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Vector in celestial mechanics
In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with
Eccentricity_vector
Vector used in astronomy
dimensionless eccentricity vector of celestial mechanics. Its first use seems to go back at least to Jakob Hermann. Various generalisations of the LRL vector have
Laplace–Runge–Lenz_vector
Amount by which an orbit deviates from a perfect circle
developed. The eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | {\displaystyle
Orbital_eccentricity
Characteristic of conic sections
eccentricity of a circle is 0. The eccentricity of a non-circular ellipse is between 0 and 1. The eccentricity of a parabola is 1. The eccentricity of
Eccentricity_(mathematics)
Celestial orbit whose trajectory is a conic section in the orbital plane
direction of the periapsis of the orbit. We can then define the eccentricity vector associated with the orbit as: e ≜ c α = r ˙ × H α − u = v × H α −
Kepler_orbit
Topics referred to by the same term
current position of an object on its orbit Eccentricity vector, in celestial mechanics, a dimensionless vector with direction pointing from apoapsis to
Eccentricity
Maintenance of a particular orbit
Solar radiation pressure will in general perturb the eccentricity (i.e. the eccentricity vector); see Orbital perturbation analysis (spacecraft). For
Orbital_station-keeping
Kepler orbit with an eccentricity of less than one
is the eccentricity of the orbit, the stated result is reached. The flight path angle is the angle between the orbiting body's velocity vector (equal
Elliptic_orbit
Orbit in which natural drifting has been minimized
eccentricity vector caused by the J 2 {\displaystyle J_{2}\,} is shown to be: where: The first term is the in-plane perturbation of the eccentricity vector
Frozen_orbit
Specifies the orbit of an object in space
where: n is a vector pointing towards the ascending node (i.e. the z-component of n is zero), e is the eccentricity vector (a vector pointing towards
Argument_of_periapsis
Component of an orbit
or line of apsides, is an imaginary line defined by an orbit's eccentricity vector. It is strictly defined for elliptic, parabolic, and hyperbolic orbits
Apse_line
Parameter of Keplerian orbits
where: v is the orbital velocity vector of the orbiting body, e is the eccentricity vector, r is the orbital position vector (segment FP in the figure) of
True_anomaly
Angle defining a position in an orbit
{\displaystyle J_{n}(x)} is the Bessel function of the first kind. Eccentricity vector Orbital eccentricity Universal variable formulation George Albert Wentworth
Eccentric_anomaly
Estimation of orbits of objects
Therefore, the ascending node vector can be defined by the cross product of these two vectors. Compute the eccentricity vector e → {\displaystyle {\vec {e}}}
Orbit_determination
List of definitions of terms and concepts commonly used in aerospace engineering
the mean anomaly. Eccentricity vector – In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Problem in celestial mechanics
_{2})\right)}{\left|\mathbf {r} _{2}-\mathbf {r} _{1}\right|^{2}}}} The eccentricity vector e {\displaystyle \mathbf {e} } is given by e = ( ( | r 1 | − | r
Lambert's_problem
Frame of reference for an orbit
{\hat {p}} } coordinate must be aligned with the eccentricity vector. Circular orbits, having no eccentricity, give no means by which to orient the coordinate
Perifocal_coordinate_system
Laws describing planetary orbits
{\displaystyle c} is the linear eccentricity. Thus the difference in areas is 2 b c . {\displaystyle 2bc.} Since the eccentricity is given by e = c a {\displaystyle
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Horizontal angle from north or other reference cardinal direction
surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane.
