit around a celestial body. It is expressed as the angle between a plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the equator, the plane of the orbit is the same as the Earths equatorial plane. The general case is that the orbit is tilted, it spends half an orbit over the northern hemisphere. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°, the inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planets equator, for planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. This reference plane is most practical for Earth-based observers, therefore, Earths inclination is, by definition, zero. Inclination could instead be measured with respect to another plane, such as the Suns equator or the invariable plane, the inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the perpendicular to the axis of rotation of the central body. An inclination of 30° could also be described using an angle of 150°, the convention is that the normal orbit is prograde, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe retrograde orbits, thus, An inclination of 0° means the orbiting body has a prograde orbit in the planets equatorial plane. An inclination greater than 0° and less than 90° also describe prograde orbits, an inclination of 63. 4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. An inclination of exactly 90° is an orbit, in which the spacecraft passes over the north and south poles of the planet. An inclination greater than 90° and less than 180° is a retrograde orbit, an inclination of exactly 180° is a retrograde equatorial orbit. For gas giants, the orbits of moons tend to be aligned with the giant planets equator, the inclination of exoplanets or members of multiple stars is the angle of the plane of the orbit relative to the plane perpendicular to the line-of-sight from Earth to the object. An inclination of 0° is an orbit, meaning the plane of its orbit is parallel to the sky. An inclination of 90° is an orbit, meaning the plane of its orbit is perpendicular to the sky
10.
Longitude of the ascending node
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The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a direction, called the origin of longitude, to the direction of the ascending node. The ascending node is the point where the orbit of the passes through the plane of reference. Commonly used reference planes and origins of longitude include, For a geocentric orbit, Earths equatorial plane as the plane. In this case, the longitude is called the right ascension of the ascending node. The angle is measured eastwards from the First Point of Aries to the node, for a heliocentric orbit, the ecliptic as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise from the First Point of Aries to the node, the angle is measured eastwards from north to the node. pp.40,72,137, chap. In the case of a star known only from visual observations, it is not possible to tell which node is ascending. In this case the orbital parameter which is recorded is the longitude of the node, Ω, here, n=<nx, ny, nz> is a vector pointing towards the ascending node. The reference plane is assumed to be the xy-plane, and the origin of longitude is taken to be the positive x-axis, K is the unit vector, which is the normal vector to the xy reference plane. For non-inclined orbits, Ω is undefined, for computation it is then, by convention, set equal to zero, that is, the ascending node is placed in the reference direction, which is equivalent to letting n point towards the positive x-axis. Kepler orbits Equinox Orbital node perturbation of the plane can cause revolution of the ascending node
11.
Argument of periapsis
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The argument of periapsis, symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the ascending node to its periapsis. For specific types of orbits, words such as perihelion, perigee, periastron, an argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis, however, especially in discussions of binary stars and exoplanets, the terms longitude of periapsis or longitude of periastron are often used synonymously with argument of periapsis. In the case of equatorial orbits, the argument is strictly undefined, where, ex and ey are the x- and y-components of the eccentricity vector e. In the case of circular orbits it is assumed that the periapsis is placed at the ascending node. Kepler orbit Orbital mechanics Orbital node
12.
