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Hohmann Transfer Orbit
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or another solar planet or asteroid. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target. The Hohmann maneuver often uses the lowest possible amount of impulse (which consumes a proportional amount of delta-v, and hence propellant) to accomplish the transfer, but requires a relatively longer travel time than higher-impulse transfers. In some cases where one orbit is much larger than the other, a bi-elliptic transfer can use ...
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Hohmann Transfer Orbit
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or another solar planet or asteroid. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target. The Hohmann maneuver often uses the lowest possible amount of impulse (which consumes a proportional amount of delta-v, and hence propellant) to accomplish the transfer, but requires a relatively longer travel time than higher-impulse transfers. In some cases where one orbit is much larger than the other, a bi-elliptic transfer can use ...
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Walter Hohmann
Walter Hohmann (; ; 18 March 1880 – 11 March 1945) was a German engineer who made an important contribution to the understanding of orbital dynamics. In a book published in 1925, Hohmann demonstrated a fuel-efficient path to move a spacecraft between two different orbits, now called a Hohmann transfer orbit. He received his Ph.D. from the RWTH Aachen University in 1920. Biography Hohmann was born in Hardheim, the son of a doctor. As a boy, he lived with his family in Port Elizabeth, South Africa for a time, before returning to Germany. He studied civil engineering at the Technical University of Munich, graduating in 1904. He then worked for the municipal councils of Vienna, Hanover and Breslau (now Wrocław) before settling in Essen, where he eventually held the post of chief architect. Hohmann became interested in space as a young boy when his father would show him the southern constellations. As soon as he read the science fiction works of French author Jules Verne an ...
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Apogee Kick Motor
An apogee kick motor (AKM) is a rocket motor that is regularly employed on artificial satellites to provide the final impulse to change the trajectory from the transfer orbit into its final (most commonly circular) orbit. For a satellite launched from the Earth, the rocket firing is done at the highest point of the transfer orbit, known as the apogee. An apogee kick motor is used, for example, for satellites launched into a geostationary orbit. As the vast majority of geostationary satellite launches are carried out from spaceports at a significant distance away from Earth's equator, the carrier rocket often only launches the satellite into an orbit with a non-zero inclination approximately equal to the latitude of the launch site. This orbit is commonly known as a "geostationary transfer orbit" or a "geosynchronous transfer orbit". The satellite must then provide thrust to bring forth the needed delta v to reach a geostationary orbit. This is typically done with a fixed on ...
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Impulse Function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form acting on ...
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Reversibility Of Orbits
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 these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near ...
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Hohmann Transfer Orbit2
Hohmann may refer to: * Hohmann (surname) (article includes list of persons named Hohmann) * Hohmann transfer orbit, in orbital mechanics * Hohmann (crater), a lunar crater * 9661 Hohmann (1996 FU13), an asteroid See also * Hohman * Homann Homann is a surname. Notable people with the surname include: * Heinrich Homann Heinrich Homann (6 March 1911 – 4 May 1994) was a communist politician and former Wehrmacht officer who held a number of offices in the German Democratic Republi ... * Homan (other) {{disambiguation ...
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Apogee
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the primary body the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''. According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e. ...
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Elliptic Orbit
In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler's 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. Velocity Under standard assumptions, no other forces acting except two spherically symmetrical bodies m1 and m2, the orbital speed (v\,) of one bod ...
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Low-energy Transfer
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as between the moons of Jupiter. The drawback of such trajectories is that they take longer to complete than higher-energy (more-fuel) transfers, such as Hohmann transfer orbits. Low-energy transfers are also known as Weak Stability Boundary trajectories, and include ballistic capture trajectories. Low-energy transfers follow special pathways in space, sometimes referred to as the Interplanetary Transport Network. Following these pathways allows for long distances to be traversed for little change in velocity, or . Example missions Missions that have used low-energy transfers include: * '' Hiten'', from JAXA * '' SMART-1'', from ESA * ''Genesis'', from NASA.
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Oberth Effect
In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver is a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well. The gain in efficiency is explained by the Oberth effect, wherein the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds. In practical terms, this means that the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity (and so, its kinetic energy) is greatest. In some cases, it is even worth spending fuel on slowing the spacecraft into a gravity well to take advantage of the efficiencies of the Oberth effect. The maneuver and effect are named after the person who first described them in ...
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Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin atmosphere (less than 1% that of Earth's), and has a crust primarily composed of elements similar to Earth's crust, as well as a core made of iron and nickel. Mars has surface features such as impact craters, valleys, dunes and polar ice caps. It has two small and irregularly shaped moons, Phobos and Deimos. Some of the most notable surface features on Mars include Olympus Mons, the largest volcano and highest known mountain in the Solar System and Valles Marineris, one of the largest canyons in the Solar System. The Borealis basin in the Northern Hemisphere covers approximately 40% of the planet and may be a large impact feature. Days and seasons on Mars are comparable to those of Earth, as the planets have a similar rotation period ...
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Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface is made up of the ocean, dwarfing Earth's polar ice, lakes, and rivers. The remaining 29% of Earth's surface is land, consisting of continents and islands. Earth's surface layer is formed of several slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's liquid outer core generates the magnetic field that shapes the magnetosphere of the Earth, deflecting destructive solar winds. The atmosphere of the Earth consists mostly of nitrogen and oxygen. Greenhouse gases in the atmosphere like carbon dioxide (CO2) trap a part of the energy from the Sun close to the surface. Water vapor is widely present in the atmosphere and forms clouds that cover most of the planet. More s ...
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