1.
Orbital elements
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Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in classical two-body systems. There are many different ways to describe the same orbit. A real orbit changes over time due to perturbations by other objects. A Keplerian orbit is merely an idealized, mathematical approximation at a particular time, the traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from a frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the center of mass. When viewed from a non-inertial frame centred on one of the bodies, only the trajectory of the body is apparent. An orbit has two sets of Keplerian elements depending on which body is used as the point of reference, the reference body is called the primary, the other body is called the secondary. The primary does not necessarily possess more mass than the secondary, and even when the bodies are of equal mass, the orbital elements depend on the choice of the primary. The main two elements that define the shape and size of the ellipse, Eccentricity —shape of the ellipse, semimajor axis —the sum of the periapsis and apoapsis distances divided by two. For circular orbits, the axis is the distance between the centers of the bodies, not the distance of the bodies from the center of mass. For paraboles or hyperboles, this is infinite, tilt angle is measured perpendicular to line of intersection between orbital plane and reference plane. Any three points on an ellipse will define the ellipse orbital plane, the plane and the ellipse are both two-dimensional objects defined in three-dimensional space. Longitude of the ascending node —horizontally orients the ascending node of the ellipse with respect to the reference frames vernal point, and finally, Argument of periapsis defines the orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis. True anomaly at epoch defines the position of the body along the ellipse at a specific time. The mean anomaly is a mathematically convenient angle which varies linearly with time and it can be converted into the true anomaly ν, which does represent the real geometric angle in the plane of the ellipse, between periapsis and the position of the orbiting object at any given time. Thus, the anomaly is shown as the red angle ν in the diagram

2.
Orbit
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In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet about a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating path around a body, to a close approximation, planets and satellites follow elliptical orbits, with the central mass being orbited at a focal point of the ellipse, as described by Keplers laws of planetary motion. For ease of calculation, in most situations orbital motion is adequately approximated by Newtonian Mechanics, historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and it assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets motions were accurately measured, theoretical mechanisms such as deferent. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model, the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. Second, he found that the speed of each planet is not constant, as had previously been thought. Third, Kepler found a relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter,5. 23/11.862, is equal to that for Venus,0. 7233/0.6152. Idealised orbits meeting these rules are known as Kepler orbits, isaac Newton demonstrated that Keplers laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the sizes are in inverse proportion to their masses. Where one body is more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, in a dramatic vindication of classical mechanics, in 1846 le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits, in relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy

3.
Orbital node
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An orbital node is one of the two points where an orbit crosses a plane of reference to which it is inclined. An orbit that is contained in the plane of reference has no nodes, common planes of reference include, For a geocentric orbit, the Earths equatorial plane. In this case, non-inclined orbits are called equatorial, for a heliocentric orbit, the ecliptic. In this case, non-inclined orbits are called ecliptic, for an orbit outside the Solar System, the plane through the primary perpendicular to a line through the observer and the primary. If a reference direction from one side of the plane of reference to the other is defined, the two nodes can be distinguished. For geocentric and heliocentric orbits, the node is where the orbiting object moves north through the plane of reference. The position of the node may be used as one of a set of parameters, called orbital elements and this is done by specifying the longitude of the ascending node The line of nodes is the intersection of the objects orbital plane with the plane of reference. It passes through the two nodes, the symbol of the ascending node is, and the symbol of the descending node is. In medieval and early times the ascending and descending nodes were called the dragons head and dragons tail. These terms originally referred to the times when the Moon crossed the apparent path of the sun in the sky, also, corruptions of the Arabic term such as ganzaar, genzahar, geuzaar and zeuzahar were used in the medieval West to denote either of the nodes. Pp. 196–197, p.65, pp. 95–96, the Greek terms αναβιβάζων and καταβιβάζων were also used for the ascending and descending nodes, giving rise to the English words anabibazon and catabibazon. For the orbit of the Moon around the Earth, the plane is taken to be the ecliptic. The gravitational pull of the Sun upon the Moon causes its nodes, called the nodes, to precess gradually westward. Eclipse Euler angles Longitude of the ascending node

