1.
Orbit
–
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.
Apsis
–
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

3.
Geosynchronous orbit
–
A geosynchronous orbit is an orbit about the Earth of a satellite with an orbital period that matches the rotation of the Earth on its axis of approximately 23 hours 56 minutes and 4 seconds. Over the course of a day, the position in the sky traces out a path, typically in a figure-8 form, whose precise characteristics depend on the orbits inclination. Satellites are typically launched in an eastward direction, a special case of geosynchronous orbit is the geostationary orbit, which is a circular geosynchronous orbit at zero inclination. A satellite in a geostationary orbit appears stationary, always at the point in the sky. Popularly or loosely, the term geosynchronous may be used to mean geostationary, specifically, geosynchronous Earth orbit may be a synonym for geosynchronous equatorial orbit, or geostationary Earth orbit. A semi-synchronous orbit has a period of ½ sidereal day. Relative to the Earths surface it has twice this period, examples include the Molniya orbit and the orbits of the satellites in the Global Positioning System. Circular Earth geosynchronous orbits have a radius of 42,164 km, all Earth geosynchronous orbits, whether circular or elliptical, have the same semi-major axis.4418 km3/s2. In the special case of an orbit, the ground track of a satellite is a single point on the equator. A geostationary equatorial orbit is a geosynchronous orbit in the plane of the Earths equator with a radius of approximately 42,164 km. A satellite in such an orbit is at an altitude of approximately 35,786 km above sea level. It maintains the position relative to the Earths surface. The theoretical basis for this phenomenon of the sky goes back to Newtons theory of motion. In that theory, the existence of a satellite is made possible because the Earth rotates. Such orbits are useful for telecommunications satellites, a perfectly stable geostationary orbit is an ideal that can only be approximated. Elliptical geosynchronous orbits can be and are designed for satellites in order to keep the satellite within view of its assigned ground stations or receivers. A satellite in a geosynchronous orbit appears to oscillate in the sky from the viewpoint of a ground station. Satellites in highly elliptical orbits must be tracked by ground stations

4.
Horseshoe orbit
–
A horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The orbital period of the body is very nearly the same as for the larger body. The loop is not closed but will drift forward or backward slightly each time, when the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, asteroids in horseshoe orbits with respect to Earth include 54509 YORP,2002 AA29,2010 SO16,2015 SO2 and possibly 2001 GO2. A broader definition includes 3753 Cruithne, which can be said to be in a compound and/or transition orbit, saturns moons Epimetheus and Janus occupy horseshoe orbits with respect to each other. The following explanation relates to an asteroid which is in such an orbit around the Sun, the asteroid is in almost the same solar orbit as Earth. Both take approximately one year to orbit the Sun and it is also necessary to grasp two rules of orbit dynamics, A body closer to the Sun completes an orbit more quickly than a body further away. If a body accelerates along its orbit, its orbit moves outwards from the Sun, if it decelerates, the orbital radius decreases. The horseshoe orbit arises because the attraction of the Earth changes the shape of the elliptical orbit of the asteroid. The shape changes are small but result in significant changes relative to the Earth. The horseshoe becomes apparent only when mapping the movement of the relative to both the Sun and the Earth. The asteroid always orbits the Sun in the same direction, however, it goes through a cycle of catching up with the Earth and falling behind, so that its movement relative to both the Sun and the Earth traces a shape like the outline of a horseshoe. Starting at point A, on the ring between L5 and Earth, the satellite is orbiting faster than the Earth and is on its way toward passing between the Earth and the Sun. But Earths gravity exerts an outward accelerating force, pulling the satellite into an orbit which decreases its angular speed. When the satellite gets to point B, it is traveling at the speed as Earth. Earths gravity is still accelerating the satellite along the orbital path, eventually, at Point C, the satellite reaches a high and slow enough orbit such that it starts to lag behind Earth. It then spends the next century or more appearing to drift backwards around the orbit when viewed relative to the Earth and its orbit around the Sun still takes only slightly more than one Earth year. Given enough time, the Earth and the satellite will be on opposite sides of the Sun, eventually the satellite comes around to point D where Earths gravity is now reducing the satellites orbital velocity

