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Orbital mechanics term
mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was derived by Johannes Kepler in 1609
Kepler's_equation
Laws describing planetary orbits
Kepler orbit Kepler problem Kepler's equation Laplace–Runge–Lenz vector Specific relative angular momentum, relatively easy derivation of Kepler's laws starting
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical
List_of_equations
Field of classical mechanics concerned with the motion of spacecraft
algebraically. Kepler's equation can be solved for E {\displaystyle E} analytically by inversion. A solution of Kepler's equation, valid for all real values
Orbital_mechanics
Mathematical equation describing the motion of a rocket
The classical rocket equation, Tsiolkovsky rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that
Tsiolkovsky_rocket_equation
Special case of the two-body problem
Binet equation Hamilton–Jacobi equation Laplace–Runge–Lenz vector Kepler orbit Kepler problem in general relativity Kepler's equation Kepler's laws of
Kepler_problem
Type of orbit
Unlike Kepler's equation, which is used to solve for true anomalies in elliptical and hyperbolic trajectories, the true anomaly in Barker's equation can
Parabolic_trajectory
Parameter of Keplerian orbits
^{2}-1}{\alpha (1+\beta ^{2})}}\right)^{3/2}k(t-T_{0})} The above equations are called Kepler's equation. For arbitrary constant λ {\displaystyle \lambda } , the
True_anomaly
In two-body, Keplerian orbital mechanics, the equation of the center is the angular difference between the actual position of a body in its elliptical
Equation_of_the_center
formulation is a method used to solve the two-body Kepler problem. It is a generalized form of Kepler's Equation, extending it to apply not only to elliptic
Universal variable formulation
Universal_variable_formulation
German astronomer and mathematician (1571–1630)
were married on 27 April 1597. In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy.
Johannes_Kepler
Concept in astrodynamics
}{2}}} The eccentric anomaly E is related to the mean anomaly M by Kepler's equation: M = e sinh E − E {\displaystyle M=e\sinh E-E} The mean anomaly
Hyperbolic_trajectory
Topics referred to by the same term
Kepler's may refer to: Kepler's Books, bookstore in Menlo Park, California Kepler's equation in orbital mechanics Kepler's laws of planetary motion, describing
Kepler's
Kepler orbit with an eccentricity of less than one
eccentricity is less than 1 then the equation of motion describes an elliptical orbit. Because Kepler's equation M = E − e sin E {\displaystyle M=E-e\sin
Elliptic_orbit
Maximum eccentricity for which a power series for Kepler's equation converges
is the maximum value of the eccentricity for which a solution to Kepler's equation, in terms of a power series in the eccentricity, converges. It is
Laplace_limit
Specifies the orbit of an object in space
orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define ϖ as the longitude
Mean_anomaly
Field-equations in general relativity
field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter-energy within it. The equations were
Einstein_field_equations
Apparent solar time minus mean solar time
The equation of time describes the discrepancy between two kinds of solar time. The two times that differ are the apparent solar time, which directly tracks
Equation_of_time
Family of solutions to related differential equations
introduced the series expansion of Bessel functions to solve Kepler's equation, a transcendental equation in astronomy. Friedrich Wilhelm Bessel had seen Lagrange's
Bessel_function
Persian polymath (died c. 869 CE)
parallax, which was later rediscovered by Johannes Kepler in 1609 and it is now known as Kepler's equation. Habash al-Hasib is the father of the astronomer
Habash_al-Hasib
Motion problem in classical mechanics
case of an attractive force. Energy drift Equation of the center Euler's three-body problem Kepler orbit Kepler problem n-body problem Three-body problem
Two-body_problem
Celestial orbit whose trajectory is a conic section in the orbital plane
the differential equation for the two body case can be completely solved mathematically and the resulting orbit which follows Kepler's laws of planetary
Kepler_orbit
Branch of engineering
mechanical systems. Mathematics – in particular, calculus, differential equations, and linear algebra. Electrotechnology – the study of electronics within
Aerospace_engineering
Mathematical concept
problems. Among other applications, the solution E {\displaystyle E} of Kepler's equation M = E − e sin E {\displaystyle M=E-e\sin E} can be expressed via
Kapteyn_series
masses, would coincide, and x is the separation. This is the radial Kepler equation. t ( x , w ) = ( | w | x ) 2 + | w | x − ln ( | w | x + 1 + | w |
Radial_trajectory
Concept in gravitational orbital mechanics
In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation
Vis-viva_equation
Measure of the efficiency of a rocket based on its propellant's mass
The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of n {\displaystyle n}
Rocket_mass_ratio
Angular speed required for a body to complete one orbit
from a set of orbital elements. This mean position is refined by Kepler's equation to produce the true position. Define the orbital period (the time
Mean_motion
Horizontal angle from north or other reference cardinal direction
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Azimuth
Equilibrium points near two orbiting bodies
to the first two. The location of L1 is the solution to the following equation, gravitation providing the centripetal force: M 1 ( R − r ) 2 − M 2 r 2
Lagrange_point
Angle defining a position in an orbit
is related to the mean anomaly M by Kepler's equation: M = E − e sin E {\displaystyle M=E-e\sin E} This equation does not have a closed-form solution
Eccentric_anomaly
Equations that describe the behavior of a physical system
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically
Equations_of_motion
Either of two extreme points in a celestial object's orbit
man-made objects. The words perihelion and aphelion were coined by Johannes Kepler to describe the orbital motions of the planets around the Sun. The words
Apsis
Gives power series for certain implict functions
Theorem on MathWorld Cornish–Fisher expansion, an application of the theorem Article on equation of time contains an application to Kepler's equation.
