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Angle defining a position in an orbit
In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit
Eccentric_anomaly
Parameter of Keplerian orbits
true anomaly f is one of three angular parameters (anomalies) that can be used to define a position along an orbit, the other two being the eccentric anomaly
True_anomaly
Specifies the orbit of an object in space
other two being the eccentric anomaly and the true anomaly. The mean anomaly at epoch, M0, is defined as the instantaneous mean anomaly at a given epoch
Mean_anomaly
Laws describing planetary orbits
is the period. Compute the mean anomaly M = nt, where t is the time since perihelion. Compute the eccentric anomaly E by solving Kepler's equation: M
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Parameters that define a specific orbit
mean anomaly and true anomaly, the eccentric anomaly is measured relative to periapsis and is not defined for circular orbits. The eccentric anomaly is
Orbital_elements
Field of classical mechanics concerned with the motion of spacecraft
(true anomaly) of θ {\displaystyle \theta } from periapsis is broken into two steps: Compute the eccentric anomaly E {\displaystyle E} from true anomaly θ
Orbital_mechanics
Concept in astrodynamics
\theta }}} The relation between the true anomaly θ and the eccentric anomaly E (alternatively the hyperbolic anomaly H) is: cosh E = cos θ + e 1 + e ⋅
Hyperbolic_trajectory
Book by Johannes Kepler (1609)
the mean anomaly (and therefore time) and eccentric anomaly. From the diagram, it is clear that the mean anomaly is simply the eccentric anomaly plus the
Astronomia_nova
Orbit in the two body case with high eccentricity
A highly elliptical orbit (HEO) or highly eccentric orbit is an orbit of one body about another with high eccentricity, usually referring to one around
Highly_elliptical_orbit
Topics referred to by the same term
Look up anomaly or anomalous in Wiktionary, the free dictionary. Anomaly, The Anomaly or Anomalies may refer to: Anomaly (natural sciences) Atmospheric
Anomaly
Either of two extreme points in a celestial object's orbit
approach Eccentric anomaly Flyby (spaceflight) Hyperbolic trajectory § Closest approach Mean anomaly Perifocal coordinate system True anomaly "apsis".
Apsis
Term in geometry; longest and shortest semidiameters of an ellipse
averaging the distance over the eccentric anomaly indeed results in the semi-major axis. averaging over the true anomaly (the true orbital angle, measured
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Kepler orbit with an eccentricity of less than one
M=E-e\sin E} has no general closed-form solution for the Eccentric anomaly (E) in terms of the Mean anomaly (M), equations of motion as a function of time also
Elliptic_orbit
Orbital mechanics term
M} is the mean anomaly, E {\displaystyle E} is the eccentric anomaly, and e {\displaystyle e} is the eccentricity. The 'eccentric anomaly' E {\displaystyle
Kepler's_equation
Speed at which a body orbits around the barycenter of a system
the primary body equal to the radius of the orbit. For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with
Orbital_speed
Angle between a reference plane and the plane of an orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Orbital_inclination
Type of orbit
equation, which is used to solve for true anomalies in elliptical and hyperbolic trajectories, the true anomaly in Barker's equation can be solved directly
Parabolic_trajectory
Celestial orbit whose trajectory is a conic section in the orbital plane
and hyperbolic orbits. For an elliptic orbit one switches to the "eccentric anomaly" E for which and consequently and the angular momentum H is Integrating
Kepler_orbit
Satellite orbit with high inclination
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Polar_orbit
Measure of amount of effort to change trajectory
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Delta-v
Time an astronomical object takes to complete one orbit around another object
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Orbital_period
Amount by which an orbit deviates from a perfect circle
"out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center". "Eccentric" first appeared in English in 1551, with the definition "...a circle in
Orbital_eccentricity
Spacecraft end-of-life orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Graveyard_orbit
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
High_Earth_orbit
Concept in celestial mechanics
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Standard gravitational parameter
Standard_gravitational_parameter
Quasi-periodic orbital trajectory
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Lissajous_orbit
Orbit around Earth between 160 and 2000 km
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Low_Earth_orbit
Type of spacecraft maneuver
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Oberth_effect
Periodic, three-dimensional orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Near-rectilinear_halo_orbit
Orbit keeping the satellite at a fixed longitude above the equator
we care about orbital debris at all?". SpaceNews.com. "AMC 9 Satellite Anomaly associated with Energetic Event & sudden Orbit Change – Spaceflight101"
Geosynchronous_orbit
Characteristic of conic sections
