1.
Apsis
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An apsis is an extreme point in an objects orbit. The word comes via Latin from Greek and is cognate with apse, for elliptic orbits about a larger body, there are two apsides, named with the prefixes peri- and ap-, or apo- added to a reference to the thing being orbited. For a body orbiting the Sun, the point of least distance is the perihelion, the terms become periastron and apastron when discussing orbits around other stars. For any satellite of Earth including the Moon the point of least distance is the perigee, for objects in Lunar orbit, the point of least distance is the pericynthion and the greatest distance the apocynthion. For any orbits around a center of mass, there are the terms pericenter and apocenter, periapsis and apoapsis are equivalent alternatives. A straight line connecting the pericenter and apocenter is the line of apsides and this is the major axis of the ellipse, its greatest diameter. For a two-body system the center of mass of the lies on this line at one of the two foci of the ellipse. When one body is larger than the other it may be taken to be at this focus. Historically, in systems, apsides were measured from the center of the Earth. In orbital mechanics, the apsis technically refers to the distance measured between the centers of mass of the central and orbiting body. However, in the case of spacecraft, the family of terms are used to refer to the orbital altitude of the spacecraft from the surface of the central body. The arithmetic mean of the two limiting distances is the length of the axis a. The geometric mean of the two distances is the length of the semi-minor axis b, the geometric mean of the two limiting speeds is −2 ε = μ a which is the speed of a body in a circular orbit whose radius is a. The words pericenter and apocenter are often seen, although periapsis/apoapsis are preferred in technical usage, various related terms are used for other celestial objects. The -gee, -helion and -astron and -galacticon forms are used in the astronomical literature when referring to the Earth, Sun, stars. The suffix -jove is occasionally used for Jupiter, while -saturnium has very rarely used in the last 50 years for Saturn. The -gee form is used as a generic closest approach to planet term instead of specifically applying to the Earth. During the Apollo program, the terms pericynthion and apocynthion were used when referring to the Moon, regarding black holes, the term peri/apomelasma was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon appeared in the scientific literature in 2002

2.
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

3.
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

4.
Comet
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Community of Metros is a system of international railway benchmarking. CoMET consists of metro systems from around the world. Each metro has a volume of at least 500 million passengers annually, the four main objectives of CoMET are, To build measures to establish metro best practice. To provide comparative information both for the board and the government. To introduce a system of measures for management and these objectives were discussed in detail at the CoMET Annual Meeting 2016, hosted by SMRT Trains of SMRT Corporation. The meeting was held at Singapore in November 2016, in the UITP conference of 1982, London Underground and Hamburger Hochbahn decided to create a benchmarking exercise to compare their two railways with additional data for other 24 metro systems. The project was successful despite the fact that metros were very different in sizes, structures, however, CoMET used the Key Performance Indicator innovatively to solve the problem. In 1994, the Mass Transit Railway of Hong Kong proposed to London Underground, Berlin U-Bahn, New York City Subway, thus, the metros can exchange performance data and investigate best practice amongst similar heavy metros. These five metros are later known as the Group of Five, over time, other large transit systems joined the group. For example, Mexico City Metro, São Paulo Metro and Tokyo Metro joined in 1996, with eight members in total, the group became known as the Community of Metros. Following the success of the CoMET, the Nova group was created in 1998 as another benchmarking association, the Nova is currently consisted of 14 metro systems from around the world. Later, Moscow Metro joined the CoMET in 1999, madrid Metro transferred from Nova to CoMET in 2004. Santiago Metro and Beijing Subway joined in 2008, taipei Metro was the last member to join the CoMET which also joined in 2010

5.
Two-body problem
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In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, the two-body problem can be re-formulated as two one-body problems, a trivial one and one that involves solving for the motion of one particle in an external potential. Since many one-body problems can be solved exactly, the corresponding two-body problem can also be solved, by contrast, the three-body problem cannot be solved in terms of first integrals, except in special cases. Let x1 and x2 be the positions of the two bodies, and m1 and m2 be their masses. The goal is to determine the trajectories x1 and x2 for all t, given the initial positions x1 and x2. The two dots on top of the x position vectors denote their second derivative with respect to time, adding and subtracting these two equations decouples them into two one-body problems, which can be solved independently. Adding equations and results in an equation describing the center of mass motion, by contrast, subtracting equation from equation results in an equation that describes how the vector r = x1 − x2 between the masses changes with time. The solutions of these independent one-body problems can be combined to obtain the solutions for the trajectories x1 and x2. The resulting equation, R ¨ =0 shows that the velocity V = dR/dt of the center of mass is constant, hence, the position R of the center of mass can be determined at all times from the initial positions and velocities. The motion of two bodies with respect to each other always lies in a plane, introducing the assumption that the force between two particles acts along the line between their positions, it follows that r × F =0 and the angular momentum vector L is constant. We now have, μ r ¨ = F r ^, Kepler orbit Energy drift Equation of the center Eulers three-body problem Gravitational two-body problem Kepler problem n-body problem Virial theorem Two-body problem Landau LD, Lifshitz EM. Two-body problem at Eric Weissteins World of Physics

