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Concept in astrodynamics
or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit (from Newtonian theory: hyperbola shape) is the trajectory of any object around a central
Hyperbolic_trajectory
Type of orbit
Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits. In 1609
Parabolic_trajectory
Concept in celestial mechanics
escape speed at its current distance. In contrast if it is on a hyperbolic trajectory its speed will always be higher than the escape speed at its current
Escape_velocity
Amount by which an orbit deviates from a perfect circle
Circular orbit: e = 0 Elliptic orbit: 0 < e < 1 Parabolic trajectory: e = 1 Hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E
Orbital_eccentricity
Field of classical mechanics concerned with the motion of spacecraft
body traveling along a hyperbolic trajectory will attain at r = ∞ {\displaystyle r=\infty } an orbital velocity called hyperbolic excess velocity ( v ∞
Orbital_mechanics
Interstellar comet in 2025
Last Alert System (ATLAS) station. The comet follows an unbound, hyperbolic trajectory past the Sun, and passed by Earth at 1.8 AU, posing no threat. The
3I/ATLAS
Astrodynamic equation
(i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two
Orbit_equation
Kepler orbit with an eccentricity of less than one
the length of the semi-major axis. The velocity equation for a hyperbolic trajectory has either ( + 1 a ) {\displaystyle (+{1 \over {a}})} , or it is
Elliptic_orbit
Method to calculate trajectory calculations for spacecraft
multi-body trajectory. On an Earth-to-Mars transfer, a hyperbolic trajectory is required to escape from Earth's gravity well, then an elliptic or hyperbolic trajectory
Patched_conic_approximation
Speed at which a body orbits around the barycenter of a system
hyperbolic trajectory If the total energy is zero, (Ek = Ep): the orbit is a parabola with focus at the other body. See radial parabolic trajectory.
Orbital_speed
Interstellar object that passed near Earth in 2017
October. A two-week observation arc had verified a strongly hyperbolic trajectory. It has a hyperbolic excess velocity (velocity at infinity, v ∞ {\displaystyle
1I/ʻOumuamua
Celestial orbit whose trajectory is a conic section in the orbital plane
Kepler's laws of planetary motion Elliptic orbit Hyperbolic trajectory Parabolic trajectory Radial trajectory Orbit modeling Copernicus. pp 513–514 Bate, Mueller
Kepler_orbit
Propulsive maneuver used to arrive at the Moon
of influence, making a hyperbolic lunar swingby. In some cases it is possible to design a TLI to target a free return trajectory, so that the spacecraft
Trans-lunar_injection
Parameters that define a specific orbit
parabolic trajectories, and negative for hyperbolic trajectories, which can hinder its usability when working with different types of trajectories. Semi-minor
Orbital_elements
Measure in astrodynamics
about 160–164 km2/s2. Specific orbital energy Orbit Parabolic trajectory Hyperbolic trajectory Wie, Bong (1998). "Orbital Dynamics". Space Vehicle Dynamics
Characteristic_energy
Transfer manoeuvre between two orbits
"Trajectories". Retrieved 26 July 2017. Also available spaceodyssey.dmns.org Archived 2017-07-28 at the Wayback Machine. Tyson Sparks, Trajectories to
Hohmann_transfer_orbit
Orbit around Earth
at this velocity will enter a parabolic trajectory; above this velocity it will enter a hyperbolic trajectory. Impulse the integral of a force over the
Geocentric_orbit
Time an astronomical object takes to complete one orbit around another object
gravitational constant. In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite. For celestial objects
Orbital_period
Specifies the orbit of an object in space
between the attractor and the object following the trajectory increases linearly with time. For the hyperbolic case, there is a formula similar to the above
Mean_anomaly
Parameter in the gravitational two-body problem
equation simplifies to ε = 0. {\displaystyle \varepsilon =0.} For a hyperbolic trajectory this specific orbital energy is either given by ε = μ 2 a . {\displaystyle
Specific_orbital_energy
Astronomical object not gravitationally bound to a star
Solar System, where it can be distinguished by its strongly hyperbolic trajectory and hyperbolic excess velocity of more than a few km/s, proving that it
Interstellar_object
bodies move away from each other or towards each other. Radial hyperbolic trajectory: a non-periodic orbit where the relative speed of the two objects
Radial_trajectory
Either of two extreme points in a celestial object's orbit