low eccentricity; when they are very different, the orbit is said be eccentric or having eccentricity near unity. This definition coincides with the
Eccentricity_(mathematics)
Periodic, three-dimensional orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Halo_orbit
Topics referred to by the same term
eccentricity, in astrodynamics, a measure of the non-circularity of an orbit Eccentric anomaly, the angle between the direction of periapsis and the current position
Eccentricity
Orbital data format
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Two-line_element_set
Table of positions of astronomical objects at given times
13th century AD – the Alfonsine Tables were compiled in Spain to correct anomalies in the Tables of Toledo, remaining the standard European ephemeris until
Ephemeris
Quantities used in astronomy
First one calculates the mean anomaly M(t) at a time t: M = (t − T) · 360°/P (modulo 360°) Next, find the eccentric anomaly E, such that E = M + e sin(E)
Thiele−Innes_elements
Movement around a celestial body that remains below its Karman line
controlled impact area and no long term space debris in case of an in-orbit anomaly. Abort Once Around, a Space Shuttle abort mode requiring an incomplete
Transatmospheric_orbit
Orbit around the barycenter of the Sun
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Heliocentric_orbit
Mathematical equation describing the motion of a rocket
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Tsiolkovsky_rocket_equation
Defining the orbit of an object in space
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Longitude of the ascending node
Longitude_of_the_ascending_node
Trajectory of Earth around the Sun
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Earth's_orbit
Specifies the orbit of an object in space
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Argument_of_periapsis
Range of low orbital altitudes
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Very_low_Earth_orbit
Concept in orbital mechanics
node to the pericenter as the argument of periapsis, ω. Define the mean anomaly, M, as the angular distance from the periapsis which the body would have
Mean_longitude
Vector quantity in celestial mechanics
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Specific_angular_momentum
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Longitude_of_periapsis
Transfer orbit used to reach geosynchronous or geostationary orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Geostationary_transfer_orbit
Outdated measure of planetary orbits
the Earth and too much close to the Earth. For example, when the eccentric anomaly is π/2, the Keplerian model says that an amount of time of π / 2 −
Equant
Low-energy trajectories in the Solar System
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Interplanetary Transport Network
Interplanetary_Transport_Network
System for specifying positions of celestial objects
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Astronomical coordinate systems
Astronomical_coordinate_systems
Type of high-latitude satellite orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Molniya_orbit
Earth-centered orbit above low Earth orbit and below geostationary orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Medium_Earth_orbit
Orbit with a fixed distance from the barycenter
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Circular_orbit
Curved path of an object around a point
(Ω) Argument of periapsis (ω) Eccentricity (e) Semimajor axis (a) True anomaly at epoch (θ0). The orbital period is simply how long an orbiting body takes
Orbit
Quasiperiodic orbit around a Lagrange point
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Libration_point_orbit
Problem in physics and celestial mechanics
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
N-body_problem
Orbit about a small Solar System body
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Terminator_orbit
Orbit around Earth
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Geocentric_orbit
Angular speed required for a body to complete one orbit
AU}}}\approx k.} Mean motion also represents the rate of change of mean anomaly, and hence can also be calculated, n = M 1 − M 0 t 1 − t 0 = M 1 − M 0
Mean_motion
Region in which an astronomical body dominates the attraction of satellites
{1}{3({\frac {m_{1}}{m_{2}}}+1)}}}} where θ {\displaystyle \theta } is the true anomaly for the less massive body in its orbit around the more massive body, an
Hill_sphere
Circular areosynchronous orbit in the Martian equatorial plane
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Areostationary_orbit
Estimate of total change in velocity of a space mission
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Delta-v_budget
Type of geocentric orbit
i = 180°). A period longer than 3.8 hours may be possible by using an eccentric orbit with p < 12352 km but a > 12352 km. If a satellite is to fly over
Sun-synchronous_orbit
Orbit of an object around the Moon
orbits. These would be useful for long-term stays in LLO. Gravitational anomalies slightly distorting the orbits of some early lunar orbiters led to the
Lunar_orbit
Equilibrium points near two orbiting bodies
2007). "Equipotential Surfaces and Lagrangian Points in Nonsynchronous, Eccentric Binary and Planetary Systems". The Astrophysical Journal. 660 (2): 1624–1635
Lagrange_point
Circular orbit above Earth's Equator and following the direction of Earth's rotation
