1.
Lincoln Near-Earth Asteroid Research
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LINEAR was responsible for the majority of asteroid discoveries from 1998 until it was overtaken by the Catalina Sky Survey in 2005. As of 15 September 2011, LINEAR had detected 231,082 new small Solar System bodies, the instruments used by the LINEAR program are located at Lincoln Laboratorys Experimental Test Site on the White Sands Missile Range near Socorro, New Mexico. In the late 1970s, the new Lincoln Laboratorys Experimental Test Site facility was built at White Sands Missile Range, the projects prototype used low-light video cameras. In 1994 a new proposal was made for automated detection of asteroids, the wide-field Air Force telescopes were designed for optical observation of Earth-orbiting spacecraft. Initial field tests used a 1024 ×1024 pixel charge-coupled device detector, while this CCD detector filled only about one fifth of the telescopes field of view, four near-earth objects were discovered. A1960 ×2560 pixel CCD which covered the telescopes two-square degree field of view was then installed, the first LINEAR telescope became fully operational in March 1998. Beginning in October 1999, a second 1.0 m telescope was added to the search effort, in 2002, a 0.5 m telescope equipped with the original CCD was brought on-line to provide follow-up observations for the discoveries made by the two search telescopes. This allowed about 20% more of the sky to be searched each night, data recorded by the telescopes is sent to a Lincoln Laboratory facility at Hanscom Air Force Base in Lexington, Massachusetts for processing. Detections are then forwarded to the Minor Planet Center, other objects discovered include 1999 AN10,2002 TD66, and 2004 FH. Stokes, Frank Shelly, Herbert E. M. Viggh, Matthew S. Blythe, and Joseph S. Stuart Near Earth Object program – discovery statistics, Jet Propulsion Laboratory

2.
MIT Lincoln Laboratory
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Research and development activities focus on long-term technology development as well as rapid system prototyping and demonstration. These efforts are aligned within key mission areas, the laboratory works with industry to transition new concepts and technology for system development and deployment. The laboratory also maintains several field sites around the world, the laboratorys inception was prompted by the Air Defense Systems Engineering Committees 1950 report that concluded the United States was unprepared for the threat of an air attack. S. Air Force suggested that MIT could provide the research needed to develop an air defense that could detect, identify, james R. Killian, then president of MIT, was not eager for MIT to become involved in air defense. He asked the Air Force if MIT could first conduct a study to evaluate the need for a new laboratory, killians proposal was approved, and a study named Project Charles was carried out between February and August 1951. The Semi-Automatic Ground Environment Air Defense System is the beginning of MIT Lincoln Laboratorys history of developing innovative technology, the system was conceived to meet the challenge of providing air defense to the continental United States. SAGE was designed to collect, analyze, and finally relay data from a multitude of radars, the key to this system was a computer that could perform reliably in real time. MITs Whirlwind computer, built in the 1940s, looked to be a candidate for the system. However, the Whirlwind was not reliable or fast enough for the processing needed for analyzing data coming in from dozens of, perhaps even 100, the magnetic core memory revolutionized computing. Computers became machines that were not just large and fast calculators, industry followed this development closely, adopting the magnetic core memory that expanded the capabilities of computers. Lincoln Laboratory quickly established a reputation for pioneering advanced electronics in air defense systems, many of the technical developments that later evolved into improved systems for the airborne detection and tracking of aircraft and ground vehicles have formed the basis for current research. Lincoln Laboratory conducts research and development pertinent to national security on behalf of the services, the Office of the Secretary of Defense. Projects focus on the development and prototyping of new technologies and capabilities, program activities extend from fundamental investigations, through simulation and analysis, to design and field testing of prototype systems. Emphasis is placed on transitioning technology to industry, the dissemination of information to the government, academia, and industry is a principal focus of Lincoln Laboratorys technical mission. Wide dissemination of information is achieved through annual technical workshops, seminars. Current news about Laboratory technical milestones is featured on the laboratorys website, MIT Lincoln Laboratory maintains a strong relationship with the MIT campus. Approximately 1700 technical staff members work on research, prototype building, the technical staff come from a broad range of scientific and engineering fields, with electrical engineering, physics, computer science and mathematics being among the most prevalent. Two-thirds of the staff hold advanced degrees, and 60% of those degrees are at the doctoral level

3.
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

4.
Near-Earth object
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A near-Earth object is any small Solar System body whose orbit brings it into proximity with Earth. By definition, a solar system body is a NEO if its closest approach to the Sun is less than 1.3 astronomical unit and it is now widely accepted that collisions in the past have had a significant role in shaping the geological and biological history of the Earth. NEOs have become of increased interest since the 1980s because of increased awareness of the potential danger some of the asteroids or comets pose, and mitigations are being researched. In January 2016, NASA announced the Planetary Defense Coordination Office to track NEOs larger than 30 to 50 meters in diameter and coordinate an effective threat response, NEAs have orbits that lie partly between 0.983 and 1.3 AU away from the Sun. When a NEA is detected it is submitted to the IAUs Minor Planet Center for cataloging, some NEAs orbits intersect that of Earths so they pose a collision danger. The United States, European Union, and other nations are currently scanning for NEOs in an effort called Spaceguard. In the United States and since 1998, NASA has a mandate to catalogue all NEOs that are at least 1 kilometer wide. In 2006, it was estimated that 20% of the objects had not yet been found. In 2011, largely as a result of NEOWISE, it was estimated that 93% of the NEAs larger than 1 km had been found, as of 5 February 2017, there have been 875 NEAs larger than 1 km discovered, of which 157 are potentially hazardous. The inventory is much less complete for smaller objects, which still have potential for scale, though not global. Potentially hazardous objects are defined based on parameters that measure the objects potential to make threatening close approaches to the Earth. Mostly objects with an Earth minimum orbit intersection distance of 0.05 AU or less, objects that cannot approach closer to the Earth than 0.05 AU, or are smaller than about 150 m in diameter, are not considered PHOs. This makes them a target for exploration. As of 2016, three near-Earth objects have been visited by spacecraft, more recently, a typical frame of reference for looking at NEOs has been through the scientific concept of risk. In this frame, the risk that any near-Earth object poses is typically seen through a lens that is a function of both the culture and the technology of human society, NEOs have been understood differently throughout history. Each time an NEO is observed, a different risk was posed and it is not just a matter of scientific knowledge. Such perception of risk is thus a product of religious belief, philosophic principles, scientific understanding, technological capabilities, and even economical resourcefulness.03 E −0.4 megatonnes. For instance, it gives the rate for bolides of 10 megatonnes or more as 1 per thousand years, however, the authors give a rather large uncertainty, due in part to uncertainties in determining the energies of the atmospheric impacts that they used in their determination