Distance of closest approach Eccentric anomaly Flyby (spaceflight) Hyperbolic trajectory § Closest approach Mean anomaly Perifocal coordinate system True
Apsis
velocity. Radial hyperbolic orbit: An open hyperbolic orbit where the object is moving at greater than the escape velocity. This is a hyperbolic orbit with
List_of_orbits
Ganymede. After this slingshot maneuver, it will possibly enter a hyperbolic trajectory around the Sun and eventually leave the Solar System. Ulysses is
List of artificial objects leaving the Solar System
List_of_artificial_objects_leaving_the_Solar_System
Fuel-efficient orbital maneuver
Nitty-Gritty of Trajectory Design Earth-to-Moon Low Energy Transfers Targeting L1 Hyperbolic Transit Orbit June 2005 Low Energy Trajectories and Chaos: Applications
Low-energy_transfer
Hyperbolic comet
(perihelion) in March 1982. It is leaving the Solar System on a hyperbolic trajectory due to a close approach to Jupiter. In the 43 years since its discovery
C/1980_E1_(Bowell)
Term in geometry; longest and shortest semidiameters of an ellipse
a = μ 2 ε {\displaystyle a={\frac {\mu }{2\varepsilon }}} for a hyperbolic trajectory, and ε = v 2 2 − μ | r | {\displaystyle \varepsilon ={\frac {v^{2}}{2}}-{\frac
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Proposed NASA space probe to travel 1000 AU from the Sun
launch between 2036 and 2041. The probe would launch on a direct hyperbolic trajectory to encounter Jupiter after six to seven months, after which the
Interstellar Probe (spacecraft)
Interstellar_Probe_(spacecraft)
The Moon's circuit around Earth
common[clarification needed] to draw the trajectory of Earth from the point of view of the Sun, and at the same time the trajectory of the Moon from the point of
Orbit_of_the_Moon
Plane curve: conic section
and hyperbolas. Hyperbolic growth Hyperbolic partial differential equation Hyperbolic sector Hyperboloid structure Hyperbolic trajectory Hyperboloid Multilateration
Hyperbola
Experiments proving existence of atomic nuclei
will take a hyperbolic trajectory in the repulsive force near the centre of the atom as shown in Figure 2. To apply the hyperbolic trajectory solutions
Rutherford scattering experiments
Rutherford_scattering_experiments
Table of positions of astronomical objects at given times
ἐφημερίς (ephēmerís) 'diary, journal') is a book with tables that gives the trajectory of naturally occurring astronomical objects and artificial satellites
Ephemeris
Trajectory of Earth around the Sun
known as the obliquity of the ecliptic), the inclination of the Sun's trajectory in the sky (as seen by an observer on Earth's surface) varies over the
Earth's_orbit
Space navigation technique
A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun. A close terrestrial analogy is provided
Gravity_assist
Orbit around Earth between 160 and 2000 km
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Low_Earth_orbit
Motion of launched objects due to gravity
sports science and natural phenomena. Galileo Galilei showed that the trajectory of a given projectile is parabolic, but the path may also be straight
Projectile_motion
Earth-centered orbit above low Earth orbit and below geostationary orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Medium_Earth_orbit
Measure of amount of effort to change trajectory
than mass ratios which would require multiplication. When designing a trajectory, delta-v budget is used as a good indicator of how much propellant will
Delta-v
Type of high-latitude satellite orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Molniya_orbit
Concept in celestial mechanics
is Kepler's third law. For parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits magnitude of μ = 2 times the magnitude
Standard gravitational parameter
Standard_gravitational_parameter
Spacecraft launch or descent maneuver
an orbit around a celestial body such as a planet or a moon. It is a trajectory optimization that uses gravity solely through the vehicle's own thrust
Gravity_turn
Physical interaction of charged particles
will take a hyperbolic trajectory in the repulsive force near the centre of the atom as shown in Figure 2. To apply the hyperbolic trajectory solutions
Coulomb_scattering
Characteristic of conic sections
eccentricity: Classification of elements of SL2(R) as elliptic, parabolic, and hyperbolic – and similarly for classification of elements of PSL2(R), the real Möbius
Eccentricity_(mathematics)
Mathematical equation describing the motion of a rocket
− 1 e 2 x + 1 {\textstyle \tanh x={\frac {e^{2x}-1}{e^{2x}+1}}} (see Hyperbolic function), this is equivalent to Δ v = c tanh ( v e c ln m 0 m 1 )
Tsiolkovsky_rocket_equation
Curved path of an object around a point
