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Hohmann Transfer
In orbital mechanics, the Hohmann transfer orbit
Hohmann transfer orbit
(/ˈhoʊmən/) is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. In general a Hohmann transfer orbit uses the lowest possible amount of energy in traveling between two objects orbiting at these radii, and so is used to send the maximum amount of mission payload with the fixed amount of energy that can be imparted by a particular rocket. Non-Hohmann transfer paths may have other advantages for a particular mission such as shorter transfer times, but will necessarily require a reduction in payload mass and/or use of a more powerful rocket.[1][2][3][4] A Hohmann transfer requires that the starting and destination points be at particular locations in their orbits relative to each other. Space missions using a Hohmann transfer must wait for this required alignment to occur, which opens a so-called launch window
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Pluto
Pluto
Pluto
(minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of bodies beyond Neptune. It was the first Kuiper belt
Kuiper belt
object to be discovered. Pluto
Pluto
was discovered by Clyde Tombaugh
Clyde Tombaugh
in 1930 and was originally considered to be the ninth planet from the Sun. After 1992, its status as a planet was questioned following the discovery of several objects of similar size in the Kuiper belt. In 2005, Eris, a dwarf planet in the scattered disc which is 27% more massive than Pluto, was discovered. This led the International Astronomical Union
International Astronomical Union
(IAU) to define the term "planet" formally in 2006, during their 26th General Assembly
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Germany
Coordinates: 51°N 9°E / 51°N 9°E / 51; 9Federal Republic
Republic
of Germany Bundesrepublik Deutschland (German)[a]FlagCoat of armsMotto:  "Einigkeit und Recht und Freiheit" (de facto) "Unity and Justice and Freedom"Anthem: "Deutschlandlied" (third verse only)[b] "Song of Germany"Location of  Germany  (dark green) – in Europe  (green & dark grey) – in the European Union  (green)Location of
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Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at  A072097). The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and the radian is now considered an SI derived unit.[1] Separately, the SI unit of solid angle measurement is the steradian. The radian is most commonly represented by the symbol rad.[2] An alternative symbol is c, the superscript letter c (for "circular measure"), the letter r, or a superscript R,[3] but these symbols are infrequently used as it can be easily mistaken for a degree symbol (°) or a radius (r)
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Sun
The Sun
Sun
is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma,[14][15] with internal convective motion that generates a magnetic field via a dynamo process.[16] It is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, i.e. 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99.86% of the total mass of the Solar System.[17] About three quarters of the Sun's mass consists of hydrogen (~73%); the rest is mostly helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron.[18] The Sun
Sun
is a G-type main-sequence star
G-type main-sequence star
(G2V) based on its spectral class. As such, it is informally referred to as a yellow dwarf
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Gravity Of Mars
The gravity of Mars
Mars
is a natural phenomenon by which all things with mass around Mars
Mars
are brought towards it. It is weaker than Earth's gravity owing to the planet's smaller mass
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Vis-viva Equation
In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight. Vis viva
Vis viva
(Latin for "living force") is a term from the history of mechanics, and it survives in this sole context
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Moon
The Moon
The Moon
is an astronomical body that orbits planet Earth, being Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, and the largest among planetary satellites relative to the size of the planet that it orbits (its primary). Following Jupiter's satellite Io, the Moon
Moon
is the second-densest satellite in the Solar System
Solar System
among those whose densities are known. The Moon
The Moon
is thought to have formed about 4.51 billion years ago, not long after Earth
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Potential Energy
U = m · g · h (gravitational) U = ½ · k · x2 U = ½ · C · V2 (electric) U = -m · B (magnetic)Part of a series of articles aboutClassical mechanics F → = m a → displaystyle vec F =m vec a Second law of motionHistory TimelineBranchesApplied Celestial Continuum Dynamics Kinematics Kinetics Statics StatisticalFundamentalsAcceleration Angular momentum Couple D'Alembert's principle Energykinetic potentialForce Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia MassMechanical power Mechanical workMoment Momentum Space Speed Time Torque Velocity Virtual workFormulationsNewton's laws of motionAnalytical mechanicsLagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of m