5.
Apollo asteroid
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The Apollo asteroids are a group of near-Earth asteroids named after 1862 Apollo, discovered by German astronomer Karl Reinmuth in the 1930s. They are Earth crossing asteroids that have an orbital semi-major axis greater than that of the Earth, as of November 2016, the steadily growing number of known Apollo asteroids has reached a total of 8,180 members. It is by far the largest group of objects, compared to the Aten, Amor. Currently, there are 1,133 numbered Apollos, asteroids are not numbered until they have been observed at two or more oppositions. There are also 1,472 Apollo asteroids that are enough. The closer their semi-major axis is to Earths, the eccentricity is needed for the orbits to cross. The largest known Apollo asteroid is 1866 Sisyphus, with a diameter of about 8.5 km, examples of known Apollo asteroids include, Apollo asteroids Apollo asteroid records List of Apollo minor planets

6.
Potentially hazardous object
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A potentially hazardous object can be known not to be a threat to Earth for the next 100 years or more, if its orbit is reasonably well determined. Potentially hazardous asteroids with some threat of impacting Earth in the next 100 years are listed on the Sentry Risk Table, as of March 2017 there are 1,786 known potentially hazardous asteroids and only 205 have an observation arc shorter than 30 days. Of the known PHAs,157 are believed to be larger than one kilometer in diameter, a calculated diameter is only a rough estimate, as it is inferred from the objects varying brightness—observed and measured at various times—and the assumed, yet unknown reflectivity of its surface. Most of the discovered PHAs are Apollo asteroids and fewer belong to the group of Aten asteroids, after several astronomical surveys, the number of known PHAs has increased tenfold since the end of the 1990s. These surveys have led to a number of 15,802 discovered near-Earth objects. Most of them are asteroids, with just some 106 near-Earth comets, the Minor Planet Centers website Unusual Minor Planets also publishes detailed statistics for these objects. This is big enough to cause devastation to human settlements unprecedented in human history in the case of a land impact. Such impact events occur on average once per 10,000 years. NEOWISE data estimates that there are 4,700 ±1,500 potentially hazardous asteroids with a greater than 100 meters. As of 2012, an estimated 20 to 30 percent of these objects have been found, Asteroids larger than 35 meters across can pose a threat to a town or city. The diameter of most small asteroids is not well determined and can only be estimated based on their brightness, for this reason NASA and the Jet Propulsion Laboratory use the more practical measure of absolute magnitude. Any asteroid with a magnitude of 22. The NASA near-Earth object program uses an assumed albedo of 0.13 for this purpose, in May 2016, the asteroid size estimates arising from the Wide-field Infrared Survey Explorer and NEOWISE missions have been questioned, but the criticism has yet to undergo peer review. Several astronomical survey projects such as Lincoln Near-Earth Asteroid Research and Catalina Sky Survey continue to search for more PHOs, both professional and amateur astronomers participate in such monitoring. This is a reflection of the character of the Solar System. The two main scales used to categorize the impact hazards of asteroids are the Palermo Technical Impact Hazard Scale, the lowest numbered PHA is 1566 Icarus. The largest known Potentially hazardous asteroid is 1999 JM8 with a diameter of ~7 km, below is listed the largest PHA discovered in a given year. Historical data of the number of discovered PHA since 1999 are displayed in the bar charts—one for the total number

7.
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

8.
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

9.
Semi-major and semi-minor axes
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In geometry, the major axis of an ellipse is its longest diameter, a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the axis, and thus runs from the centre, through a focus. Essentially, it is the radius of an orbit at the two most distant points. For the special case of a circle, the axis is the radius. One can think of the axis as an ellipses long radius. The semi-major axis of a hyperbola is, depending on the convention, thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction. Thus a and b tend to infinity, a faster than b, the semi-minor axis is a line segment associated with most conic sections that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve, in an ellipse, the one, in a hyperbola. The semi-major axis is the value of the maximum and minimum distances r max and r min of the ellipse from a focus — that is. In astronomy these extreme points are called apsis, the semi-minor axis of an ellipse is the geometric mean of these distances, b = r max r min. The eccentricity of an ellipse is defined as e =1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with one focus at the origin, the mean value of r = ℓ / and r = ℓ /, for θ = π and θ =0 is a = ℓ1 − e 2. In an ellipse, the axis is the geometric mean of the distance from the center to either focus. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse, the semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the axis that connects two points on the ellipses edge. The semi-minor axis b is related to the axis a through the eccentricity e. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction

10.
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

11.
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

12.
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

13.
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

14.
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

15.
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