Azimuth
Term in geometry; longest and shortest semidiameters of an ellipse
an ellipse is related to the semi-minor axis's length b through the eccentricity e and the semi-latus rectum ℓ {\displaystyle \ell } , as follows: b =
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Cartesian vectors of position and velocity of an orbiting body in space
and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle \mathbf {r}
Orbital_state_vectors
Vector quantity in celestial mechanics
body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided
Specific_angular_momentum
Part of a line that is bounded by two distinct end points; line with two endpoints
a circle), a line segment is called a chord (of that curve). If V is a vector space over R {\displaystyle \mathbb {R} } or C , {\displaystyle \mathbb
Line_segment
Periodic change in the direction of a rotation axis
precession, the angular momentum is a constant, but the angular velocity vector changes orientation with time. What makes this possible is a time-varying
Precession
and their notations. Note that bold text indicates that the quantity is a vector. List of letters used in mathematics and science Glossary of mathematical
List of common physics notations
List_of_common_physics_notations
Surface formed by rotating an ellipse
{a^{2}}{c^{2}}}.} In both cases, eo and ep may be identified as the eccentricity (see ellipse). These formulas are identical in the sense that the formula
Spheroid
Parameters that define a specific orbit
particular use case. Eccentricity ( e ) — shape of the ellipse, describing how much it deviates from a perfect a circle. An eccentricity of 0 (zero) describes
Orbital_elements
Plane curve
points are the same. The elongation of an ellipse is measured by its eccentricity e {\displaystyle e} , a number ranging from e = 0 {\displaystyle e=0}
Ellipse
Spacecraft launch or descent maneuver
{k}}} is a unit vector in the vertical direction, and m {\displaystyle m} is the instantaneous vehicle mass. By constraining the thrust vector to point parallel
Gravity_turn
Plane curve: conic section
called the focal distance or linear eccentricity. The quotient c a {\displaystyle {\tfrac {c}{a}}} is the eccentricity e {\displaystyle e} . The equation
Hyperbola
Orbit around Earth
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
Geocentric_orbit
Curved path of an object around a point
At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune. As two objects
Orbit
within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude
Gravity_of_Earth
Brown dwarf
leaves a wide range of possible orbits; both low-eccentricity, coplanar orbits and high-eccentricity, misaligned orbits would be consistent with observation
HR_2562_B
orbit: An orbit that has an eccentricity of 0 and whose path traces a circle. Elliptic orbit: An orbit with an eccentricity greater than 0 and less than
List_of_orbits
Java Simulations Easy axis Ebullioscopic constant Eccentric anomaly Eccentricity vector Echea Echo (phenomenon) Echo chamber Echogenicity Eckert number Eckman
Index_of_physics_articles_(E)
Property of waves that can oscillate with more than one orientation
field vector, while θ1 and θ2 represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing
Polarization_(waves)
Geographic coordinate specifying north-south position
Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, and
Latitude
Overview of and topical guide to geometry
(mathematics) (also known as magnitude) Position vector Scalar multiplication Vector addition Zero vector Complex plane Imaginary axis Linear interpolation
Outline_of_geometry
Spaceflight maneuver
orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta-v) at the orbital nodes (i.e. the point where the initial and desired
Orbital_inclination_change
When the angular frequency of a system matches its natural vibrational frequency
overall circular motion leaves the eccentricity of the ellipse-shaped trajectory. the center of the eccentricity is located at a distance of ( a + b
Rotational–vibrational coupling
Rotational–vibrational_coupling
Classical approach to the many-body problem of astronomy
¨ i {\displaystyle \ \mathbf {\ddot {r}} _{i}\ } is the acceleration vector of body i {\displaystyle i} , G {\displaystyle G} is the gravitational constant
Perturbation_(astronomy)
Field of classical mechanics concerned with the motion of spacecraft
p} is the semi-latus rectum, while e {\displaystyle e} is the orbital eccentricity, all obtainable from the various forms of the six independent orbital
Orbital_mechanics
Transfer orbit used to reach geosynchronous or geostationary orbit
(direction). The inclination and eccentricity must both be reduced to zero to obtain a geostationary orbit. If only the eccentricity of the orbit is reduced to
Geostationary_transfer_orbit
Concept in astrodynamics
escape the central object's gravitational field; expressed as orbital eccentricity designated by any number more than 1. Under simplistic assumptions a