Asteroid
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Asteroids are minor planets, especially those of the inner Solar System. The larger ones have also been called planetoids and these terms have historically been applied to any astronomical object orbiting the Sun that did not show the disc of a planet and was not observed to have the characteristics of an active comet. As minor planets in the outer Solar System were discovered and found to have volatile-based surfaces that resemble those of comets, in this article, the term asteroid refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There are millions of asteroids, many thought to be the remnants of planetesimals. The large majority of known asteroids orbit in the belt between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects, individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups, C-type, M-type, and S-type. These were named after and are identified with carbon-rich, metallic. The size of asteroids varies greatly, some reaching as much as 1000 km across, asteroids are differentiated from comets and meteoroids. In the case of comets, the difference is one of composition, while asteroids are composed of mineral and rock, comets are composed of dust. In addition, asteroids formed closer to the sun, preventing the development of the aforementioned cometary ice, the difference between asteroids and meteoroids is mainly one of size, meteoroids have a diameter of less than one meter, whereas asteroids have a diameter of greater than one meter. Finally, meteoroids can be composed of either cometary or asteroidal materials, only one asteroid,4 Vesta, which has a relatively reflective surface, is normally visible to the naked eye, and this only in very dark skies when it is favorably positioned. Rarely, small asteroids passing close to Earth may be visible to the eye for a short time. As of March 2016, the Minor Planet Center had data on more than 1.3 million objects in the inner and outer Solar System, the United Nations declared June 30 as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, the first asteroid to be discovered, Ceres, was found in 1801 by Giuseppe Piazzi, and was originally considered to be a new planet. In the early half of the nineteenth century, the terms asteroid. Asteroid discovery methods have improved over the past two centuries. This task required that hand-drawn sky charts be prepared for all stars in the band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would, hopefully, the expected motion of the missing planet was about 30 seconds of arc per hour, readily discernible by observers
13.
Mars trojan
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The Mars trojans are a group of objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars, the origin of the Mars trojans is not well understood. One theory suggests that they were captured in its Lagrangian points as the Solar System was forming, however, spectral studies of the Mars trojans indicate this may not be the case. One explanation for this involves asteroids wandering into the Mars Lagrangian points later in the Solar Systems formation and this is also questionable considering the very low mass of Mars
14.
Lagrangian point
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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
15.
Mars crosser
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A Mars-crosser is an asteroid whose orbit crosses that of Mars. The known numbered Mars-crossers are listed here and they include the two numbered Mars trojans 5261 Eureka and 1998 VF31. Many databases, for instance the JPL Small-Body Database, only list asteroids with a greater than 1.3 AU as Mars-crossers. An asteroid with a less than this is classed as a near-Earth object even though it is crossing the orbit of Mars as well as crossing that of Earth. Nevertheless, these objects are listed on this page, a grazer is an object with a perihelion below the aphelion of Mars but above the Martian perihelion. The JPL SBDB lists 13,500 Mars-crossing asteroids, only 18 MCAs are brighter than absolute magnitude 12.5, which typically makes these asteroids with H<12.5 more than 13 km in diameter depending on the albedo. The smallest known MCAs have a magnitude of around 24 and are typically less than 100 meters in diameter. Instead, they are categorized as Near Earth Objects
16.
Jean Meeus
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Jean Meeus is a Belgian astronomer specializing in celestial mechanics. The asteroid 2213 Meeus was named after him by the International Astronomical Union in 1981 for his contributions to the field, jean Meeus studied mathematics at the University of Leuven in Belgium, where he received the Degree of Licentiate in 1953. From then until his retirement in 1993, he was a meteorologist at Brussels Airport and his area of interest is spherical and mathematical astronomy. In 1986 he won the Amateur Achievement Award of the Astronomical Society of the Pacific, calculate MJD, Equation of Time and Solar Declination in Excel, CAD or your other programs. Sunlit Design claims accuracy of ±270 milliseconds for the equation of time, ±30 arcseconds for solar declination, and ±4 arcminutes for solar hour angle
17.
Mars Trojan asteroid
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The Mars trojans are a group of objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars, the origin of the Mars trojans is not well understood. One theory suggests that they were captured in its Lagrangian points as the Solar System was forming, however, spectral studies of the Mars trojans indicate this may not be the case. One explanation for this involves asteroids wandering into the Mars Lagrangian points later in the Solar Systems formation and this is also questionable considering the very low mass of Mars
18.