speeds the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free"
Orbit
Equilibrium points near two orbiting bodies
an orbiting object and cannot be modeled as a contour map) curves the trajectory into a path around (rather than away from) the point. Because the source
Lagrange_point
Temporary orbit used during the launch of a spacecraft
a trajectory to the parking orbit, then coasts for a while, then engines fire again to enter the final desired trajectory. An alternative trajectory that
Parking_orbit
Orbital data format
correctly compute the state at a time of interest. TLEs can describe the trajectories only of Earth-orbiting objects. TLEs are widely used as input for projecting
Two-line_element_set
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
Laws describing planetary orbits
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Range of low orbital altitudes
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Very_low_Earth_orbit
Angle between a reference plane and the plane of an orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Orbital_inclination
Orbital perturbations
(non-rotating) inertial reference frame. Put in more general terms, a perturbed trajectory can be analysed as if assembled of points, each of which is contributed
Osculating_orbit
Orbit around the barycenter of the Sun
orbit in which a propulsive maneuver is used to set a spacecraft on a trajectory, also known as Mars transfer orbit, which will place it as far as Mars
Heliocentric_orbit
System for specifying positions of celestial objects
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Astronomical coordinate systems
Astronomical_coordinate_systems
Quasi-periodic orbital trajectory
Animation of WMAP's trajectory In orbital mechanics, a Lissajous orbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic
Lissajous_orbit
Orbit keeping the satellite at a fixed longitude above the equator
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Geosynchronous_orbit
Type of spacecraft maneuver
{{2V_{\text{esc}}}{\Delta v}}}.} Similar effects happen in closed and hyperbolic orbits. If the vehicle travels at velocity v at the start of a burn that
Oberth_effect
Movement during spaceflight
modelled as a point mass for preliminary design purposes. A low-thrust trajectory is typically computed using optimal control theory. In astronautics, the
Orbital_maneuver
Spacecraft end-of-life orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Graveyard_orbit
(LINEAR) Hyperbolic trajectory N/A N/A N/A LINEAR C/1999 S4 (LINEAR) Hyperbolic trajectory N/A N/A N/A LINEAR C/1999 T2 (LINEAR) Hyperbolic trajectory N/A
List of comets discovered by the LINEAR project
List_of_comets_discovered_by_the_LINEAR_project
Circular orbit above Earth's Equator and following the direction of Earth's rotation
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Geostationary_orbit
Spaceflight where spacecraft orbits an astronomical body
placed on a trajectory where it could remain in space for at least one orbit. To do this around the Earth, it must be on a free trajectory which has an
Orbital_spaceflight
Natural object in space that releases gas
v_{\infty }\!} ) and have notably hyperbolic trajectories. A rough calculation shows that there might be four hyperbolic comets per century within Jupiter's
Comet
Application of mechanical dynamics to model the flight of space vehicles
accurate for interplanetary trajectories than for translunar trajectories. The patch point between the hyperbolic trajectory relative to the departure planet
Spacecraft_flight_dynamics
Defining the orbit of an object in space
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Longitude of the ascending node
Longitude_of_the_ascending_node
Type of geocentric orbit
Bibcode:1992ESABu..72...76R. Low, Samuel Y. W. (January 2022). "Designing a Reference Trajectory for Frozen Repeat Near-Equatorial Low Earth Orbits". AIAA Journal of Spacecraft
Sun-synchronous_orbit
Orbital mechanics term
0 ≤ e < 1 {\displaystyle 0\leq e<1} ). The hyperbolic Kepler equation is used for hyperbolic trajectories ( e > 1 {\displaystyle e>1} ). The radial Kepler
Kepler's_equation
Periodic, three-dimensional orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Near-rectilinear_halo_orbit
Moment in time used as a reference point in astronomy
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Epoch_(astronomy)
Chart used to plan spacecraft launches
goals before the end of the fiscal year 1981. Orbit Parabolic trajectory Hyperbolic trajectory Goldman, Elliot. "Launch Window Optimization: The 2005 Mars
Porkchop_plot
Path on the surface of the Earth or another body directly below an aircraft or satellite
