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Type of orbital maneuver
In astronautics and aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in
Bi-elliptic_transfer
Transfer manoeuvre between two orbits
In some cases where one orbit is much larger than the other, a bi-elliptic transfer can use even less impulse, at the cost of even greater travel time
Hohmann_transfer_orbit
Movement during spaceflight
require less delta-v than a Hohmann transfer maneuver. The bi-elliptic transfer consists of two half elliptic orbits. From the initial orbit, a delta-v
Orbital_maneuver
Elliptical orbit used to move a spacecraft from one circular orbit to another
used to transfer a spacecraft between two circular orbits of different altitudes in the same plane Bi-elliptic transfer, a slower method of transfer, but
Transfer_orbit
Fuel-efficient orbital maneuver
spend much time within 10 km of the surface. Spaceflight portal Bi-elliptic transfer Delta-v budget Gravity assist Interplanetary Transport Network Orbital
Low-energy_transfer
Kepler orbit with an eccentricity of less than one
elongated orbit (e near 1). Examples of elliptic orbits or trajectories for satellites include Hohmann transfer orbits, Molniya orbits, and tundra orbits
Elliptic_orbit
Field of classical mechanics concerned with the motion of spacecraft
middle. The Hohmann transfer orbit requires a minimal delta-v. A bi-elliptic transfer can require less energy than the Hohmann transfer, if the ratio of
Orbital_mechanics
Estimate of total change in velocity of a space mission
Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bi-elliptic transfer
Delta-v_budget
Speed at which a body orbits around the barycenter of a system
interaction with a planet. Escape velocity Delta-v budget Hohmann transfer orbit Bi-elliptic transfer Lissauer, Jack J.; de Pater, Imke (2019). Fundamental Planetary
Orbital_speed
Orbit around the barycenter of the Sun
possible energy requirements. Transfer injections can place spacecraft into either a Hohmann transfer orbit or bi-elliptic transfer orbit. Trans-Mars injections
Heliocentric_orbit
Type of spacecraft maneuver
later when they are burned. Astronomy portal Spaceflight portal Bi-elliptic transfer Gravity assist Propulsive efficiency Robert B. Adams, Georgia A.
Oberth_effect
Application of mechanical dynamics to model the flight of space vehicles
While this takes a longer transfer time, a bi-elliptic transfer can require less total propellant than the Hohmann transfer when the ratio of initial
Spacecraft_flight_dynamics
Transfer orbit used to reach geosynchronous or geostationary orbit
space mission design, a geostationary transfer orbit (GTO) or geosynchronous transfer orbit is a highly elliptical type of geocentric orbit, usually with
Geostationary_transfer_orbit
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
Mathematical equation describing the motion of a rocket
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Tsiolkovsky_rocket_equation
Laws describing planetary orbits
heliostatic model of the planets with a heliocentric model that described elliptical orbits with planetary velocities that vary accordingly. The three laws
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Periodic, three-dimensional orbit
2024. SOHO – The Trip to the L1 Halo Orbit Low Energy Interplanetary Transfers Using Halo Orbit Hopping Method with STK/Astrogator Gaia's Lissajous Type
Halo_orbit
Either of two extreme points in a celestial object's orbit
comets, and the asteroids of the Solar System. There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ap-, apo- (from
Apsis
Equilibrium points near two orbiting bodies
magnetospheric effects, and from having direct line-of-sight to Earth for data transfer. The three collinear Lagrange points (L1, L2, L3) were discovered by the
Lagrange_point
Amount by which an orbit deviates from a perfect circle
circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic (escape orbit or capture orbit), and greater than
Orbital_eccentricity
Parameter in the gravitational two-body problem
{{\text{km}}^{2}}{{\text{s}}^{2}}}} (squared kilometer per squared second). For an elliptic orbit the specific orbital energy is the negative of the additional energy
Specific_orbital_energy
Orbit keeping the satellite at a fixed longitude above the equator
geosynchronous satellites directly into a geosynchronous transfer orbit (GTO), an elliptical orbit with an apogee at GSO height and a low perigee. On-board
Geosynchronous_orbit
Concept in gravitational orbital mechanics
lost in the system while the work is being done. For any Keplerian orbit (elliptic, parabolic, hyperbolic, or radial), the vis-viva equation is as follows:
Vis-viva_equation
Polish-Russian early spaceflight scientist
death he worked in Moscow. He was the first person to describe the bi-elliptic transfer technique of changing orbits, in 1934. In 1934, Sternfeld won the