5261 Eureka
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5261 Eureka is the first Mars trojan discovered. It was discovered by David H. Levy and Henry Holt at Palomar Observatory on June 20,1990 from the Palomar Observatory and it trails Mars at a distance varying by only 0.3 AU during each revolution. Minimum distances from the Earth, Venus, and Jupiter, are 0.5,0.8, long-term numerical integration shows that the orbit is stable. At least five other asteroids in near-1,1 resonances with Mars have been discovered and they are 2001 FR127,2001 FG24,1999 ND43,1998 QH56 and 1998 SD4. The infrared spectrum for 5261 Eureka is typical for an A-type asteroid, a-class asteroids are tinted red in hue, with a moderate albedo. On November 28,2011, a satellite of 5261 Eureka was found. It has yet to be named, and its designation is S/20111. The moon is about 0.46 km in diameter and orbits 2.1 km from Eureka, the satellites existence was announced in September 2014. S. Tabachnik and N. W. Evans, Cartography for Martian Trojans, The Astrophysical Journal 517,1999, pp. L63-L66
19.
Numerical integration
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This article focuses on calculation of definite integrals. The term numerical quadrature is more or less a synonym for numerical integration, Some authors refer to numerical integration over more than one dimension as cubature, others take quadrature to include higher-dimensional integration. The basic problem in numerical integration is to compute an approximate solution to a definite integral ∫ a b f d x to a degree of accuracy. If f is a smooth function integrated over a number of dimensions. The term numerical integration first appears in 1915 in the publication A Course in Interpolation, Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area and that is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates and this construction must be performed only by means of compass and straightedge. The ancient Babylonians used the trapezoidal rule to integrate the motion of Jupiter along the ecliptic, for a quadrature of a rectangle with the sides a and b it is necessary to construct a square with the side x = a b. For this purpose it is possible to use the fact, if we draw the circle with the sum of a and b as the diameter. The similar geometrical construction solves a problem of a quadrature for a parallelogram, problems of quadrature for curvilinear figures are much more difficult. The quadrature of the circle with compass and straightedge had been proved in the 19th century to be impossible, nevertheless, for some figures a quadrature can be performed. The quadratures of a surface and a parabola segment done by Archimedes became the highest achievement of the antique analysis. The area of the surface of a sphere is equal to quadruple the area of a circle of this sphere. The area of a segment of the cut from it by a straight line is 4/3 the area of the triangle inscribed in this segment. For the proof of the results Archimedes used the Method of exhaustion of Eudoxus, in medieval Europe the quadrature meant calculation of area by any method. More often the Method of indivisibles was used, it was less rigorous, john Wallis algebrised this method, he wrote in his Arithmetica Infinitorum series that we now call the definite integral, and he calculated their values. Isaac Barrow and James Gregory made further progress, quadratures for some algebraic curves, christiaan Huygens successfully performed a quadrature of some Solids of revolution
20.
Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets, of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury. The Solar System formed 4.6 billion years ago from the collapse of a giant interstellar molecular cloud. The vast majority of the mass is in the Sun. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being composed of rock. The four outer planets are giant planets, being more massive than the terrestrials. All planets have almost circular orbits that lie within a flat disc called the ecliptic. The Solar System also contains smaller objects, the asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptunes orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets, identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris. In addition to two regions, various other small-body populations, including comets, centaurs and interplanetary dust clouds. Six of the planets, at least four of the dwarf planets, each of the outer planets is encircled by planetary rings of dust and other small objects. The solar wind, a stream of charged particles flowing outwards from the Sun, the heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium, it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for long-period comets, the Solar System is located in the Orion Arm,26,000 light-years from the center of the Milky Way. For most of history, humanity did not recognize or understand the concept of the Solar System, the invention of the telescope led to the discovery of further planets and moons. The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99. 86% of the known mass. The Suns four largest orbiting bodies, the giant planets, account for 99% of the mass, with Jupiter. The remaining objects of the Solar System together comprise less than 0. 002% of the Solar Systems total mass, most large objects in orbit around the Sun lie near the plane of Earths orbit, known as the ecliptic
21.