5.
Orbit of the Moon
–
Not to be confused with Lunar orbit. The Moon orbits Earth in the direction and completes one revolution relative to the stars in approximately 27.323 days. Earth and the Moon orbit about their barycentre, which lies about 4,600 km from Earths center, on average, the Moon is at a distance of about 385,000 km from Earths centre, which corresponds to about 60 Earth radii. With a mean velocity of 1.022 km/s, the Moon appears to move relative to the stars each hour by an amount roughly equal to its angular diameter. The Moon differs from most satellites of planets in that its orbit is close to the plane of the ecliptic. The plane of the orbit is inclined to the ecliptic by about 5°. The properties of the orbit described in this section are approximations, the Moons orbit around Earth has many irregularities, whose study has a long history. The orbit of the Moon is distinctly elliptical, with an eccentricity of 0.0549. The non-circular form of the lunar orbit causes variations in the Moons angular speed and apparent size as it moves towards, the mean angular movement relative to an imaginary observer at the barycentre is 13. 176° per day to the east. The Moons elongation is its angular distance east of the Sun at any time, at new moon, it is zero and the Moon is said to be in conjunction. At full moon, the elongation is 180° and it is said to be in opposition, in both cases, the Moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270°, the Moon is said to be in quadrature, the orientation of the orbit is not fixed in space, but rotates over time. This orbital precession is also called apsidal precession and is the rotation of the Moons orbit within the orbital plane, the Moons apsidal precession is distinct from, and should not be confused with its axial precession. The mean inclination of the orbit to the ecliptic plane is 5. 145°. The rotational axis of the Moon is also not perpendicular to its plane, so the lunar equator is not in the plane of its orbit. Therefore, the angle between the ecliptic and the equator is always 1. 543°, even though the rotational axis of the Moon is not fixed with respect to the stars. The period from moonrise to moonrise at the poles is quite close to the sidereal period, when the sun is the furthest below the horizon, the moon will be full when it is at its highest point. The nodes are points at which the Moons orbit crosses the ecliptic, the Moon crosses the same node every 27.2122 days, an interval called the draconic or draconitic month

6.
Molniya orbit
–
A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of −90 degrees and an orbital period of one half of a sidereal day. Molniya orbits are named after a series of Soviet/Russian Molniya communications satellites which have been using this type of orbit since the mid-1960s.4 degrees north, to get a continuous high elevation coverage of the Northern Hemisphere, at least three Molniya spacecraft are needed. The reason that the inclination should have the value 63. 4° is that then the argument of perigee is not perturbed by the J2 term of the field of the Earth. Much of the area of the former Soviet Union, and Russia in particular, is located at high latitudes, to broadcast to these latitudes from a geostationary orbit would require considerable power due to the low elevation angles. A satellite in a Molniya orbit is better suited to communications in these regions because it looks directly down on them, an additional advantage is that considerably less launch energy is needed to place a spacecraft into a Molniya orbit than into a geostationary orbit. It is necessary to have at least three spacecraft if permanent high elevation coverage is needed for an area like the whole of Russia where some parts are as far south as 45° N. If three spacecraft are used, each spacecraft is active for periods of eight hours per orbit centered at apogee as illustrated in figure 9. The Earth completes half a rotation in 12 hours, so the apogees of successive Molniya orbits will alternate between one half of the hemisphere and the other half. For example if the apogee longitudes are 90° E and 90° W, said next spacecraft has the visibility displayed in figure 3 and the switch-over can take place. Note that the two spacecraft at the time of switch-over are separated about 1500 km, so that the stations only have to move the antennas a few degrees to acquire the new spacecraft. To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63. 4° and that this is the case follows from equation of the article Orbital perturbation analysis as the factor then is zero. The reason why the orbital period shall be half a day is that the geometry relative to the ground stations should repeat every 24 hours. In fact, the precise ideal orbital period resulting in a ground track repeating every 24 hours is not precisely half a sidereal day, but rather half a synodic day. For a Molniya orbit, the inclination is selected such that Δ ω as given by the formula above is zero but Δ Ω, as given by the other equation, will be −0. 0742° per orbit. The rotational period of the Earth relative to the node will therefore be only 86,129 seconds,35 seconds less than the day which is 86,164 seconds. The primary use of the Molniya orbit was for the satellite series of the same name. After two launch failures in 1964, the first successful satellite to use this orbit was Molniya 1-01 launched on April 23,1965. The early Molniya-1 satellites were used for military communications starting in 1968