Hyperbolic_trajectory
Highly elliptical and highly inclined synchronous orbit
(approximately 63.4°), an orbital period of one sidereal day, and a typical eccentricity between 0.2 and 0.3. A satellite placed in this orbit spends most of
Tundra_orbit
Special case of the two-body problem
hyperbola. The eccentricity e {\displaystyle e} is related to the total energy E {\displaystyle E} (cf. the Laplace–Runge–Lenz vector) e = 1 + 2 E L 2
Kepler_problem
Velocity of an object as the rate of distance change between the object and a point
observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative
Radial_velocity
Angle between a reference plane and the plane of an orbit
{\displaystyle i} can be computed from the orbital momentum vector h {\displaystyle h} (or any vector perpendicular to the orbital plane) as i = arccos h
Orbital_inclination
Specifies the orbit of an object in space
required for a particular body to complete one orbit. In time T, the radius vector sweeps out 2π radians, or 360°. The average rate of sweep, n, is then n
Mean_anomaly
Laws in physics about force and motion
ISSN 0002-9505. Mungan, Carl E. (1 March 2005). "Another comment on "Eccentricity as a vector"". European Journal of Physics. 26 (2): L7–L9. doi:10.1088/0143-0807/26/2/L01
Newton's_laws_of_motion
Way to determine a preliminary orbit from initial observations in astronomy
observations, the position vectors of the observation points (in Equatorial Coordinate System), the direction cosine vector of the orbiting body from the
Gauss's_method
Type of high-latitude satellite orbit
properties: Argument of perigee: 270° Inclination: 63.4° Period: 718 minutes Eccentricity: 0.74 Semi-major axis: 26,600 km (16,500 mi) The argument of perigee
Molniya_orbit
Type of geocentric orbit
other orbital parameters such as argument of periapsis and the orbital eccentricity evolve, due to higher-order perturbations in the Earth's gravitational
Sun-synchronous_orbit
Application of mechanical dynamics to model the flight of space vehicles
{a} ,} where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate
Spacecraft_flight_dynamics
Measure of amount of effort to change trajectory
mass. The actual acceleration vector would be found by adding thrust per mass on to the gravity vector and the vectors representing any other forces acting
Delta-v
Calculating the Sun's location in the sky at a given time and place
perihelion. The number 0.0167 is the current value of the eccentricity of the Earth's orbit. The eccentricity varies very slowly over time, but for dates fairly
Position_of_the_Sun
Term from classical mechanics
vanishingly small. The vector direction is postulated to be normal to the plane containing the position and velocity vectors of the particle, following
Areal_velocity
Defining the orbit of an object in space
longitude is taken to be the positive x-axis. k is the unit vector (0, 0, 1), which is the normal vector to the xy reference plane. For non-inclined orbits (with
Longitude of the ascending node
Longitude_of_the_ascending_node
Orbit around Earth between 160 and 2000 km
of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in
Low_Earth_orbit
Speed at which a body orbits around the barycenter of a system
it needs to move faster to cover the same area. For orbits with small eccentricity, the length of the orbit is close to that of a circular one, and the
Orbital_speed
Area of the Solar System beyond the planets, comprising small bodies
mean-motion resonances removes the higher-eccentricity objects from the cold belt, truncating its eccentricity distribution. Being distant from the Sun
Kuiper_belt
Quadric surface that looks like a deformed sphere
scale factor, x is an n-dimensional random row vector with median vector μ (which is also the mean vector if the latter exists), Σ is a positive definite
Ellipsoid
Concept in gravitational orbital mechanics
elliptical orbit (and hence also a circular orbit) the velocity and radius vectors are perpendicular at apoapsis and periapsis, conservation of angular momentum
Vis-viva_equation
Natural satellites of the planet Saturn
are irregular satellites, which have high orbital inclinations and eccentricities mixed between prograde and retrograde. These moons are probably captured
Moons_of_Saturn
American scientist (1839–1903)
equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried
Josiah_Willard_Gibbs
Relationship between two figures of the same shape and size, or mirroring each other
a vector from one of the vertices of one of the figures to the corresponding vertex of the other figure. Translate the first figure by this vector so
Congruence_(geometry)
Diagrammatic representation of Sun's position over a period of time
governed by the combined effects of Earth's axial tilt and its orbital eccentricity. An analemma can be photographed by keeping a camera at a fixed location
Analemma
Motion problem in classical mechanics