(385250) 2001 DH47
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2001 DH47, also written as 2001 DH47, is a small asteroid orbiting near the L5 point of Mars. 2001 DH47 was discovered on February 1,2001 by the Spacewatch program, observing from Steward Observatory, Kitt Peak and its orbit is characterized by low eccentricity, moderate inclination and a semi-major axis of 1.52 AU. Its orbit is determined as it is currently based on 45 observations with a data-arc span of 3,148 days. It has a magnitude of 19.7 which gives a characteristic diameter of 562 m. It was identified as Mars trojan by H. Scholl, F. Marzari and P. Tricarico in 2005, recent calculations confirm that it is indeed a stable L5 Mars trojan with a libration period of 1365 yr and an amplitude of 11°. These values as well as its short-term orbital evolution are similar to those of 5261 Eureka. Long-term numerical integrations show that its orbit is stable on Gyr time-scales. 5261 Eureka 1999 UJ71998 VF312007 NS22011 SC1912011 SL252011 UN632001 DH47 Ivashchenko,2007, Minor Planet Electronic Circular, 2007-P09. Dynamics of Mars Trojans Scholl, H. Marzari, F. Tricarico, P.2005, Icarus, Volume 175, Issue 2, p. 397–408. Three new stable L5 Mars Trojans de la Fuente Marcos, C. de la Fuente Marcos, R.2013, Monthly Notices of the Royal Astronomical Society, Letters, Vol.432, Issue 1,2001 DH47 data at MPC2001 DH47 data at AstDyS-2. 2001 DH47 at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
22.
2011 SC191
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2011 SC191, also written as 2011 SC191, is a small asteroid orbiting near the L5 point of Mars. 2011 SC191 was first observed on March 21,2003 by the Near-Earth Asteroid Tracking project at Palomar Observatory using the Samuel Oschin telescope, the object was subsequently lost and re-discovered on October 31,2011 by the Mt. Lemmon Survey. Its orbit is characterized by low eccentricity, moderate inclination and an axis of 1.52 AU. Upon discovery, it was classified as Mars-crosser by the Minor Planet Center and its orbit is well determined as it is currently based on 45 observations with a data-arc span of 3,146 days. 2011 SC191 has a magnitude of 19.3 which gives a characteristic diameter of 600 m. Recent calculations indicate that it is a stable L5 Mars trojan with a period of 1300 yr. These values as well as its short-term orbital evolution are similar to those of 5261 Eureka and its eccentricity oscillates mainly due to secular resonances with the Earth and the oscillation in inclination is likely driven by secular resonances with Jupiter. Long-term numerical integrations show that its orbit is stable on Gyr time-scales. Garradd, G. J. Grauer, A. D. Hill, R. E. Kowalski, R. A. Larson, S. M. McNaught, R. H. Birtwhistle, P.2011, Minor Planet Electronic Circular, 2011-T02. Three new stable L5 Mars Trojans de la Fuente Marcos, C. de la Fuente Marcos, R.2013, Monthly Notices of the Royal Astronomical Society, Letters, Vol.432, Issue 1, pp. 31–35. Orbital clustering of Martian Trojans, An asteroid family in the solar system. Christou, A. A.2013, Icarus, Vol.224, Issue 1,2011 SC191 data at MPC.2011 SC191 data at AstDyS-2. 2011 SC191 at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
23.
2011 SL25
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2011 SL25, also written as 2011 SL25, is a small minor body that has been identified as a L5 Mars trojan candidate. 2011 SL25 was discovered on September 21,2011 at the Alianza S4 Observatory on Cerro Burek in Argentina and it follows a relatively eccentric orbit with a semi-major axis of 1.52 AU. This object has noticeable orbital inclination and its orbit was initially poorly constrained, with only 76 observations over 42 days, but was recovered in January 2014. 2011 SL25 has a magnitude of 19.5 which gives a characteristic diameter of 575 m. Recent calculations indicate that it is a stable L5 Mars Trojan candidate with a period of 1400 yr. Values as well as its short-term orbital evolution are similar to those of 5261 Eureka, long-term numerical integrations show that its orbit is stable on Gyr time-scales. It appears to be stable at least for 4.5 Gyr, Orbital clustering of Martian Trojans, An asteroid family in the inner solar system. Christou, A. A.2013, Icarus, Vol.224, Issue 1,2011 SL25 data at MPC.2011 SL25 data at AstDyS-2. 2011 SL25 at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
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2011 UN63
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2011 UN63, also written as 2011 UN63, is a small minor body orbiting near the L5 point of Mars. 2011 UN63 was first observed on September 27,2009 by the Mt. Lemmon Survey, lost, it was re-discovered on October 21,2011 again by the Mt. Lemmon Survey. 2011 UN63 follows a low eccentricity orbit with an axis of 1.52 AU. This object has moderate orbital inclination and it was classified as Mars-crosser by the Minor Planet Center upon discovery. Its orbit is well determined as it is currently based on 64 observations with a data-arc span of 793 days. This asteroid has a magnitude of 19.7 which gives a characteristic diameter of 560 m. Recent calculations indicate that it is a stable L5 Mars trojan asteroid with a period of 1350 yr. These values as well as its short-term orbital evolution are similar to those of 5261 Eureka or 2011 SC191, long-term numerical integrations show that its orbit is very stable on Gyr time-scales. Orbital clustering of Martian Trojans, An asteroid family in the solar system. Christou, A. A.2013, Icarus, Vol.224, Issue 1,2011 UN63 data at MPC2011 UN63 data at AstDyS-2. 2011 UN63 at the JPL Small-Body Database Discovery · Orbit diagram · Orbital elements · Physical parameters
25.
