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Concept in orbital mechanics
Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally
Mean_longitude
derived from the longitude of periapsis (e.g., mean longitude and true longitude) will also be compound. Sometimes, the term longitude of periapsis is
Longitude_of_periapsis
Parameters that define a specific orbit
for circular orbits. Mean longitude at epoch ( L0 ) — mean longitude at the epoch time. Mean longitude is similar to mean anomaly, in that it increases
Orbital_elements
Period of time for the ecliptic longitude of the Sun to increase 360°
the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever the longitude reaches
Tropical_year
Moment in time used as a reference point in astronomy
time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference
Epoch_(astronomy)
Specifies the orbit of an object in space
the mean longitude, the angular distance of the body from the same reference direction, assuming it moves with uniform angular motion as with the mean anomaly
Mean_anomaly
Book by Simon Newcomb
since "1900, Jan. 0, Greenwich Mean noon", measured in Julian centuries of 36,525 days. The Sun's geometric mean longitude, freed from aberration is given
Newcomb's_Tables_of_the_Sun
Defining the orbit of an object in space
The longitude of the ascending node, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit
Longitude of the ascending node
Longitude_of_the_ascending_node
System for specifying positions of celestial objects
ecliptic longitude β, ecliptic latitude Galactic coordinates l, galactic longitude b, galactic latitude Miscellaneous λo, observer's longitude ϕo, observer's
Astronomical coordinate systems
Astronomical_coordinate_systems
East-West geographic coordinate
Longitude (/ˈlɒndʒɪtjuːd/, AU and UK also /ˈlɒŋɡɪ-/) is a geographic coordinate that specifies the east-west position of a point on the surface of the
Longitude
Trajectory of Earth around the Sun
is the eccentricity. The reference lists the longitude of perihelion, which is the sum of the longitude of the ascending node and the argument of perihelion
Earth's_orbit
Orbit around Earth between 160 and 2000 km
this in turn corresponds to an altitude of 2,042 km (1,269 mi) above the mean radius of Earth, which is consistent with some of the upper altitude limits
Low_Earth_orbit
Either of two extreme points in a celestial object's orbit
the so-called longitude of the periapsis (also called longitude of the pericenter). For the orbit of the Earth, this is called the longitude of perihelion
Apsis
Internationally accepted civil calendar
long-standing obstacle to calendar reform. Ancient tables provided the Sun's mean longitude. The German mathematician Christopher Clavius, the architect of the
Gregorian_calendar
Type of geocentric orbit
revolution of the planet around the Sun, its orbital plane (specifically the longitude of the ascending node) precesses through one complete revolution around
Sun-synchronous_orbit
Alias for the UTC+00:00 time zone
navigation, it is considered equivalent to UT1 (the modern form of mean solar time at 0° longitude); but this meaning can differ from UTC by up to 0.9 s. The
Greenwich_Mean_Time
Laws describing planetary orbits
So the mean anomaly M is proportional to time t since perihelion: M = n t , {\displaystyle M=nt,} where n is the mean motion. When the mean anomaly M
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
The Moon's circuit around Earth
tropical month is similar, but the longitude for the equinox of date is used. For the anomalistic year, the mean anomaly (λ−ω) is used (equinox does
Orbit_of_the_Moon
Circular orbit above Earth's Equator and following the direction of Earth's rotation
area of the earth's surface, extending 81° away in latitude and 77° in longitude. They appear stationary in the sky, which eliminates the need for ground
Geostationary_orbit
Angle between a reference plane and the plane of an orbit
S2CID 126328423. Retrieved 27 February 2022. Heider, K.P. (3 April 2009). "The mean plane (invariable plane) of the Solar System passing through the barycenter"
Orbital_inclination
Equilibrium points near two orbiting bodies
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Lagrange_point
Orbit keeping the satellite at a fixed longitude above the equator
Geostationary satellites also tend to drift around one of two stable longitudes of 75° and 255° without station keeping. Many objects in geosynchronous
Geosynchronous_orbit
Speed at which a body orbits around the barycenter of a system
mass of the most massive body. The term can be used to refer to either the mean orbital speed (i.e. the average speed over an entire orbit) or its instantaneous
Orbital_speed
Movement around a celestial body that remains below its Karman line
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Transatmospheric_orbit
Table of positions of astronomical objects at given times
motion/planetary stations, planetary ingresses, sidereal time, positions for the mean and true nodes of the moon, the phases of the Moon, and the positions of
Ephemeris
Amount by which an orbit deviates from a perfect circle
eccentricity of 0.94, and then HD 80606 b of 0.93226 +0.00064 −0.00069. The mean eccentricity of an object is the average eccentricity as a result of perturbations
Orbital_eccentricity
Specifies the orbit of an object in space
reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis. However, especially in discussions
Argument_of_periapsis
Periodic, three-dimensional orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Near-rectilinear_halo_orbit
Type of spacecraft maneuver
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Oberth_effect
Orbital data format
Satellites within the TLE but instead a new format, the CCSDS OMM (Orbit Mean-Elements Message), started being used in 2020 that supports nine-digit Satellite