6.
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

7.
Barycentric coordinates (astronomy)
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The barycenter is the center of mass of two or more bodies that are orbiting each other, or the point around which they both orbit. It is an important concept in such as astronomy and astrophysics. The distance from a center of mass to the barycenter can be calculated as a simple two-body problem. In cases where one of the two objects is more massive than the other, the barycenter will typically be located within the more massive object. Rather than appearing to orbit a center of mass with the smaller body. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km from the Earths center, when the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, as well as for many binary asteroids and it is also the case for Jupiter and the Sun, despite the thousandfold difference in mass, due to the relatively large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the center of mass of two or more bodies, the International Celestial Reference System is a barycentric one, based on the barycenter of the Solar System. In geometry, the barycenter is synonymous with centroid, the geometric center of a two-dimensional shape. The barycenter is one of the foci of the orbit of each body. This is an important concept in the fields of astronomy and astrophysics. If a is the distance between the centers of the two bodies, r1 is the axis of the primarys orbit around the barycenter. When the barycenter is located within the massive body, that body will appear to wobble rather than to follow a discernible orbit. The following table sets out some examples from the Solar System, figures are given rounded to three significant figures. If Jupiter had Mercurys orbit, the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun, but even if the Earth had Eris orbit, the Sun–Earth barycenter would still be within the Sun. To calculate the motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids. If all the planets were aligned on the side of the Sun. The calculations above are based on the distance between the bodies and yield the mean value r1

8.
Comet Lulin
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Comet Lulin is a non-periodic comet. It was discovered by Ye Quanzhi and Lin Chi-Sheng from Lulin Observatory and it peaked in brightness and arrived at perigee for observers on Earth on February 24,2009, at magnitude +5, and at 0.411 AU from Earth. The comet was near conjunction with Saturn on February 23, and it was expected to pass near Comet Cardinal on May 12,2009. The comet became visible to the eye from dark-sky sites around February 7. It passed near the double star Zubenelgenubi on February 6, near Spica on February 15 and 16, near Gamma Virginis on February 19 and it also passed near the planetary nebula NGC2392 on March 14, and near the double star Wasat around March 17. When SWIFT observed comet Lulin on 28 January 2009, the comet was shedding nearly 800 US gallons of water each second, the comet was first photographed by astronomer Lin Chi-Sheng with a 0. 41-metre telescope at the Lulin Observatory in Nantou, Taiwan on July 11,2007. However, it was the 19-year-old Ye Quanzhi from Sun Yat-sen University in China who identified the new object from three of the photographs taken by Lin. Initially, the object was thought to be a magnitude 18.9 asteroid, the discovery occurred as part of the Lulin Sky Survey project to identify small objects in the Solar System, particularly Near-Earth Objects. The comet was named Comet Lulin after the observatory, and its designation is Comet C/2007 N3. Astronomer Brian Marsden of the Smithsonian Astrophysical Observatory calculated that Comet Lulin reached its perihelion on January 10,2009, the orbit of Comet Lulin is very nearly a parabola, according to Marsden. The comet had an epoch 2009 eccentricity of 0.999986 and it is moving in a retrograde orbit at a very low inclination of just 1. 6° from the ecliptic. Given the extreme orbital eccentricity of this object, different epochs can generate quite different heliocentric unperturbed two-body best-fit solutions to the distance of this object. For objects at such high eccentricity, the Suns barycentric coordinates are more stable than heliocentric coordinates, using JPL Horizons, the barycentric orbital elements for epoch 2014-Jan-01 generate a semi-major axis of about 1200 AU and a period of about 42,000 years. On February 4,2009, a team of Italian astronomers witnessed a phenomenon in Comet Lulins tail. Team leader Ernesto Guido explains, We photographed the comet using a remotely controlled telescope in New Mexico, while we were looking, part of the comets plasma tail was torn away. Guido and colleagues believe the event was caused by a disturbance in the solar wind hitting the comet. Magnetic mini-storms in comet tails have been observed before—most famously in 2007 when NASAs STEREO spacecraft watched a coronal mass ejection crash into Comet Encke, Encke lost its tail in dramatic fashion, much as Comet Lulin did on February 4. Orbital simulation from JPL / Horizons Ephemeris

9.
Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point

10.
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