1.
Molniya orbit
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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

2.
Elliptic orbit
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In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1, this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0, in a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1, in a gravitational two-body problem with negative energy both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit, examples of elliptic orbits include, Hohmann transfer orbit, Molniya orbit and tundra orbit. A is the length of the semi-major axis, the velocity equation for a hyperbolic trajectory has either +1 a, or it is the same with the convention that in that case a is negative. Conclusions, For a given semi-major axis the orbital energy is independent of the eccentricity. ν is the true anomaly. The angular momentum is related to the cross product of position and velocity. Here ϕ is defined as the angle which differs by 90 degrees from this and this set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit, the two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit, another set of six parameters that are commonly used are the orbital elements. In the Solar System, planets, asteroids, most comets, the following chart of the perihelion and aphelion of the planets, dwarf planets and Halleys Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity, note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halleys Comet and Eris. A radial trajectory can be a line segment, which is a degenerate ellipse with semi-minor axis =0. Although the eccentricity is 1, this is not a parabolic orbit, most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed and it is an open orbit corresponding to the part of the degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. In the case of point masses one full orbit is possible, the velocities at the start and end are infinite in opposite directions and the potential energy is equal to minus infinity. The radial elliptic trajectory is the solution of a problem with at some instant zero speed

3.
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

4.
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

5.
Molniya (satellite)
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Molniya were military communications satellites used by the Soviet Union. The satellites were placed into highly elliptical orbits known as Molniya orbits, characterised by an inclination of +63.4 degrees. Such orbits allowed them to remain visible to sites in polar regions for extended periods, the Molniya program was authorized by a government decree in late 1960. The first launch took place on June 4,1964 and ended in failure when the 8K78 booster core stage lost thrust 287 seconds into launch due to a servo motor. The next attempt was on August 22 and reached orbit successfully, publicly referred to as Kosmos 41, it nonetheless operated for nine months. The first operational satellite, Molniya 1-01, was launched on April 23,1965. Since October 1967, Molniya satellites have used by Russia to broadcast their national Orbita television network. Molniya-1 spacecraft Molniya, A short history of development Molniya constellation Molniya 1-4

6.
Tundra orbit
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A Tundra orbit is a highly elliptical geosynchronous orbit with a high inclination and an orbital period of one sidereal day. A satellite placed in this orbit spends most of its time over an area of the Earth. The ground track of a satellite in an orbit is a closed figure eight. These orbits are similar to Molniya orbits, which have the same inclination. The only current known user of Tundra orbits is the EKS satellite, until 2016, Sirius Satellite Radio, now part of Sirius XM Holdings operated a constellation of three satellites in Tundra orbits for satellite radio. The RAAN and mean anomaly of each satellite was offset by 120° so that when one satellite moved out of position, the three satellites were launched in 2000 and moved into circular disposal orbits in 2016, Sirius XM now broadcasts only from geostationary satellites. Tundra and Molniya orbits are used to high latitude users with higher elevation angles than a geostationary orbit. An argument of perigee of 270° places apogee at the northernmost point of the orbit, an argument of perigee of 90° would likewise serve the high southern latitudes. An argument of perigee of 0° or 180° would cause the satellite to dwell over the equator, the Tundra and Molniya orbits use a sin−1 √4/5 ≈63. 4° inclination to null the secular perturbation of the argument of perigee caused by the Earths equatorial bulge. With any inclination other than 63. 4° or its supplement,116. 6°, the argument of perigee would change steadily over time, and apogee would occur either before or after the highest latitude is reached

7.
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

8.
Altitude (astronomy)
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The horizontal coordinate system is a celestial coordinate system that uses the observers local horizon as the fundamental plane. It is expressed in terms of angle and azimuth. This coordinate system divides the sky into the upper hemisphere where objects are visible, the great circle separating the hemispheres is called the celestial horizon. The celestial horizon is defined as the circle on the celestial sphere whose plane is normal to the local gravity vector. In practice, the horizon can be defined as the tangent to a still liquid surface such as a pool of mercury. The pole of the upper hemisphere is called the zenith, the pole of the lower hemisphere is called the nadir. There are two independent horizontal angular coordinates, Altitude, sometimes referred to as elevation, is the angle between the object and the local horizon. For visible objects it is an angle between 0 degrees to 90 degrees, alternatively, zenith distance may be used instead of altitude. More details on the computation of azimuth and zenith angle can be found at Solar azimuth angle, the horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object in the sky changes with time, horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an objects altitude is 0°, it is on the horizon, if at that moment its altitude is increasing, it is rising, but if its altitude is decreasing, it is setting. However, all objects on the sphere are subject to diurnal motion. One can determine whether altitude is increasing or decreasing by instead considering the azimuth of the celestial object, if the azimuth is between 180° and 360°, it is setting. There are the special cases, As seen from the north pole all directions are south. Viewed from either pole, a star has constant altitude, the Sun, Moon, and planets can rise or set over the span of a year when viewed from the poles because their declinations are constantly changing. As seen from the equator, objects on the poles stay at fixed points on the horizon. Note that the above considerations are strictly speaking true for the horizon only. That is, the horizon as it would appear for an observer at sea level on a perfectly smooth Earth without an atmosphere

9.
Communications satellite
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Communications satellites are used for television, telephone, radio, internet, and military applications. There are over 2,000 communications satellites in Earth’s orbit, Wireless communication uses electromagnetic waves to carry signals. These waves require line-of-sight, and are thus obstructed by the curvature of the Earth, the purpose of communications satellites is to relay the signal around the curve of the Earth allowing communication between widely separated points. Communications satellites use a range of radio and microwave frequencies. To avoid signal interference, international organizations have regulations for which frequency ranges or bands certain organizations are allowed to use and this allocation of bands minimizes the risk of signal interference. The concept of the communications satellite was first proposed by Arthur C. Clarke, building on work by Konstantin Tsiolkovsky and on the 1929 work by Herman Potočnik Das Problem der Befahrung des Weltraums — der Raketen-motor, in October 1945 Clarke published an article titled Extraterrestrial Relays in the British magazine Wireless World. The article described the fundamentals behind the deployment of artificial satellites in geostationary orbits for the purpose of relaying radio signals, thus, Arthur C. Clarke is often quoted as being the inventor of the communications satellite and the term Clarke Belt employed as a description of the orbit. Decades later a project named Communication Moon Relay was a project carried out by the United States Navy. Its objective was to develop a secure and reliable method of communication by using the Moon as a passive reflector. The first artificial Earth satellite was Sputnik 1, put into orbit by the Soviet Union on October 4,1957, it was equipped with an on-board radio-transmitter that worked on two frequencies,20.005 and 40.002 MHz. Sputnik 1 was launched as a step in the exploration of space, while incredibly important it was not placed in orbit for the purpose of sending data from one point on earth to another. And it was the first artificial satellite in the leading to todays satellite communications. The first artificial satellite used solely to further advances in communications was a balloon named Echo 1. Echo 1 was the worlds first artificial communications satellite capable of relaying signals to other points on Earth and it soared 1,600 kilometres above the planet after its Aug.12,1960 launch, yet relied on humanitys oldest flight technology — ballooning. Launched by NASA, Echo 1 was a 30-metre aluminized PET film balloon served as a passive reflector for radio communications. The worlds first inflatable satellite — or satelloon, as they were informally known — helped lay the foundation of todays satellite communications, the idea behind a communications satellite is simple, Send data up into space and beam it back down to another spot on the globe. Echo 1 accomplished this by serving as an enormous mirror,10 stories tall