we care about orbital debris at all?". SpaceNews.com. "AMC 9 Satellite Anomaly associated with Energetic Event & sudden Orbit Change – Spaceflight101"
Geostationary_orbit
Propulsive maneuver used to arrive at the Moon
velocity, changing its orbit from a circular low Earth orbit to a highly eccentric orbit. The mission phase following TLI – while the spacecraft is flying
Trans-lunar_injection
around the sun), by converting true anomaly ν {\displaystyle \nu } to "eccentric anomaly": E = atan2 ( 1 − e 2 sin ν , e + cos ν ) {\displaystyle
Equation_of_the_center
Parameter in the gravitational two-body problem
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Specific_orbital_energy
Maintenance of a particular orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Orbital_station-keeping
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Radial_trajectory
is defined as period of original orbit E is defined as change of eccentric anomaly between spacecraft and final position e1 is defined as orbital eccentricity
Orbit_phasing
The Moon's circuit around Earth
longitude for the equinox of date is used. For the anomalistic year, the mean anomaly (λ−ω) is used (equinox does not matter). For the draconic month, (λ−Ω)
Orbit_of_the_Moon
Astrodynamic equation
{\displaystyle \mathbf {r} } makes with the axis of periapsis (also called the true anomaly). The parameter ℓ {\displaystyle \ell } is the angular momentum of the
Orbit_equation
Spaceflight where spacecraft orbits an astronomical body
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Orbital_spaceflight
Time period during which a rocket must launch to reach its target
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Launch_window
Spacecraft launch or descent maneuver
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Gravity_turn
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
List_of_orbits
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
very near that of the larger body, and if its orbit is a little more eccentric than that of the larger body, during every period it appears to trace
Horseshoe_orbit
Spaceflight maneuver
\omega \,} is the argument of periapsis f {\displaystyle f\,} is the true anomaly n {\displaystyle n\,} is the mean motion a {\displaystyle a\,} is the semi-major
Orbital_inclination_change
Orbit of an astronomical body equal to that body's average rotational period
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Synchronous_orbit
Orbital perturbations
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Osculating_orbit
Type of orbit around an astronomical body
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Near-equatorial_orbit
Plane curve
y)=(a\cos t,\,b\sin t),\ 0\leq t<2\pi \,.} The parameter t (called the eccentric anomaly in astronomy) is not the angle of ( x ( t ) , y ( t ) ) {\displaystyle
Ellipse
Kind of planetary orbit
Ariane 5 flight VA241. However, due to launch crew error resulting in anomaly and a deviation of the trajectory, the satellites were not inserted into
Supersynchronous_orbit
Transfer manoeuvre between two orbits
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Hohmann_transfer_orbit
Moment in time used as a reference point in astronomy
astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction
Epoch_(astronomy)
Temporary orbit used during the launch of a spacecraft
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Parking_orbit
Cartesian vectors of position and velocity of an orbiting body in space
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Orbital_state_vectors
Classical approach to the many-body problem of astronomy
orbits. In 25,000 years' time, Earth will have a more circular (less eccentric) orbit than Venus. It has been shown that long-term periodic disturbances
Perturbation_(astronomy)
Type of orbital maneuver
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Bi-elliptic_transfer
Complex type of orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Rosetta_orbit
Kind of planetary orbit
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Subsynchronous_orbit
American surveyor (1754–1820)
Andrew Ellicott, to Mr. Robert Patterson. A Method of Calculating the Eccentric Anomaly of the Planets." Transactions of the American Philosophical Society
Andrew_Ellicott
Fuel-efficient orbital maneuver
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Low-energy_transfer
Symbols for constants, special functions
ISBN 978-0-8176-3832-0. Introduce variables ζ and η related to the true anomaly f and the eccentric anomaly E by… Knuth, Donald (April–June 1976). "Big Omicron and big
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Movement during spaceflight
its orbit, usually described as adjusting the orbiting spacecraft's true anomaly. A space rendezvous is a sequence of orbital maneuvers during which two
Orbital_maneuver
Type of spacecraft orbit
Jones, Andrew (2024-03-14). "Surprise Chinese lunar mission hit by launch anomaly". SpaceNews. Retrieved 2024-03-14. Jones, Andrew (2024-08-20). "Chinese
Distant_retrograde_orbit
Space navigation technique
is usually executed in the Earth-Moon system. Dynamical friction Flyby anomaly, an anomalous delta-v increase during gravity assists Gravitational keyhole
Gravity_assist
Measure in astrodynamics
periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital
Characteristic_energy
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