Jet Propulsion Laboratory
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The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, California and Pasadena, California, United States. The JPL is managed by the nearby California Institute of Technology for NASA, the laboratorys primary function is the construction and operation of planetary robotic spacecraft, though it also conducts Earth-orbit and astronomy missions. It is also responsible for operating NASAs Deep Space Network and they are also responsible for managing the JPL Small-Body Database, and provides physical data and lists of publications for all known small Solar System bodies. The JPLs Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks, JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Malinas thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this GALCIT Rocket Project in 1939. In 1941, Malina, Parsons, Forman, Martin Summerfield, in 1943, von Kármán, Malina, Parsons, and Forman established the Aerojet Corporation to manufacture JATO motors. The project took on the name Jet Propulsion Laboratory in November 1943, during JPLs Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate range ballistic missiles. These missiles were the first US ballistic missiles developed at JPL and it also developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, and the forerunner of the Aerobee sounding rocket. At various times, it carried out testing at the White Sands Proving Ground, Edwards Air Force Base. A lunar lander was developed in 1938-39 which influenced design of the Apollo Lunar Module in the 1960s. The team lost that proposal to Project Vanguard, and instead embarked on a project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful flights in 1956 and 1957. Using a spare Juno I, the two organizations then launched the United States first satellite, Explorer 1, on February 1,1958, JPL was transferred to NASA in December 1958, becoming the agencys primary planetary spacecraft center. JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo, JPL also led the way in interplanetary exploration with the Mariner missions to Venus, Mars, and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA, as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earths orbit. JPL was early to employ women mathematicians, in the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as their first woman engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams, when founded, JPLs site was a rocky flood-plain just outside the city limits of Pasadena. Almost all of the 177 acres of the U. S, the city of La Cañada Flintridge, California was incorporated in 1976, well after JPL attained international recognition with a Pasadena address
26.
ArXiv
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In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14,1991, arXiv. org passed the half-million article milestone on October 3,2008, by 2014 the submission rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX file format, around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Additional modes of access were added, FTP in 1991, Gopher in 1992. The term e-print was quickly adopted to describe the articles and its original domain name was xxx. lanl. gov. Due to LANLs lack of interest in the rapidly expanding technology, in 1999 Ginsparg changed institutions to Cornell University and it is now hosted principally by Cornell, with 8 mirrors around the world. Its existence was one of the factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists regularly upload their papers to arXiv. org for worldwide access, Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. The annual budget for arXiv is approximately $826,000 for 2013 to 2017, funded jointly by Cornell University Library, annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. As of 14 January 2014,174 institutions have pledged support for the period 2013–2017 on this basis, in September 2011, Cornell University Library took overall administrative and financial responsibility for arXivs operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it was supposed to be a three-hour tour, however, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. The lists of moderators for many sections of the arXiv are publicly available, additionally, an endorsement system was introduced in 2004 as part of an effort to ensure content that is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, new authors from recognized academic institutions generally receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for allegedly restricting scientific inquiry, perelman appears content to forgo the traditional peer-reviewed journal process, stating, If anybody is interested in my way of solving the problem, its all there – let them go and read about it. The arXiv generally re-classifies these works, e. g. in General mathematics, papers can be submitted in any of several formats, including LaTeX, and PDF printed from a word processor other than TeX or LaTeX. The submission is rejected by the software if generating the final PDF file fails, if any image file is too large. ArXiv now allows one to store and modify an incomplete submission, the time stamp on the article is set when the submission is finalized
27.
