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Construction in representation theory
In mathematics, the orbit method (also known as the Kirillov theory, the method of coadjoint orbits and by a few similar names) establishes a correspondence
Orbit_method
Technique in quantum chemistry
combination of atomic orbitals (LCAO) is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry
Linear combination of atomic orbitals
Linear_combination_of_atomic_orbitals
Taoist energy-cultivation technique
Sixteen-Character Method for Longevity” (長生一十六字妙訣). The Qing-dynasty physician You Cheng (尤乘) later used the term “Microcosmic Orbit Method” (小週天法) in his
Microcosmic_orbit
Chemical theory
In chemistry, frontier molecular orbital theory is an application of molecular orbital theory describing HOMO–LUMO interactions. In 1952, Kenichi Fukui
Frontier molecular orbital theory
Frontier_molecular_orbital_theory
Theory of molecular orbitals by Erich Hückel
The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear
Hückel_method
Curved path of an object around a point
mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Alternatively, it is known as an orbital revolution
Orbit
Russian mathematician
topological groups and Lie groups. In particular he introduced the orbit method into representation theory. He is an emeritus professor at the University
Alexandre_Kirillov
Estimation of orbits of objects
discovered. The basic methods were discovered in the 17th century and have been continuously refined. Observations are the raw data fed into orbit determination
Orbit_determination
Function describing an electron in an atom
In quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function describes
Atomic_orbital
, the Kirillov orbit method gives a heuristic method in representation theory. It connects the Fourier transforms of coadjoint orbits, which lie in the
Kirillov_character_formula
velocity method is that eccentricity of the planet's orbit can be measured directly. One of the main disadvantages of the radial-velocity method is that
Methods of detecting exoplanets
Methods_of_detecting_exoplanets
Field of classical mechanics concerned with the motion of spacecraft
a method for finding the orbit of a body following a parabolic path from three observations. This was used by Edmund Halley to establish the orbits of
Orbital_mechanics
Angle between a reference plane and the plane of an orbit
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital
Orbital_inclination
Process of modeling orbits
perturbation methods are often used to model the orbit in order to achieve better accuracy. The study of orbital motion and mathematical modeling of orbits began
Orbit_modeling
Function used in quantum chemistry
orbitals (STOs) or Slater-type functions (STFs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method
Slater-type_orbital
Orbit around the barycenter of the Sun
heliocentric orbit (also called circumsolar orbit) is an orbit around the Sun. The inner planets are mainly influenced by the Sun's gravity, and orbit points
Heliocentric_orbit
Computational method in Chemistry
The fragment molecular orbital method (FMO) is a computational method that can be used to calculate very large molecular systems with thousands of atoms
Fragment_molecular_orbital
Approximation method in quantum physics
spin-orbitals. By invoking the variational method, one can derive a set of N {\displaystyle N} coupled equations for the N {\displaystyle N} spin orbitals
Hartree–Fock_method
Way to determine a preliminary orbit from initial observations in astronomy
In orbital mechanics (a subfield of celestial mechanics), Gauss's method is used for preliminary orbit determination from at least three observations
Gauss's_method
Circular orbit above Earth's Equator and following the direction of Earth's rotation
A geostationary orbit, also referred to as a GEO or GSO, is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude above Earth's equator, 42
Geostationary_orbit
Elliptical orbit used to move a spacecraft from one circular orbit to another
slower method of transfer, but one that may be more efficient than a Hohmann transfer orbit Geostationary transfer orbit or geosynchronous transfer orbit is
Transfer_orbit
Model of electronic band structures of solids
located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding
Tight_binding
Recipe for constructing a quantum analog of a classical physical theory
of the theory was to understand and generalize Alexandre Kirillov's orbit method in representation theory. The geometric quantization procedure falls
Geometric_quantization
Classical approach to the many-body problem of astronomy
conic is known as the osculating orbit and its orbital elements at any particular time are what are sought by the methods of general perturbations. General
Perturbation_(astronomy)
remainder method (voting systems) Level-set method Linear combination of atomic orbitals molecular orbital method (molecular orbitals) Method of characteristics
List of mathematics-based methods
List_of_mathematics-based_methods
Method for describing the electronic structure of molecules using quantum mechanics
In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It
Molecular_orbital_theory
Method of colouring fractal images
In mathematics, an orbit trap is a method of colouring fractal images based upon how close an iterative function, used to create the fractal, approaches
Orbit_trap
Spacecraft end-of-life orbit
graveyard orbit, also called a junk orbit or disposal orbit, is an orbit that lies away from common operational orbits. One significant graveyard orbit is a
Graveyard_orbit
Method for approximating many-body systems
Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster
Coupled_cluster
Parameters that define a specific orbit
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems
Orbital_elements
coadjoint orbits. In the Kirillov method of orbits, representations of G {\displaystyle G} are constructed geometrically starting from the coadjoint orbits. In
Coadjoint_representation
Orbit keeping the satellite at a fixed longitude above the equator
A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours
Geosynchronous_orbit
Method in computational chemistry
out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely
Mulliken_population_analysis
American physical chemist (born 1966)
electron transfer (PCET), Enzymatic Processes, and the Nuclear-Electronic Orbital method. A part of this research engages in the study of the Kinetic isotope
Sharon_Hammes-Schiffer
First planet from the Sun
days) and sidereal day (58.65 Earth days) are in a 3:2 ratio, in a spin–orbit resonance. Consequently, one solar day (sunrise to sunrise) on Mercury lasts
Mercury_(planet)
American physicist and chemist (1896–1986)
responsible for the early development of molecular orbital theory, i.e. the elaboration of the molecular orbital method of computing the structure of molecules.
Robert_S._Mulliken
Method of launching rockets at altitude from a conventional horizontal-takeoff aircraft
Air-launch-to-orbit (ALTO) is the method of launching smaller rockets at altitude from a heavier conventional horizontal-takeoff aircraft, to carry satellites
Air-launch-to-orbit
Periodic, three-dimensional orbit
Halo orbit A halo orbit is a periodic, non-planar orbit associated with one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics
Halo_orbit
Interplay between observation, experiment, and theory in science
The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental
Scientific_method
Transfer orbit used to reach geosynchronous or geostationary orbit
transfer orbit (GTO) or geosynchronous transfer orbit is a highly elliptical type of geocentric orbit, usually with a perigee as low as low Earth orbit (LEO)
Geostationary_transfer_orbit
One of two foundational theories of quantum chemistry
orbital (MO) theory, that were developed to use the methods of quantum mechanics to describe chemical bonding. It focuses on how the atomic orbitals of
Valence_bond_theory
The Fenske–Hall method is a molecular orbital method in computational chemistry, usually applied to inorganic compounds. This method was developed in Richard
Fenske–Hall_method
Transfer manoeuvre between two orbits
astronautics, the Hohmann transfer orbit (/ˈhoʊmən/) is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around
Hohmann_transfer_orbit
Method for conducting round trip human flights to the Moon
Earth orbit rendezvous (EOR) is a method for conducting round trip human flights to the Moon, involving the use of space rendezvous to assemble, and possibly
Earth_orbit_rendezvous
Indirect method for finding extrasolar planets and brown dwarfs
sets of Keplerian orbital parameters. This analysis may be implemented using the Markov chain Monte Carlo (MCMC) method. The method has been applied to
Doppler_spectroscopy
American Professor of Chemistry
Wisconsin–Madison. Weinhold is best known for developing natural bond orbital methods and associated applications in physical and computational quantum chemistry
Frank_A._Weinhold
Time an astronomical object takes to complete one orbit around another object
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy
Orbital_period
Hypothetical Solar System planet
the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs)—bodies beyond Neptune that orbit the Sun at distances averaging
Planet_Nine
Relativistic interaction in quantum physics
In quantum mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin
Spin–orbit_interaction
Wave-like behavior of an electron in a molecule
molecular orbitals can be obtained from the "Linear combination of atomic orbitals molecular orbital method" ansatz. Here, the molecular orbitals are expressed
Molecular_orbital
of Mathematicians in Nice in 1970. In 1988 a conference entitled "The Orbit Method in Representation Theory" was held at the University of Copenhagen in
Lajos_Pukánszky
Quantum mechanical description of electronic structure
molecular orbital theory, whilst avoiding many of their weaknesses. For example, unlike the widely used Hartree–Fock molecular orbital method, Coulson–Fischer
Coulson–Fischer_theory
unitary representations of some classes of Lie groups by means of the orbit method as well as in harmonic analysis on Lie groups and mathematical physics
Polarization_(Lie_algebra)
Objects intentionally placed into orbit
artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication
Satellite
Proposed method of Moon landing
ascent is a method of landing a spacecraft on the Moon or another planetary surface directly, without first assembling the vehicle in Earth orbit, or carrying
Direct_ascent
French mathematician (born 1943)
Jussieu, and at the École normale supérieure. Duflo has worked on the orbit method of Alexander Kirillov. He introduced the Duflo isomorphism, an isomorphism
Michel_Duflo
Largest dwarf planet in the Solar System
ring of bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Sun. It is the largest
Pluto
Stabilization, by means of small system perturbations, of unstable periodic orbits
Ott–Grebogi–Yorke (OGY) method and Pyragas continuous control. Both methods require a previous determination of the unstable periodic orbits of the chaotic system
Control_of_chaos
Model for predicting molecular geometry
and Element 118. n = 2, 4.) Calculated by Two-component Spin-Orbit Methods. A Spin-Orbit Induced Isomer of (118)F4". Journal of Physical Chemistry A.