4.
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

5.
Heliocentric orbit
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A heliocentric orbit is an orbit around the barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroids in the Solar System are in such orbits, the moons of planets in the Solar System, by contrast, are not in heliocentric orbits as they orbit their respective planet. A similar phenomenon allows the detection of exoplanets by way of the radial velocity method, the helio- prefix is derived from the Greek word helios, meaning sun, and also Helios, the personification of the Sun in Greek mythology. The first spacecraft to be put in an orbit is Luna 1. A trans-Mars injection is an orbit in which a propulsive maneuver is used to set a spacecraft on a trajectory, also known as Mars transfer orbit. Every two years, low-energy transfer windows open up which allow movement between planets with the lowest possible delta-v requirements, transfer injections can place spacecraft into either a Hohmann transfer orbit or bi-elliptic transfer orbit. Trans-Mars injections can be either a single maneuver burn, such as used by the NASA MAVEN orbiter, or a series of perigee kicks. Earths orbit Geocentric orbit Heliocentrism Astrodynamics Low-energy transfer List of artificial objects in heliocentric orbit List of orbits

6.
Geocentric orbit
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A geocentric orbit or Earth orbit involves any object orbiting the Earth, such as the Moon or artificial satellites. In 1997 NASA estimated there were approximately 2,465 artificial satellite orbiting the Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. Over 16,291 previously launched objects have decayed into the Earths atmosphere, altitude as used here, the height of an object above the average surface of the Earths oceans. Analemma a term in astronomy used to describe the plot of the positions of the Sun on the celestial sphere throughout one year, apogee is the farthest point that a satellite or celestial body can go from Earth, at which the orbital velocity will be at its minimum. Eccentricity a measure of how much an orbit deviates from a perfect circle, eccentricity is strictly defined for all circular and elliptical orbits, and parabolic and hyperbolic trajectories. Equatorial plane as used here, an imaginary plane extending from the equator on the Earth to the celestial sphere, escape velocity as used here, the minimum velocity an object without propulsion needs to have to move away indefinitely from the Earth. An object at this velocity will enter a parabolic trajectory, above this velocity it will enter a hyperbolic trajectory, impulse the integral of a force over the time during which it acts. Inclination the angle between a plane and another plane or axis. In the sense discussed here the reference plane is the Earths equatorial plane, orbital characteristics the six parameters of the Keplerian elements needed to specify that orbit uniquely. Orbital period as defined here, time it takes a satellite to make one orbit around the Earth. Perigee is the nearest approach point of a satellite or celestial body from Earth, sidereal day the time it takes for a celestial object to rotate 360°. For the Earth this is,23 hours,56 minutes,4.091 seconds, solar time as used here, the local time as measured by a sundial. Velocity an objects speed in a particular direction, since velocity is defined as a vector, both speed and direction are required to define it. The following is a list of different geocentric orbit classifications, Low Earth orbit - Geocentric orbits ranging in altitude from 160 kilometers to 2,000 kilometres above mean sea level. At 160 km, one revolution takes approximately 90 minutes, medium Earth orbit - Geocentric orbits with altitudes at apogee ranging between 2,000 kilometres and that of the geosynchronous orbit at 35,786 kilometres. Geosynchronous orbit - Geocentric circular orbit with an altitude of 35,786 kilometres, the period of the orbit equals one sidereal day, coinciding with the rotation period of the Earth. The speed is approximately 3,000 metres per second, high Earth orbit - Geocentric orbits with altitudes at apogee higher than that of the geosynchronous orbit. A special case of high Earth orbit is the elliptical orbit

7.
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

8.
Astrodynamics
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Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of objects is usually calculated from Newtons laws of motion. It is a discipline within space mission design and control. General relativity is an exact theory than Newtons laws for calculating orbits. Until the rise of space travel in the century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik, the field was termed space dynamics, the fundamental techniques, such as those used to solve the Keplerian problem, are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared, johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of motion in his 1687 book. The following rules of thumb are useful for situations approximated by classical mechanics under the assumptions of astrodynamics outlined below the rules. The specific example discussed is of a satellite orbiting a planet, Keplers laws of planetary motion, Orbits are elliptical, with the heavier body at one focus of the ellipse. Special case of this is an orbit with the planet at the center. A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured, the square of a satellites orbital period is proportional to the cube of its average distance from the planet. Without applying force, the period and shape of the satellites orbit wont change, a satellite in a low orbit moves more quickly with respect to the surface of the planet than a satellite in a higher orbit, due to the stronger gravitational attraction closer to the planet. If thrust is applied at one point in the satellites orbit, it will return to that same point on each subsequent orbit. Thus one cannot move from one orbit to another with only one brief application of thrust. Thrust applied in the direction of the satellites motion creates an elliptical orbit with an apoapse 180 degrees away from the firing point, the consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the circular orbit and wish to dock, unless they are very close. This will change the shape of its orbit, causing it to gain altitude and actually slow down relative to the leading craft, the space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods requiring hours or even days to complete