Ary_Abramovich_Sternfeld
Concept in celestial mechanics
angular speed, and T is the orbital period. This can be generalized for elliptic orbits: μ = 4 π 2 a 3 T 2 , {\displaystyle \mu ={\frac {4\pi ^{2}a^{3}}{T^{2}}}
Standard gravitational parameter
Standard_gravitational_parameter
Angle between a reference plane and the plane of an orbit
ISBN 0-521-54620-6. Arctic Communications System Utilizing Satellites in Highly Elliptical Orbits, Lars Løge – Section 3.1, Page 17 Moon formation and orbital evolution
Orbital_inclination
Term in geometry; longest and shortest semidiameters of an ellipse
orbital period T of a small body orbiting a central body in a circular or elliptical orbit is: T = 2 π a 3 μ , {\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{\mu
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Time an astronomical object takes to complete one orbit around another object
orbital period T of two point masses orbiting each other in a circular or elliptic orbit is: T = 2 π a 3 G M {\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{GM}}}}
Orbital_period
Concept in celestial mechanics
gravitational influence of the primary. If an object is in a circular or elliptical orbit, its speed is always less than the escape speed at its current distance
Escape_velocity
Center of mass of multiple bodies orbiting each other
the Solar System's barycenter. The barycenter is one of the foci of the elliptical orbit of each body. This is an important concept in the fields of astronomy
Barycenter_(astronomy)
Problem in physics and celestial mechanics
Keplerian trajectories (elliptical, circular, parabolic, or hyperbolic), with all trajectories having the same eccentricity e. For elliptical trajectories, e
N-body_problem
Concept in astrodynamics
the planet's sphere of influence using hyperbolic trajectories. Like an elliptical orbit, a hyperbolic trajectory for a given system can be defined (ignoring
Hyperbolic_trajectory
Table of positions of astronomical objects at given times
Tycho Brahe. 1627 – the Rudolphine Tables of Johannes Kepler based on elliptical planetary motion became the new standard. 1679 – La Connaissance des Temps
Ephemeris
Horizontal angle from north or other reference cardinal direction
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Azimuth
Quasi-periodic orbital trajectory
science fiction novel Artemis by Andy Weir, a Lissajous orbit is used as a transfer point for routine travel to and from the Moon. Libration point orbit Possibly
Lissajous_orbit
Propulsive maneuver used to arrive at the Moon
As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with an apogee near to the
Trans-lunar_injection
Orbital data format
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Two-line_element_set
Measure of amount of effort to change trajectory
velocity changes due to gravity, e.g. in an elliptic orbit. For examples of calculating delta-v, see Hohmann transfer orbit, gravitational slingshot, and Interplanetary
Delta-v
Earth-centered orbit above low Earth orbit and below geostationary orbit
velocity Geostationary Earth orbit (GEO) High Earth orbit (HEO) Highly elliptical orbit (HEO) Graveyard orbit International Space Station List of orbits
Medium_Earth_orbit
The Moon's circuit around Earth
distance in the orbit (of ELP) which is the semimajor axis of the Moon's elliptical orbit via Kepler's laws. The constant in the ELP expressions for the distance
Orbit_of_the_Moon
Orbit with a fixed distance from the barycenter
units: v = G M r − r S {\displaystyle v={\sqrt {\frac {GM}{r-r_{S}}}}} Elliptic orbit List of orbits Two-body problem Lissauer, Jack J.; de Pater, Imke
Circular_orbit
Circular orbit above Earth's Equator and following the direction of Earth's rotation
place geostationary satellites directly into a geostationary transfer orbit (GTO), an elliptical orbit with an apogee at GEO height and a low perigee. On-board
Geostationary_orbit
Classical approach to the many-body problem of astronomy
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Perturbation_(astronomy)
Specifies the orbit of an object in space
In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed
Mean_anomaly
Region in which an astronomical body dominates the attraction of satellites
{\sqrt[{3}]{\frac {m}{3M}}}.} If the orbit of the secondary about the primary is elliptical, the Hill radius is maximum at the apocenter, where r {\displaystyle r}
Hill_sphere
Orbit around Earth between 160 and 2000 km
sources define LEO in terms of altitude. The altitude of an object in an elliptic orbit can vary significantly along the orbit. Even for circular orbits
Low_Earth_orbit
Specifies the orbit of an object in space
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Argument_of_periapsis
Characteristic of conic sections
conic sections by eccentricity: Classification of elements of SL2(R) as elliptic, parabolic, and hyperbolic – and similarly for classification of elements