dots on top of the x position vectors denote their second derivative with respect to time, or their acceleration vectors. Adding and subtracting these
Two-body_problem
Moving wave that has oscillations perpendicular to the direction of the wave
Let d ^ {\displaystyle {\widehat {d}}} be the direction of propagation (a vector with unit length), and o → {\displaystyle {\vec {o}}} any reference point
Transverse_wave
Periodic, three-dimensional orbit
9:2 resonant NRHO, with a period of about 7 days and a high orbital eccentricity, bringing the station within 3,000 kilometers (1,900 mi) of the lunar
Near-rectilinear_halo_orbit
Coordinates comprising a distance and an angle
{1-\epsilon \cos \varphi }}} where ϵ {\displaystyle \epsilon } is the eccentricity and ℓ {\displaystyle \ell } is the semi-latus rectum (the perpendicular
Polar_coordinate_system
Trajectory of Earth around the Sun
an ellipse with the Earth–Sun barycenter as one focus with a current eccentricity of 0.0167. Since this value is close to zero, the center of the orbit
Earth's_orbit
Distance from the Earth surface to a point near its center
{1-e^{2}}{a^{2}}}N(\varphi )^{3},} where e {\displaystyle e} is the eccentricity of the earth. This is the radius that Eratosthenes measured in his arc
Earth_radius
Time period during which a rocket must launch to reach its target
another planet using the simple low-energy Hohmann transfer orbit, if eccentricity of orbits is not a factor, launch periods are periodic according to the
Launch_window
Orbit keeping the satellite at a fixed longitude above the equator
whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km
Geosynchronous_orbit
Astrodynamic equation
attraction is four times as strong. The parameter e {\displaystyle e} is the eccentricity of the orbit, and is given by e = 1 + 2 E ℓ 2 m 3 μ 2 {\displaystyle
Orbit_equation
Topics referred to by the same term
whose slope at any equilibrium price vector is non-zero Regular moon, a natural satellite that has low eccentricity and a relatively close and prograde
Regular
Circular orbit above Earth's Equator and following the direction of Earth's rotation
properties: Inclination: 0° Period: 1436 minutes (one sidereal day) Eccentricity: 0 Argument of perigee: undefined Semi-major axis: 42,164 km An inclination
Geostationary_orbit
Circumellipse of a triangle whose center is the triangle's centroid
center is the centroid). Hence both ellipses are similar (have the same eccentricity). A Steiner ellipse is the only ellipse, whose center is the centroid
Steiner_ellipse
The Moon's circuit around Earth
degree on the celestial sphere, each hour. The orbit of the Moon has an eccentricity of 0.0549, with perigee and apogee distances of 363,300 km (225744 mi)
Orbit_of_the_Moon
Type of spacecraft maneuver
{F}{m}}\cdot v=a\cdot v,} where a {\displaystyle a} is the acceleration vector. From this, it can be seen that the rate of gain of specific energy of every
Oberth_effect
Parameter in the gravitational two-body problem
momentum divided by the reduced mass; e {\displaystyle e} is the orbital eccentricity; a {\displaystyle a} is the semi-major axis. It is a kind of specific
Specific_orbital_energy
Attraction of masses and energy
on relativity in the 20th century. Eventually, astronomers noticed an eccentricity in the orbit of the planet Mercury which could not be explained by Newton's
Gravity
{\displaystyle \varpi =\Omega +\omega } which are derived from the orbital state vectors. Define the following: i, inclination ω, argument of perihelion Ω, longitude
Longitude_of_periapsis
Type of orbit
celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity (e) equal to 1 and is an unbound orbit that is exactly on the border
Parabolic_trajectory
Earth-centered orbit above low Earth orbit and below geostationary orbit
377 mi). The Molniya orbit has a high inclination of 63.4° and high eccentricity of 0.722 with a period of 12 hours, so a satellite spends most of its
Medium_Earth_orbit
Either of two extreme points in a celestial object's orbit
axis of the Earth measured from the plane of the ecliptic. The Earth's eccentricity and other orbital elements are not constant, but vary slowly due to the
Apsis
Orbit in the two body case with high eccentricity
highly eccentric orbit is an orbit of one body about another with high eccentricity, usually referring to one around Earth. Examples of inclined HEO orbits
Highly_elliptical_orbit
Equilibrium points near two orbiting bodies
of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly Types of two-body orbits by eccentricity Circular orbit
Lagrange_point
Space navigation technique
except adding the planet's velocity to that of the spacecraft requires vector addition as shown below. Due to the reversibility of orbits, gravitational
Gravity_assist
Potentially hazardous near-Earth asteroid
April, when Apophis is in the outer portions of its orbit. In fact, the eccentricity and semi-major axis are such that (before 2029) Apophis is always receding
99942_Apophis