Lagrange_reversion_theorem
motion Kepler's equation Keplerian elements Kepler orbit Kepler problem Kepler problem in general relativity Kepler space telescope Kepler photometer Keplerian
List of things named after Johannes Kepler
List_of_things_named_after_Johannes_Kepler
Periodic, three-dimensional orbit
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Halo_orbit
Book by Johannes Kepler (1609)
triangle is proportional to sine of the eccentric anomaly. This is the Kepler equation. If we write M {\textstyle M} for the mean anomaly, E {\textstyle E}
Astronomia_nova
Estimate of extraterrestrial civilizations
The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way Galaxy
Drake_equation
Algorithm for finding zeros of functions
apply his method in an iterative manner to a nonpolynomial equation, specifically Kepler's equation, which were the first published uses of Newton's method
Newton's_method
Elliptical orbit used to move a spacecraft from one circular orbit to another
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Transfer_orbit
Specifies the orbit of an object in space
were favorable) is equal to the time of its periastron. Apsidal precession Kepler orbit Orbital mechanics Orbital node Iglesias-Marzoa, Ramón; López-Morales
Argument_of_periapsis
Speed at which a body orbits around the barycenter of a system
semi-major axis of the elliptical orbit. This expression is called the vis-viva equation. For the Earth at perihelion, the value is: 1.327 × 10 20 m 3 s − 2 ⋅
Orbital_speed
Concept in celestial mechanics
asymptotically approach the hyperbolic excess speed v∞, satisfying the equation: v ∞ 2 = V 2 − v e 2 . {\displaystyle {v_{\infty }}^{2}=V^{2}-{v_{\text{e}}}^{2}
Escape_velocity
Branch of astronomy
more than force, and developing a method to use a single polar coordinate equation to describe any orbit, even those that are parabolic and hyperbolic. This
Celestial_mechanics
Formulation of classical mechanics using momenta
Hamilton's equations consist of 2n first-order differential equations, while Lagrange's equations consist of n second-order equations. Hamilton's equations usually
Hamiltonian_mechanics
Polynomial equation of degree 3
In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is
Cubic_equation
position. The phase angle can be converted in terms of time using Kepler's Equation: t = T 1 2 π ( E − e 1 sin E ) {\displaystyle t={\frac {T_{1}}{2\pi
Orbit_phasing
Outdated measure of planetary orbits
since perigee (where the period is 2 π {\displaystyle 2\pi } , see Kepler equation), whereas the equant model gives π / 2 − arctan ( e ) , {\displaystyle
Equant
Measure of aircraft/spacecraft efficiency
and fuel fractions in aviation, see Fuel Fraction. Tsiolkovsky rocket equation "SOYUZ-2 Launch Vehicle / Power Characteristics". JSC SRC Progress. Retrieved
Payload_fraction
Time an astronomical object takes to complete one orbit around another object
perfect sphere of uniform density, it is possible to rewrite the first equation without measuring the mass as: T = a 3 r 3 3 π G ρ {\displaystyle T={\sqrt
Orbital_period
Parameters that define a specific orbit
anomaly can be found from the eccentric anomaly and eccentricity using Kepler's equation: M = E − e sin E . {\displaystyle M\ =\ E-e\sin E~.} Mean
Orbital_elements
Quantities used in astronomy
that E = M + e sin(E) (Kepler's equation). From E and the orbital eccentricity e follow the rectangular coordinates within the Kepler orbit: X = cos(E) −
Thiele−Innes_elements
Spaceflight operation
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Orbit_insertion
Danish astronomer (1679–1764)
determined the sun parallax, 9", an approximative solution to the Kepler equation. Horrebow also learned how to correct inherent flaws in instruments
Peder_Horrebow
Examining complex systems as a whole
dynamical systems, entirely mathematically, as demonstrated by Johannes Kepler's equation (1619) for the orbit of Mars before Newton's Principia appeared in
Systems_thinking
Space navigation technique
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Gravity_assist
Orbit with a fixed distance from the barycenter
r {\displaystyle r} is the distance from the center of mass. The orbit equation in polar coordinates, which in general gives r in terms of θ, reduces to:[clarification
Circular_orbit
Term in geometry; longest and shortest semidiameters of an ellipse