VSEPR_theory
Shape approximation
variational method. Many modern electronic structure methods employ the approximation. Among them APW method, the linear muffin-tin orbital method (LMTO) and
Muffin-tin_approximation
Propulsive maneuver used to arrive at the Moon
place the Hagoromo microsatellite in a lunar orbit. Following that, it explored a novel low delta-v TLI method with a 6-month transfer time (compared to
Trans-lunar_injection
Semiempirical quantum chemistry method
original Hückel method only considers pi orbitals, the extended method also includes the sigma orbitals. The extended Hückel method can be used for determining
Extended_Hückel_method
Gas giant planet orbiting Nu Octantis A
method. This planet is notable for its unusual orbit, which lies halfway between the orbit of the two stars in the Nu Octantis system. Such orbital configuration
Nu_Octantis_Ab
Planet outside of the Solar System
oriented orbit will be observed to transit the star is somewhat small. The Kepler telescope used this method. Radial velocity or Doppler method As a planet
Exoplanet
mathematics of chaotic dynamical systems, in the Pyragas method of stabilizing a periodic orbit, an appropriate continuous controlling signal is injected
Pyragas_method
Mathematical function
(LCAO) method for the representation of electron orbitals in molecules and numerous properties that depend on these. The use of Gaussian orbitals in electronic
Gaussian_orbital
Organic reaction in which a pi bond and sigma bond are interconverted
analysis through the frontier-orbital method: the sigma bond in the reactant will open in such a way that the resulting p-orbitals will have the same symmetry
Electrocyclic_reaction
Method of launching an object into outer space via a large gun or cannon
satellites into Earth's orbit (although after-launch propulsion of the satellite would be necessary to achieve a stable orbit), and could also launch
Space_gun
Academic journal
Self-consistent molecular-orbital methods. 12. Further extensions of Gaussian-type basis sets for use in molecular-orbital studies of organic molecules
The Journal of Chemical Physics
The_Journal_of_Chemical_Physics
of the Poincaré group Wigner–Eckart theorem Stone–von Neumann theorem Orbit method Kirillov character formula Weyl character formula Discrete series representation
List of representation theory topics
List_of_representation_theory_topics
closely related to the orbit method, which relates the irreducible representations of a nilpotent Lie group to its coadjoint orbits. Dixmier (1963) introduced
Dixmier_mapping
Laws describing planetary orbits
astronomy, Kepler's laws of planetary motion give good approximations for the orbits of planets around the Sun. They were published by Johannes Kepler from 1609
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Orbit about a small Solar System body
Terminator orbits are spacecraft orbits about a small Solar System body in which the orbital plane is held approximately perpendicular to the body–Sun
Terminator_orbit
Association of atoms to form chemical compounds
Heitler–London method forms the basis of what is now called valence bond theory. In 1929, the linear combination of atomic orbitals molecular orbital method (LCAO)
Chemical_bond
Exoplanet orbiting 82 G. Eridani
exoplanet, possibly rocky, orbiting the solar-type star 82 G. Eridani. It is at least five times more massive than Earth and has an orbit partially within the
HD_20794_d
Situation in which an astronomical object's orbital period matches its rotational period
Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the bodies reaches a state where there is no longer any net change in
Tidal_locking
Method for solving differential equations
Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations (ODE). The method is a member of the Runge–Kutta
Dormand–Prince_method
Branch of chemistry
Hückel method calculations (using a simple linear combination of atomic orbitals (LCAO) method to determine electron energies of molecular orbitals of π
Computational_chemistry
Topics referred to by the same term
name of SANSA Space Science, South Africa Hückel molecular orbital method, a simple method for the determination of electron energies Human milk oligosaccharide
HMO_(disambiguation)
Shape of the Moon's sunlit portion as viewed from Earth