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Kinetic Energy
Ek = ½mv2 Ek = Et+ErPart of a series of articles aboutClassical mechanics F → = m a → displaystyle vec F =m vec a Second law of motionHistory TimelineBranchesApplied Celestial Continuum Dynamics Kinematics Kinetics Statics StatisticalFundamentalsAcceleration Angular momentum Couple D'Alembert's principle Energykinetic potentialForce Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia MassMechanical power Mechanical workMoment Momentum Space Speed Time Torque Velocity Virtual workFormulationsNewton's laws of motionAnalytical mechanicsLagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanicsCore topic
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Impulse Function
In mathematics, the Dirac delta function, or δ function, is a generalized function, or distribution that was historically introduced by the physicist Paul Dirac
Paul Dirac
for modelling the density of an idealized point mass or point charge, as a function that is equal to zero everywhere except for zero and whose integral over the entire real line is equal to one.[1][2][3] As there is no function that has these properties, the computations that were done by the theoretical physicists appeared to mathematicians as nonsense, until the introduction of distributions by Laurent Schwartz, for formalizing and validating mathematically these computations
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Astronomical Unit
The astronomical unit (symbol: au,[1][2][3] ua,[4] or AU) is a unit of length, roughly the distance from Earth
Earth
to the Sun. However, that distance varies as Earth
Earth
orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, it was defined exactly as 7011149597870700000♠149597870700 metres or about 150 million kilometres (93 million miles) since 2012.[5] The astronomical unit is used primarily for measuring distances within the Solar System
Solar System
or around other stars
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Kurd Lasswitz
Kurd Lasswitz (German: Kurd Laßwitz, IPA: [ˈkʊʁt ˈlasvɪt͡s]; 20 April 1848 – 17 October 1910) was a German author, scientist, and philosopher. He has been called "the father of German science fiction".[1] He sometimes used the pseudonym Velatus.Contents1 Biography 2 Works 3 References 4 External linksBiography[edit] Lasswitz studied mathematics and physics at the University of Breslau and the University of Berlin, and earned his doctorate in 1873. He spent most of his career as a teacher at the Gymnasium Ernestinum in Gotha
Gotha
(1876–1908).[2]:87–88 Works[edit] His first published science fiction story was Bis zum Nullpunkt des Seins ("To the Zero Point of Existence", 1871), depicting life in 2371, but he earned his reputation with his 1897 novel Auf zwei Planeten, which describes an encounter between humans and a Martian civilization that is older and more advanced
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Two Planets
Two Planets (German: Auf zwei Planeten, lit. On Two Planets, 1897) is an influential science fiction novel postulating intelligent life on Mars
Mars
by Kurd Lasswitz. It was first published in hardcover by Felber in two volumes in 1897; there have been many editions since, including abridgements by the author's son Erich Lasswitz (Cassianeum, 1948) and Burckhardt Kiegeland and Martin Molitor (Verlag Heinrich Scheffler, 1969). The 1948 abridgement, with "incidental parts" of the text taken from the 1969 version, was the basis of the first translation into English by Hans H. Rudnick, published in hardcover by Southern Illinois University Press in 1971
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Venus
Venus
Venus
is the second planet from the Sun, orbiting it every 224.7 Earth days.[12] It has the longest rotation period (243 days) of any planet in the Solar System
Solar System
and rotates in the opposite direction to most other planets (meaning the Sun
Sun
would rise in the west and set in the east).[13] It does not have any natural satellites. It is named after the Roman goddess of love and beauty
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Earth
Earth
Earth
is the third planet from the Sun
Sun
and the only object in the Universe
Universe
known to harbor life. According to radiometric dating and other sources of evidence, Earth
Earth
formed over 4.5 billion years ago.[24][25][26] Earth's gravity interacts with other objects in space, especially the Sun
Sun
and the Moon, Earth's only natural satellite. Earth
Earth
revolves around the Sun
Sun
in 365.26 days, a period known as an Earth
Earth
year
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