a hyperbola, it is the one that does not intersect the hyperbola. The equation of an ellipse is ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , {\displaystyle
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Equations in physical cosmology
The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern cosmic expansion
Friedmann_equations
Angle between a reference plane and the plane of an orbit
Horizontal coordinate system Axial parallelism Axial tilt Azimuth Beta angle Kepler orbits Kozai mechanism Orbital inclination change Orbital pole Space Shuttle
Orbital_inclination
Quasi-periodic orbital trajectory
the Three-Body Problem, and Space Mission Design" (PDF). International Conference on Differential Equations. Berlin: World Scientific. pp. 1167–1181.
Lissajous_orbit
Concept in aerospace engineering
kg}})=0.7998} . The mass fraction plays an important role in the rocket equation: Δ v = − v e ln m f m 0 {\displaystyle \Delta v=-v_{\text{e}}\ln {\frac
Propellant_mass_fraction
Laplace limit, concerning series solutions to Kepler's equation Laplacian vector field Laplace's equation Laplace operator Discrete Laplace operator Laplace–Beltrami
List of things named after Pierre-Simon Laplace
List_of_things_named_after_Pierre-Simon_Laplace
Parameter in the gravitational two-body problem
mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time: ε = ε k + ε p = v 2 2
Specific_orbital_energy
Equation giving the form of a central force
Kepler problem of calculating the orbit of an inverse square law may be read off from the Binet equation as the solution to the differential equation
Binet_equation
Amount by which an orbit deviates from a perfect circle
also helps understand its near-circular orbits and other unique features. Equation of time Tidal circularization While its orbit was initially hyperbolic
Orbital_eccentricity
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Process that leads to gradual decrease of the distance between two orbiting bodies
approximate drag deceleration αo as a function of orbit radius R using the drag equation below: α o = 1 2 ρ ( R ) v 2 c d A m {\displaystyle \alpha _{o}\,=\,{\tfrac
Orbital_decay
Center of mass of multiple bodies orbiting each other
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Barycenter_(astronomy)
Vector used in astronomy
\cdot \mathbf {L} =L^{2}} Rearranging yields the solution for the Kepler equation 1 r = m k L 2 + A L 2 cos θ {\displaystyle {\frac {1}{r}}={\frac
Laplace–Runge–Lenz_vector
Decomposition of periodic functions
to solve Kepler's equation. His work was published in 1819, unaware of Fourier's work which remained unpublished until 1822. The heat equation is a partial
Fourier_series
Point where an orbit crosses a plane of reference to which it is inclined
Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period
Orbital_node
gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Problem in physics and celestial mechanics
publications by Cleminshaw: Cleminshaw, C. H.: "Celestial Speeds", 4 1953, equation, Kepler, orbit, comet, Saturn, Mars, velocity.[full citation needed] Cleminshaw
N-body_problem
Formulation of classical mechanics
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics
Hamilton–Jacobi_equation
Mathematical constant related to the cosine function
of the regularized beta function. This value can be obtained using Kepler's equation, along with other equivalent closed forms. I 1 2 − 1 ( 1 2 , 3 2 )
Dottie_number
Transfer manoeuvre between two orbits
{mv^{2}}{2}}-{\frac {GMm}{r}}={\frac {-GMm}{2a}}.} Solving this equation for velocity results in the vis-viva equation, v 2 = μ ( 2 r − 1 a ) , {\displaystyle v^{2}=\mu
Hohmann_transfer_orbit
Type of spacecraft maneuver
every part of the rocket is proportional to its speed and, given this, the equation can be integrated (numerically or otherwise) to calculate the overall change
Oberth_effect
Polynomial equation of degree 5
mathematics, a quintic equation is one which can be expressed as a quintic function equaling zero. The general form of a quartic equation is a x 5 + b x 4 +
Quintic_equation
Period of time for the ecliptic longitude of the Sun to increase 360°
being elliptical, using well-known procedures (including solving Kepler's equation). They do not take into account periodic variations due to factors
Tropical_year
Classical approach to the many-body problem of astronomy