successive recurrences of the same phase: due to the eccentricity of the Moon's orbit, this duration is not perfectly constant but averages about 29.5 days. The
Lunar_phase
Modular space station in low Earth orbit
The International Space Station (ISS) is a space station in low Earth orbit (LEO). It is the product of the International Space Station program and is
International_Space_Station
Relative directions of orbit or rotation
Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is
Retrograde and prograde motion
Retrograde_and_prograde_motion
Medical condition
Orbital emphysema (/ˈɔː(r)bɪt(ə)l ˌemfɪˈsiːmə/, also known as pneumo-orbit) is a medical condition that refers to the trapping of air within the loose
Orbital_emphysema
Type of low-energy spacecraft transfer
capture is a low energy method for a spacecraft to achieve an orbit around a distant planet or moon with no fuel required to go into orbit. In the ideal case
Ballistic_capture
Approach to finding numerical solutions of ordinary differential equations
Johnson resorts to the Euler method in calculating the re-entry of astronaut John Glenn from Earth orbit. Crank–Nicolson method Gradient descent similarly
Euler_method
Vehicle or machine designed to fly in space
the Solar System. Orbital spacecraft may be recoverable or not. Most are not. Recoverable spacecraft may be subdivided by a method of reentry to Earth
Spacecraft
Basis sets used in quantum chemistry
chemistry, more specifically in ab initio quantum chemistry methods, to calculate the molecular orbitals of chemical systems within Hartree–Fock theory or density
STO-nG_basis_sets
American chemist
With Michael B. Hall, he developed the Fenske-Hall method, an ab initio molecular orbital method. Fenske was one of ten children born to Bernard and
Richard_F._Fenske
Goldilocks super-Earth orbiting Gliese 667 C
(also known as GJ 667 Cc, HR 6426 Cc, or HD 156384 Cc) is an exoplanet orbiting within the habitable zone of the red dwarf star Gliese 667 C, which is
Gliese_667_Cc
Eighth planet from the Sun
Neptune is the eighth and farthest known planet orbiting the Sun. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive
Neptune
Extrasolar planet orbiting TOI-2431
TOI-2431 b is an extrasolar planet orbiting the orange dwarf star TOI-2431. It was initially detected by the transit method in 2019, and with additional observations
TOI-2431_b
Software for computational chemistry
fragment molecular orbital (FMO) method, the Effective Fragment Potential (EFP) method, and the Effective Fragment Molecular Orbital method (EFMO). The GAMESS
GAMESS_(US)
Moon beyond the Solar System
indirect detection method that measures the velocity shift and resulting stellar spectrum shift associated with an orbiting planet. This method is also known
Exomoon
Set of points linked through the evolution function of a dynamical system
partition of the phase space. Understanding the properties of orbits by using topological methods is one of the objectives of the modern theory of dynamical
Orbit_(dynamics)
Large, round non-stellar astronomical object
a large, rounded astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The
Planet
NASA orbiter mission to Venus (1989–1994)
booster, and the first spacecraft to test aerobraking as a method for circularizing its orbit. Magellan was the fifth successful NASA mission to Venus,
Magellan_(spacecraft)
Quantum-mechanical framework for simulating molecules and solids
of the corresponding KS orbital-dependent energy density functionals. This can be in principle done for any arbitrary orbital-dependent functional, but
Optimized effective potential method
Optimized_effective_potential_method
Exoplanet Kepler 296 d
Kepler-296d is an exoplanet orbiting the M-dwarf star Kepler-296, located in the constellation Draco. It was discovered in 2014 by the Kepler space telescope
Kepler-296d
International publisher that specialises in science fiction and fantasy books
Orbit Books is an international publisher that specialises in science fiction and fantasy books. It is a division of Hachette Book Group, owned by Lagardère
Orbit_Books
Measure of close approach in astronomy
Minimum orbit intersection distance (MOID) is a measure used in astronomy to assess potential close approaches and collision risks between astronomical
Minimum orbit intersection distance
Minimum_orbit_intersection_distance
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