Eccentricity_(mathematics)
Balloon — Ballute — Beam-powered propulsion — Bernoulli's equation — Bi-elliptic transfer — Big dumb booster — Bipropellant rocket — Bleed air — Booster rocket
Index of aerospace engineering articles
Index_of_aerospace_engineering_articles
Space navigation technique
gravitational slingshot encounters with Earth Delta-v budget Low-energy transfer, a type of gravitational assist where a spacecraft is gravitationally snagged
Gravity_assist
Type of orbit
equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape
Parabolic_trajectory
Branch of engineering
quantitative methods. Noise control – the study of the mechanics of sound transfer. Aeroacoustics – the study of noise generation via either turbulent fluid
Aerospace_engineering
Spacecraft end-of-life orbit
graveyard orbit is a few hundred kilometers beyond the operational orbit. The transfer to a graveyard orbit beyond geostationary orbit requires the same amount
Graveyard_orbit
traces the path of an ellipse. Geostationary or geosynchronous transfer orbit (GTO): An elliptic orbit where the perigee is at the altitude of a low Earth
List_of_orbits
Satellite orbit with high inclination
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Polar_orbit
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
HEO use this orbit. A special case of a high Earth orbit is the highly elliptical orbit where altitude at perigee may reach as low as 2,000 km (1,200 mi)
High_Earth_orbit
Trajectory of Earth around the Sun
relationship between the lines of solstices, equinoxes, and apsides of Earth's elliptical orbit. The six Earth images are positions along the orbital ellipse, which
Earth's_orbit
Region of space gravitationally dominated by a given body
x. hdl:11449/42361. ISSN 0035-8711. Seefelder, Wolfgang (2002). Lunar Transfer Orbits Utilizing Solar Perturbations and Ballistic Capture. Munich: Herbert
Sphere of influence (astrodynamics)
Sphere_of_influence_(astrodynamics)
Point where an orbit crosses a plane of reference to which it is inclined
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Orbital_node
Kind of planetary orbit
a supersynchronous elliptical transfer orbit, an orbit with a somewhat larger apogee than the more typical geostationary transfer orbit (GTO) typically
Supersynchronous_orbit
Parameter of Keplerian orbits
orbit, the other two being the eccentric anomaly and the mean anomaly. For elliptic orbits, the true anomaly ν can be calculated from orbital state vectors
True_anomaly
Angle defining a position in an orbit
parameter that defines the position of a body that is moving along an elliptic Kepler orbit, the angle measured at the center of the ellipse between the
Eccentric_anomaly
Astrodynamic equation
as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory)
Orbit_equation
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Longitude_of_periapsis
Type of geocentric orbit
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Sun-synchronous_orbit
{\displaystyle r_{min}} . Spaceflight portal Bi-elliptic transfer Delta-v budget Geostationary transfer orbit Halo orbit Lissajous orbit List of orbits
Low thrust relative orbital transfer
Low_thrust_relative_orbital_transfer
Moment in time used as a reference point in astronomy
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Epoch_(astronomy)
Process that leads to gradual decrease of the distance between two orbiting bodies
propulsion is approximately 150 km (93 mi) while the lowest perigee of an elliptical revolution is approximately 90 km (56 mi). A simplified decay model for
Orbital_decay
Periodic, three-dimensional orbit
than those of an elliptical orbit of the same maximum diameter, and other segments have a curvature less than that of an elliptical orbit of the same
Near-rectilinear_halo_orbit
Circular areosynchronous orbit in the Martian equatorial plane
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Areostationary_orbit
Parameters that define a specific orbit
and periapsis (long axis of the ellipse). This value is positive for elliptical orbits, undefined for parabolic trajectories, and negative for hyperbolic
Orbital_elements
Spaceflight operation
Higher energy orbits like geostationary orbit are often reached via elliptical transfer orbits. One type of orbit insertion is used when capturing into orbit
Orbit_insertion
straight line. There are three types of radial trajectories (orbits). Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse
Radial_trajectory
Orbit of an object around the Moon
the Moon was Lunar Orbiter 1 on August 14, 1966. The first orbit was an elliptical orbit, with an apolune of 1,008 nautical miles (1,867 km; 1,160 mi) and
Lunar_orbit
Spaceflight where spacecraft orbits an astronomical body
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Orbital_spaceflight
Concept in orbital mechanics