primary body. In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically
Perturbation_(astronomy)
Mathematical model of waves on a shallow water surface
In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow
Korteweg–De_Vries_equation
Region of space gravitationally dominated by a given body
like the patched conic approximation, have been described. The general equation describing the radius of the sphere r SOI {\displaystyle r_{\text{SOI}}}
Sphere of influence (astrodynamics)
Sphere_of_influence_(astrodynamics)
Key result in Hamiltonian mechanics and statistical mechanics
to recognize this as the fundamental equation of statistical mechanics. It is referred to as the Liouville equation because its derivation for non-canonical
Liouville's theorem (Hamiltonian)
Liouville's_theorem_(Hamiltonian)
Property of a dynamical system where solutions near an equilibrium point remain so
stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that
Lyapunov_stability
Movement during spaceflight
orbit, it is said to be coasting. The Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using
Orbital_maneuver
Formulation of classical mechanics
This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Newton's laws and the concept of forces are
Lagrangian_mechanics
Quasilinear first-order ordinary differential equation
classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid
Euler's equations (rigid body dynamics)
Euler's_equations_(rigid_body_dynamics)
Region in which an astronomical body dominates the attraction of satellites
about the primary (assuming that m ≪ M {\displaystyle m\ll M} ). The above equation can also be written as m r H 2 − M r 2 ( 1 − r H r ) − 2 + M r 2 ( 1 −
Hill_sphere
Nonlinear partial differential equation
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables
Sine-Gordon_equation
Way to determine a preliminary orbit from initial observations in astronomy
however, by increasing the accuracy of sub-components, such as solving Kepler's equation. Another way to increase the accuracy is through more observations
Gauss's_method
Type of orbital maneuver
required changes in velocity can be obtained directly from the vis-viva equation v 2 = μ ( 2 r − 1 a ) , {\displaystyle v^{2}=\mu \left({\frac {2}{r}}-{\frac
Bi-elliptic_transfer
Branch of mathematics
Friedrich Wilhelm Bessel also introduced Fourier series to solve Kepler's equation. His work was published in 1819, unaware of Fourier's work which remained
Fourier_analysis
Equation explaining structure of a spherical body of isotropic material
In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is
Tolman–Oppenheimer–Volkoff equation
Tolman–Oppenheimer–Volkoff_equation
German astronomer and mathematician (1784–1846)
functions were used by Joseph-Louis Lagrange and Bessel to solve the Kepler's equation. Bessel later systematically studied the mathematical properties of
Friedrich_Wilhelm_Bessel
Astrodynamic equation
In astrodynamics, an orbit equation defines the path of orbiting body m 2 {\displaystyle m_{2}\,\!} around central body m 1 {\displaystyle m_{1}\,\!} relative
Orbit_equation
Gravitational loss of momentum and energy by bodies moving through surrounding matter
f(v)\ } is the number density distribution of the stars The result of the equation is the gravitational acceleration produced on the object under consideration
Dynamical_friction
Plane curve constructed from a given curve and fixed point
Euclidean geometry, for a plane curve C and a given fixed point O, the pedal equation of the curve is a relation between r and p where r is the distance from
Pedal_equation
System of two stars orbiting each other
245°.211 Find the eccentric anomaly E, such that E = M + e sin(E) (Kepler's equation): E = 224°.436 From E and e calculate the true anomaly ν, where tan(ν/2)
Binary_star
mechanics, the Udwadia–Kalaba formulation is a method for deriving the equations of motion of a constrained mechanical system. The method was first described
Udwadia–Kalaba_formulation
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KEPLERS EQUATION
KEPLERS EQUATION
Surname or Lastname
English
English : occupational name for a boatman or boatbuilder, from an agent derivative of Middle English kele ‘ship’, ‘barge’ (from Middle Dutch kiel).Americanized spelling of German Kühler, from a variant of an old personal name (see Keeling) or a variant of Kuhl.
