1.
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

2.
Apsidal precession
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In celestial mechanics, perihelion precession, apsidal precession or orbital precession is the precession of the orbit of a celestial body. More precisely, it is the rotation of the line joining the apsides of an orbit. Perihelion is the closest point to the Sun, the apsidal precession is the first derivative of the argument of periapsis, one of the six primary orbital elements of an orbit. The precession of the apsides was discovered in the eleventh century by al-Zarqālī. ωtotal = ωGeneral Relativity + ωquadrupole + ωtide + ωperturbations For Mercury, from classical mechanics, if stars and planets are considered to be purely spherical masses, then they will obey a simple 1/r2 force law and hence execute closed elliptical orbits. The good resulting approximation of the bulge is useful for understanding the interiors of such planets. For the shortest-period planets, the interior induces precession of a few degrees per year. Newton derived an early theorem which attempted to explain apsidal precession and this theorem is historically notable, but it was never widely used and it proposed forces which have been found not to exist, making the theorem invalid. This theorem of revolving orbits remained largely unknown and undeveloped for over three centuries until 1995, however, his theorem did not account for the apsidal precession of the Moon without giving up the inverse-square law of Newtons law of universal gravitation. Additionally, the rate of apsidal precession calculated via Newtons theorem of revolving orbits is not as accurate as it is for newer methods such as by perturbation theory. An apsidal precession of the planet Mercury was noted by Urbain Le Verrier in the mid-19th century and accounted for by Einsteins general theory of relativity. In the case of Mercury, half of the axis is circa 5. 79×1010 m, the eccentricity of its orbit is 0.206. From these and the speed of light, it can be calculated that the apsidial precession during one period of revolution is ϵ =5. 028×10−7 radians. Because of apsidal precession the Earths argument of periapsis slowly increases, the Earths polar axis, and hence the solstices and equinoxes, precess with a period of about 26000 years in relation to the fixed stars. This interaction between the anomalistic and tropical cycle is important in the climate variations on Earth, called the Milankovitch cycles. An equivalent is known on Mars. The figure illustrates the effects of precession on the northern hemisphere seasons, notice that the areas swept during a specific season changes through time

3.
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

4.
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

5.
Attitude control
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Attitude control is controlling the orientation of an object with respect to an inertial frame of reference or another entity. The integrated field that studies the combination of sensors, actuators and algorithms is called Guidance, Navigation, a spacecrafts attitude must typically be stabilized and controlled for a variety of reasons. Propulsion system thrusters are fired only occasionally to make desired changes in spin rate, if desired, the spinning may be stopped through the use of thrusters or by yo-yo de-spin. The Pioneer 10 and Pioneer 11 probes in the solar system are examples of spin-stabilized spacecraft. Three-axis stabilization is a method of spacecraft attitude control in which the spacecraft is held fixed in the desired orientation without any rotation. One method is to use thrusters to continually nudge the spacecraft back. Thrusters may also be referred to as control systems, or reaction control systems. The space probes Voyager 1 and Voyager 2 employ this method, another method for achieving three-axis stabilization is to use electrically powered reaction wheels, also called momentum wheels, which are mounted on three orthogonal axes aboard the spacecraft. They provide a means to trade angular momentum back and forth between spacecraft and wheels, to rotate the vehicle on a given axis, the reaction wheel on that axis is accelerated in the opposite direction. To rotate the back, the wheel is slowed. This is done during maneuvers called momentum desaturation or momentum unload maneuvers, most spacecraft use a system of thrusters to apply the torque for desaturation maneuvers. A different approach was used by the Hubble Space Telescope, which had sensitive optics that could be contaminated by thruster exhaust, there are advantages and disadvantages to both spin stabilization and three-axis stabilization. Many spacecraft have components that require articulation, Voyager and Galileo, for example, were designed with scan platforms for pointing optical instruments at their targets largely independently of spacecraft orientation. Many spacecraft, such as Mars orbiters, have solar panels that must track the Sun so they can provide power to the spacecraft. Cassinis main engine nozzles are steerable, knowing where to point a solar panel, or scan platform, or a nozzle — that is, how to articulate it—requires knowledge of the spacecrafts attitude. Because AACS keeps track of the attitude, the Suns location. It logically falls to one subsystem, then, to manage both attitude and articulation, the name AACS may even be carried over to a spacecraft even if it has no appendages to articulate. Many sensors generate outputs that reflect the rate of change in attitude and these require a known initial attitude, or external information to use them to determine attitude

6.
Box orbit
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In stellar dynamics a box orbit refers to a particular type of orbit that can be seen in triaxial systems, i. e. systems that do not possess a symmetry around any of its axes. They contrast with the orbits that are observed in spherically symmetric or axisymmetric systems. In a box orbit, the star oscillates independently along the three different axes as it moves through the system, as a result of this motion, it fills in a box-shaped region of space. Unlike loop orbits, the stars on box orbits can come close to the center of the system. As a special case, if the frequencies of oscillation in different directions are commensurate, such orbits are sometimes called boxlets. Horseshoe orbit Lissajous curve List of orbits