Two-line_element_set
Mathematical equation describing the motion of a rocket
following system: In the following derivation, "the rocket" is taken to mean "the rocket and all of its unexpended propellant". Newton's second law of
Tsiolkovsky_rocket_equation
Range of low orbital altitudes
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Very_low_Earth_orbit
Orbit around the barycenter of the Sun
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Heliocentric_orbit
Theoretical description of motion of Earth's moon
l {\displaystyle l} the Moon's mean anomaly (angular distance of the mean longitude of the Moon from the mean longitude of its perigee Γ {\displaystyle
Lunar_theory
Spacecraft end-of-life orbit
Orientation i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly
Graveyard_orbit
Celestial coordinate system used to describe Solar System objects
subject to small periodic oscillations. Ecliptic longitude Ecliptic longitude or celestial longitude (symbols: heliocentric ℓ, geocentric λ) measures
Ecliptic_coordinate_system
Concept in celestial mechanics
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Standard gravitational parameter
Standard_gravitational_parameter
Angle defining a position in an orbit
a position along an orbit, the other two being the true anomaly and the mean anomaly. Consider the ellipse with equation given by: x 2 a 2 + y 2 b 2 =
Eccentric_anomaly
Parameter of Keplerian orbits
because there is no uniquely determined line of nodes. One uses the true longitude instead: l = arccos r x | r | {\displaystyle l=\arccos {r_{x} \over
True_anomaly
Measure of amount of effort to change trajectory
non-reversed thrust. For rockets, "absence of external forces" is taken to mean the absence of gravity drag and atmospheric drag, as well as the absence
Delta-v
Periodic, three-dimensional orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Halo_orbit
Complex type of orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Rosetta_orbit
Spaceflight maneuver
primarily the argument of periapsis which is in turn connected to the longitude of the ascending node. This can result in two very different orbits with
Orbital_inclination_change
Kind of planetary orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Supersynchronous_orbit
Configuration of two or more astronomical objects
longitude of the periapsis difference and the mean longitude difference. The longitude of the periapsis is the sum of the mean longitude and the mean
Co-orbital_configuration
Quasi-periodic orbital trajectory
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Lissajous_orbit
Earth-centered orbit above low Earth orbit and below geostationary orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Medium_Earth_orbit
Time an astronomical object takes to complete one orbit around another object
a circular orbit barely above the surface of a sphere of any radius and mean density ρ (in kg/m3), the above equation simplifies to T = 3 π G ρ {\displaystyle
Orbital_period
Satellite orbit with high inclination
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Polar_orbit
Propulsive maneuver used to arrive at the Moon
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Trans-lunar_injection
Term in geometry; longest and shortest semidiameters of an ellipse
which an arbitrary point is given by (x, y). The semi-major axis is the mean value of the maximum and minimum distances r max {\displaystyle r_{\text{max}}}
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Type of orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Parabolic_trajectory
Orbital perturbations
and other planetary satellites), the orbit can be described by a set of mean elements with secular and periodic terms. In the case of minor planets, a
Osculating_orbit
Characteristic of conic sections
transformations. Classification of discrete distributions by variance-to-mean ratio; see cumulants of some discrete probability distributions for details
Eccentricity_(mathematics)
Angular speed required for a body to complete one orbit
Astronomy portal Gaussian gravitational constant Kepler orbit Mean anomaly Mean longitude Mean motion resonance Orbital elements Do not confuse μ, the gravitational
Mean_motion
Transfer orbit used to reach geosynchronous or geostationary orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Geostationary_transfer_orbit
Type of orbit around an astronomical body
is undefined, as well as its related classical orbital elements, the longitude of the ascending node and the argument of periapsis. In these cases, alternative
Near-equatorial_orbit
Cartesian vectors of position and velocity of an orbiting body in space
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Orbital_state_vectors
Fuel-efficient orbital maneuver
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Low-energy_transfer
Problem in physics and celestial mechanics
particle mesh methods, adaptive meshes can increase computational efficiency. Mean field methods approximate the system of particles with a time-dependent Boltzmann
N-body_problem
Measure in astrodynamics
respect to the Earth. When simplified to a two-body problem, this would mean the MAVEN escaped Earth on a hyperbolic trajectory slowly decreasing its
Characteristic_energy
Arab astronomer and clockmaker (1304–1375)
calculations to find the longitude of the planets. The longitude of the planets was defined as a function of the mean longitude and the anomaly. Rather
Ibn_al-Shatir
Concept in celestial mechanics
the term escape velocity can be ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. Escape velocity
Escape_velocity
Type of high-latitude satellite orbit
centered at the apogee passage, the longitudinal plane is almost fixed, the longitude of the satellite varies by only ±2.7°. The views of the Earth from these