List of minor planets
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This is a list of numbered minor planets in the Solar System, in numerical order. As of March 2017 there are 488,449 numbered minor planets, only 20,570 or approximately 4% of all numbered minor planets are currently named, mostly for people and figures from mythology and fiction. The Jupiter trojan 1974 FV1 is currently the lowest-numbered unnamed minor planet, Minor planets also include dwarf planets of which 5 have been officially recognized by the IAU with potentially hundreds more to follow in the future. The data is sourced from the Minor Planet Center, for an overview of all existing partial lists, see § Main index. The example above shows the beginning of the first table in partial list 189,001 to 190,000, in this example, all 5 bodies were discovered at Palomar Observatory by a trio of astronomers, Cornelis van Houten, Ingrid van Houten-Groeneveld and Tom Gehrels. For more information, see § Orbital groups, as only 189004 Capys has been named yet, the other four bodies only display their number in the permanent designation column. The provisional designation displayed in this example is an uncommon survey designation, the MPC credits more than 1000 professional and amateur astronomers as discoverers of minor planets. Many of them have discovered only a few minor planets or even just co-discovered a single one, moreover a discoverer does not need to be a human being. There are about 300 programs, surveys and observatories credited as discoverers, among these, a small group of U. S. programs and surveys actually account for most of all discoveries made so far. As the total of numbered minor planets is growing by the thousands on a monthly basis, all statistical figures are constantly changing. After discovery, minor planets generally receive a designation, e. g.1989 AC, then a leading sequential number in parenthesis, e. g.1989 AC. Optionally, a name can be given, replacing the part of the designation. In modern times, a minor planet receives a number only after it has been observed several times over at least 4 oppositions. Minor planets whose orbits are not precisely known are known by their provisional designation and this rule was not necessarily followed in earlier times, and some bodies received a number but subsequently became lost minor planets. In 2000,719 Albert was the last numbered asteroids to be recovered after having been lost for nearly 89 years, only after a number is assigned is the minor planet eligible to receive a name. Usually the discoverer has up to 10 years to pick a name, for the reasons mentioned above, the sequence of numbers only approximately matches the timeline of discovery. In extreme cases, such as lost minor planets, there may be a mismatch, for instance the high-numbered 69230 Hermes was originally discovered in 1937. Only after it was rediscovered could its orbit be established and a number assigned, in the partial lists, numbered minor planets are categorized into one of 8 distinct orbital groups
28.
Small Solar System body
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A Small Solar System Body is an object in the Solar System that is neither a planet, nor a dwarf planet, nor a natural satellite. The term was first defined in 2006 by the International Astronomical Union, all other objects, except satellites, orbiting the Sun shall be referred to collectively as Small Solar System Bodies. These currently include most of the Solar System asteroids, most Trans-Neptunian Objects, comets and this encompasses all comets and all minor planets other than those that are dwarf planets. Except for the largest, which are in equilibrium, natural satellites differ from small Solar System bodies not in size. The orbits of satellites are not centered on the Sun, but around other Solar System objects such as planets, dwarf planets. Some of the larger small Solar System bodies may be reclassified in future as dwarf planets, the orbits of the vast majority of small Solar System bodies are located in two distinct areas, namely the asteroid belt and the Kuiper belt. These two belts possess some internal structure related to perturbations by the planets, and have fairly loosely defined boundaries. Other areas of the Solar System also encompass small bodies in smaller concentrations and these include the near-Earth asteroids, centaurs, comets, and scattered disc objects