Relationship between two lines that meet at a right angle
orthogonality conditions, such as that between a surface and its normal vector. A line is said to be perpendicular to another line if the two lines intersect
Perpendicular
Hungarian and American mathematician and physicist (1903–1957)
Macrae 1992, pp. 170–171. Regis, Ed (1987). Who Got Einstein's Office?: Eccentricity and Genius at the Institute for Advanced Study. Reading, Massachusetts:
John_von_Neumann
Time of day when the sun appears above the horizon
the solstice and the earliest or latest sunrise time is caused by the eccentricity of Earth's orbit and the tilt of its axis, and is described by the analemma
Sunrise
Mathematical equation describing the motion of a rocket
complicated analysis based on the propagation of the spacecraft's state vector and the integration of thrust are used to predict orbital motion. Assume
Tsiolkovsky_rocket_equation
anomaly, equation of the centre and radius vector of a planet, in terms of the mean anomaly and eccentricity. Monthly Notices of the Royal Astronomical
Equation_of_the_center
Class of problems in classical mechanics
origin of a coordinate system. The vector r joining O to the present position of the particle is known as the position vector. Therefore, a central force must
Classical central-force problem
Classical_central-force_problem
Orbital data format
mechanism Lagrangian point n-body problem Orbit equation Orbital state vectors Perturbation Retrograde and prograde motion Specific orbital energy Specific
Two-line_element_set
Concept in geometry and physics
plane of an object. Other parameters, such as the orbital period, the eccentricity of the orbit and the phase of the orbit are more easily changed by propulsion
Orbital_plane
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
Girl/Female
Indian, Traditional
Beautiful Eyes
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : from a pet form of the female personal names Elizabeth or Isabel.
Boy/Male
Indian, Sanskrit
Hero of the Raghus
Biblical
blackness; heat
Boy/Male
American, Australian, British, English, French, Hebrew, Italian, Latin
Garden
Girl/Female
Indian
Smile, Happiness
Surname or Lastname
English
English : patronymic from Grave 1.
Surname or Lastname
English and French
English and French : from an Anglo-Norman French form of the Old Norse personal name þórfinnr, composed of the elements þórr, the name of the god of thunder in Scandinavian mythology (see Thor) + the ethnic name Finnr ‘Finn’. This may have absorbed another name, Turpius, Turpinus (from Latin turpis ‘ugly’, ‘base’), one of the self-abasing names adopted as a mark of humility by the early Christians. It was borne by the archbishop of Rheims in the Charlemagne legend.A Turpin of unknown geographic origin is documented in Montreal in 1681.
Boy/Male
English
Spear fighter.
Girl/Female
Norse
Bolli's daughter.
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
ECCENTRICITY VECTOR
n.
Same as Radius vector.
n.
The ratio of the distance between the center and the focus of an ellipse or hyperbola to its semi-transverse axis.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
A celestial body which revolves about the sun in an orbit of a moderate degree of eccentricity. It is distinguished from a comet by the absence of a coma, and by having a less eccentric orbit. See Solar system.
n.
Singularity; strangeness; eccentricity; irregularity; uncouthness; as, the oddness of dress or shape; the oddness of an event.
n.
One who has some peculiarity or eccentricity of character, which he indulges in odd or whimsical ways.
n.
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
n.
The extreme movement given to a sliding or vibrating reciprocating piece by a cam, crank, eccentric, or the like; travel; stroke; as, the throw of a slide valve. Also, frequently, the length of the radius of a crank, or the eccentricity of an eccentric; as, the throw of the crank of a steam engine is equal to half the stroke of the piston.
n.
The state of being eccentric; deviation from the customary line of conduct; oddity.
n.
The state or quality of being centric; centricalness.
n.
A peculiarity of physical or mental constitution or temperament; a characteristic belonging to, and distinguishing, an individual; characteristic susceptibility; idiocrasy; eccentricity.
n.
A sudden turn or start of the mind; a temporary eccentricity; a freak; a fancy; a capricious notion; a humor; a caprice.
pl.
of Eccentricity
n.
The ratio of the distance of the center of the orbit of a heavenly body from the center of the body round which it revolves to the semi-transverse axis of the orbit.
n.
A person of marked eccentricity.
a.
Resembling fantasies in irregularity, caprice, or eccentricity; irregular; oddly shaped; grotesque.
n.
The distance of the center of figure of a body, as of an eccentric, from an axis about which it turns; the throw.
a.
A personal frailty or failing; foible; eccentricity; a weakness or defect.