Molniya_orbit
Orbit of an object around the Moon
000 kilometres, about one-sixth of the distance between it and Earth. For mean distance and mass data for the bodies (for verification of the foregoing
Lunar_orbit
Astrodynamic equation
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Orbit_equation
Curved path of an object around a point
his laws. These six Keplerian elements are as follows: Inclination (i) Longitude of the ascending node (Ω) Argument of periapsis (ω) Eccentricity (e) Semimajor
Orbit
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
000 kilometres, about one-sixth of the distance between it and Earth. For mean distance and mass data for the bodies (for verification of the foregoing
High_Earth_orbit
Kind of planetary orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Subsynchronous_orbit
In celestial mechanics, true longitude is the ecliptic longitude at which an orbiting body could actually be found if its inclination were zero. Together
True_longitude
Indian mathematician and astronomer (1114–1185)
PC Useful constants. An SI day or mean solar day equals 86400 SI seconds. From the mean longitude referred to the mean ecliptic and the equinox J2000 given
Bhāskara_II
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Areosynchronous_orbit
Celestial coordinate system
Apparent longitude is celestial longitude corrected for aberration and nutation as opposed to mean longitude. Apparent longitude is used in the definition
Apparent_longitude
Maintenance of a particular orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Orbital_station-keeping
Classical approach to the many-body problem of astronomy
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Perturbation_(astronomy)
Circular areosynchronous orbit in the Martian equatorial plane
Two stable longitudes exist - 17.92°W and 167.83°E. Satellites placed at any other longitude will tend to drift to these stable longitudes over time.
Areostationary_orbit
Orbit of an astronomical body equal to that body's average rotational period
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Synchronous_orbit
Time standard used in astronomical ephemerides
Sun's mean longitude at a time, indicated by interval T (in units of Julian centuries of 36525 mean solar days), reckoned from Greenwich Mean Noon on
Ephemeris_time
Concept in astrodynamics
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 is proportional to time
Hyperbolic_trajectory
Time in astronomy
Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This
Local_mean_time
Path on the surface of the Earth or another body directly below an aircraft or satellite
every day. This ground track is shifted east or west depending on the longitude of the ascending node, which can vary over time due to perturbations of
Satellite_ground_track
Temporary orbit used during the launch of a spacecraft
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Parking_orbit
Orbital plane that is tipped away from the equator
satellite to rise over a fixed location on the earth's surface at the same mean solar time every day. These orbits have an inclination governed by the equation:
Inclined_orbit
Time period during which a rocket must launch to reach its target
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Launch_window
Low-energy trajectories in the Solar System
Orientation i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly
Interplanetary Transport Network
Interplanetary_Transport_Network
Hindu god of the Moon
R\sin(m-a)}{360}}} – Surya Siddhanta II.39.43 where m is the Moon's mean longitude, a is the longitude at apogee, P is epicycle of apsis, R=3438'. Besides worship
Chandra
Type of astronomical orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Semi-synchronous_orbit
Type of spacecraft orbit
Orientation i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly
Distant_retrograde_orbit
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Horseshoe_orbit
Martian orbit around the Sun
March 2020. Retrieved 22 March 2020.; Mean Anomaly (deg) 19.412 = (Mean Longitude (deg) 355.45332) – (Longitude of perihelion (deg) 336.04084) This article
Orbit_of_Mars
Field of classical mechanics concerned with the motion of spacecraft
M = E − ϵ sin E , {\displaystyle M=E-\epsilon \sin E,} where M is the mean anomaly, E is the eccentric anomaly, and ϵ {\displaystyle \epsilon } is the
Orbital_mechanics
Quasiperiodic orbit around a Lagrange point
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Libration_point_orbit
Vector quantity in celestial mechanics
Orientation i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis Position M Mean anomaly ν, θ, f True anomaly
Specific_angular_momentum
Highly elliptical and highly inclined synchronous orbit
inclination, e {\displaystyle e} is the eccentricity, n {\displaystyle n} is mean motion in degrees per day, J 2 {\displaystyle J_{2}} is the perturbing factor
Tundra_orbit
Orbit around Earth
the height of an object above the average surface of the Earth's oceans (mean sea level). Analemma a term in astronomy used to describe the plot of the
Geocentric_orbit
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
List_of_orbits
Transfer manoeuvre between two orbits
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Hohmann_transfer_orbit
Islamic mathematician (c. 780 – c. 850)
Jewish year and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Hebrew calendar. Similar material
Al-Khwarizmi
Spaceflight where spacecraft orbits an astronomical body
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Orbital_spaceflight
Space navigation technique
f True anomaly E Eccentric anomaly L Mean longitude l True longitude Variation T Orbital period n Mean motion v Orbital speed t0 Epoch Maneuvers
Gravity_assist
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