circular orbit, in the same orbital period as the actual body in its elliptical orbit. From these definitions, the mean longitude, L, is the angular distance
Mean_longitude
Concept in aerospace engineering
orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit
Propellant_mass_fraction
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
because the gravitational attraction of the Earth changes the shape of the elliptical orbit of the asteroid. The shape changes are very small but result in
Horseshoe_orbit
System for specifying positions of celestial objects
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Astronomical coordinate systems
Astronomical_coordinate_systems
Type of orbit around an astronomical body
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Near-equatorial_orbit
Spaceflight maneuver
[citation needed] For Hohmann transfer orbits, the initial orbit and the final orbit are 180 degrees apart. Because the transfer orbital plane has to include
Orbital_inclination_change
List of definitions of terms and concepts commonly used in aerospace engineering
require less delta-v than a Hohmann transfer maneuver. The bi-elliptic transfer consists of two half-elliptic orbits. From the initial orbit, a first
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Measure in astrodynamics
was negative, and MAVEN – instead of heading to infinity – entered an elliptical orbit around the Sun. But the maximal velocity on the new orbit could
Characteristic_energy
Motion problem in classical mechanics
of a pair of such objects will orbit their mutual center of mass in an elliptical pattern, unless they are moving fast enough to escape one another entirely
Two-body_problem
Highly elliptical and highly inclined synchronous orbit
A Tundra orbit (Russian: орбита «Тундра») is a highly elliptical geosynchronous orbit with a high inclination (approximately 63.4°), an orbital period
Tundra_orbit
Orbital mechanics term
with a specific type of orbit. The standard Kepler equation is used for elliptic orbits ( 0 ≤ e < 1 {\displaystyle 0\leq e<1} ). The hyperbolic Kepler equation
Kepler's_equation
Maintenance of a particular orbit
symmetry of the Earth relative the North/South axis, sometimes called the ellipticity of the Earth equator. The eccentricity (i.e. the eccentricity vector)
Orbital_station-keeping
Cartesian vectors of position and velocity of an orbiting body in space
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Orbital_state_vectors
Defining the orbit of an object in space
plane can cause precession of the ascending node. Parameters Describing Elliptical Orbits, web page, accessed May 17, 2007. Orbital Elements and Astronomical
Longitude of the ascending node
Longitude_of_the_ascending_node
Vector quantity in celestial mechanics
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Specific_angular_momentum
Complex type of orbit
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Rosetta_orbit
Range of low orbital altitudes
rural internet access among others. Spacecraft may be put into a highly elliptical orbit around Earth with a perigee as low as 80 to 90 km (50 to 56 mi)
Very_low_Earth_orbit
Curved path of an object around a point
non-repeating trajectory. To a close approximation, planets, and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse
Orbit
Type of high-latitude satellite orbit
communications and remote sensing coverage over high latitudes. It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270
Molniya_orbit
Path on the surface of the Earth or another body directly below an aircraft or satellite
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Satellite_ground_track
Orbit around Earth
circle. Elliptic orbit An orbit with an eccentricity greater than 0 and less than 1 whose orbit traces the path of an ellipse. Hohmann transfer orbit An
Geocentric_orbit
Low-energy trajectories in the Solar System
energy, transport along the network would take a long time. Interplanetary transfer orbits are solutions to the gravitational three-body problem, which, for
Interplanetary Transport Network
Interplanetary_Transport_Network
Movement around a celestial body that remains below its Karman line
t0 Epoch Maneuvers Bi-elliptic transfer Collision avoidance (spacecraft) Delta-v Delta-v budget Gravity assist Gravity turn Hohmann transfer Inclination change
Transatmospheric_orbit
Orbit of an astronomical body equal to that body's average rotational period
and south above a point on the planet's equator, whereas a body in an elliptical orbit will appear to oscillate eastward and westward. As seen from the
Synchronous_orbit
Time period during which a rocket must launch to reach its target
agencies. To go to another planet using the simple low-energy Hohmann transfer orbit, if eccentricity of orbits is not a factor, launch periods are periodic
Launch_window
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