Boy/Male
Gaelic
Little champion.
Surname or Lastname
German and Jewish (Ashkenazic)
German and Jewish (Ashkenazic) : nickname derived from German drei ‘three’, Middle High German drī(e), with the addition of the suffix -er. This was the name of a medieval coin worth three hellers (see Heller), and it is possible that the German surname may have been derived from this word. More probably, the nickname is derived from some other connection with the number three, too anecdotal to be even guessed at now.North German and Scandinavian : occupational name for a turner of wood or bone, from an agent derivative of Middle Low German dreien, dregen ‘to turn’. See also Dressler.Jewish (Ashkenazic) : occupational name from Yiddish dreyer ‘turner’, or a nickname from a homonym meaning ‘swindler, cheat’.English : variant spelling of Dryer.
Surname or Lastname
English and Scottish
English and Scottish : variant of Keillor.German : variant of Keller.
Male
Greek
(ΚηφεÏÏ‚) Greek name KEPHEUS means "gardener." In mythology, this is the name of a king of Ethiopia, the husband of Kassiopeia.
Surname or Lastname
German
German : from Middle High German kellaere ‘cellarman’, ‘cellar master’ (Latin cellarius, denoting the keeper of the cella ‘store chamber’, ‘pantry’). Hence an occupational name for the overseer of the stores, accounts, or household in general in, for example, a monastery or castle. Kellers were important as trusted stewards in a great household, and in some cases were promoted to ministerial rank. The surname is widespread throughout central Europe.English : either an occupational name for a maker of caps or cauls, from Middle English kellere, or an occupational name for an executioner, from Old English cwellere.Irish : reduced form of Kelleher.Scottish : variant of Keillor.
Surname or Lastname
English
English : variant of Feller.
Female
Greek
(ΚασσιÎπεια) Greek name KASSIOPEIA means "she whose words excel." In mythology, this is the name of one of the fifty Nereids who became the wife of Kepheus and mother of AndromÄ“de.Â
Girl/Female
Greek
Flaming.
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : patronymic from Seller 1–4.
Surname or Lastname
English (Norfolk)
English (Norfolk) : habitational name from Madehurst in Sussex, which gets its name from Old English mǣd ‘meadow’ (see Mead 1) + hyrst ‘wooded hill’. This place name appears in 12th-century records in the Normanized form Medl(i)ers. The surname is found in Norfolk as early as the 13th century in the form de Medlers; the landowning family that bore it was in vassalage to the Earl of Surrey, who had large estates in both Sussex and Norfolk.
Surname or Lastname
English (northern)
English (northern) : occupational name from Middle English prok(e)tour ‘steward’ (reduced from Old French procurateour, Latin procurator ‘agent’, from procurare ‘to manage’). The term was used most commonly of an attorney in a spiritual court, but also of other officials such as collectors of taxes and agents licensed to collect alms on behalf of lepers and enclosed orders of monks.John Proctor (d. 1757) was a prominent citizen of Boston, MA, and is buried in the King’s Chapel Burying Ground there.
Surname or Lastname
English (Devon)
English (Devon) : unexplained.Respelling of French Calard, a derivative of Old French cale, denoting a kind of close-fitting cap worn by women (see Cale).Possibly an Americanized spelling of German Kallart or Kellert, variants of Keller.
Surname or Lastname
Respelling of German Ehlers.English
Respelling of German Ehlers.English : habitational name from High and Low Ellers in West Yorkshire, named from Old English alras, plural of alor ‘alder’.
Surname or Lastname
English
English : occupational name for an innkeeper, from Middle English (h)osteler (Old French (h)ostelier, an agent derivative of hostel, meaning a sizeable house in which guests could be lodged in separate rooms, derived from Late Latin hospitalis, from the genitive case of hospes ‘guest’). This term was at first applied to the secular officer in a monastery who was responsible for the lodging of visitors, but it was later extended to keepers of commercial hostelries, and this is probably the usual sense of the surname. The more restricted modern English sense, ‘groom’, is also a possible source.German : from a short form of a Germanic personal name formed with a cognate of Old High German Åst(an) (see Oest).
KEPLERS EQUATION
KEPLERS EQUATION
KEPLERS EQUATION
KEPLERS EQUATION
KEPLERS EQUATION
KEPLERS EQUATION
KEPLERS EQUATION
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