with eccentricity less than one, and thus excludes parabolic and hyperbolic trajectories. Direct orbits are by far the most common for artificial satellites
Satellite_ground_track
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Orbit_phasing
Orbital radius at which a satellite might break up due to gravitational force
case (for example) of a body passing the primary on a parabolic or hyperbolic trajectory. The rigid-body Roche limit is a simplified calculation for a spherical
Roche_limit
Astronomical database
passing stars it is impossible to know if an object with a weak hyperbolic trajectory will truly be ejected or gently nudged back inward. The galactic
JPL Horizons On-Line Ephemeris System
JPL_Horizons_On-Line_Ephemeris_System
Estimate of total change in velocity of a space mission
propulsion system. Delta-v is a scalar quantity dependent only on the desired trajectory and not on the mass of the space vehicle. For example, although more fuel
Delta-v_budget
Quasiperiodic orbit around a Lagrange point
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Libration_point_orbit
Second brightest naked-eye comet of 2020
arc was needed to refine the uncertainties and either confirm its hyperbolic trajectory, or determine its orbital period of thousands or millions of years
C/2020_F8_(SWAN)
Highly elliptical and highly inclined synchronous orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Tundra_orbit
Entrance of one object in another's orbit
passing object (perturbations), eventually putting the object on a hyperbolic trajectory. Rogue planets can theoretically be formed in this way, and planets
Gravitational_capture
Complex type of orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Rosetta_orbit
Series of orbital maneuvers
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Space_rendezvous
Classical approach to the many-body problem of astronomy
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Perturbation_(astronomy)
Possibly hyperbolic comet
experiencing a planetary encounter. C/1980 E1 (Bowell) reached a hyperbolic trajectory after an encounter with Jupiter on 9 December 1980. C/2024 L5 experienced
C/2024_L5_(ATLAS)
Specifies the orbit of an object in space
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Argument_of_periapsis
Low-energy trajectories in the Solar System
The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points
Interplanetary Transport Network
Interplanetary_Transport_Network
Satellite orbit with high inclination
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Polar_orbit
Angle defining a position in an orbit
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Eccentric_anomaly
Orbit of an object around the Moon
perturbations that make most unstable, and leave only a few orbital trajectories possible for indefinite frozen orbits. These would be useful for long-term
Lunar_orbit
Thought experiment about gravity
will leave Earth in a parabolic (at exactly escape velocity) or hyperbolic trajectory. Newton's original plan for Philosophiæ Naturalis Principia Mathematica
Newton's_cannonball
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
When the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces
Horseshoe_orbit
Periodic, three-dimensional orbit
travel between stars or planets Lissajous orbit – Quasi-periodic orbital trajectory, another Lagrangian-point orbit which generalizes halo orbits. Near-rectilinear
Halo_orbit
Non-periodic comet
Boris Skorichenko and Doug George on December 17, 1989. It has a hyperbolic trajectory around the Sun, but still weakly bound to it by its barycenter.
C/1989 Y1 (Skorichenko–George)
C/1989_Y1_(Skorichenko–George)
Great Comet of 2024
planetary perturbations, the outbound orbit will become hyperbolic. This weakly hyperbolic trajectory may or may not result in the comet being ejected from
Comet_Tsuchinshan–ATLAS
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Longitude_of_periapsis
Orbit with a fixed distance from the barycenter
Types General Box Circular Elliptical / Highly elliptical Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic
Circular_orbit
Parameter of Keplerian orbits
\alpha \beta <1} parabolic orbit α β = 1 {\displaystyle \alpha \beta =1} hyperbolic orbit α β > 1 {\displaystyle \alpha \beta >1} linear orbit α = β {\displaystyle
True_anomaly
Kind of planetary orbit
use of supersynchronous orbits are for the launch and transfer orbit trajectory of new commsats intended for geosynchronous orbits. In this approach,
Supersynchronous_orbit
Region in which an astronomical body dominates the attraction of satellites
satellite orbit is stable Interplanetary Transport Network – Low-energy trajectories in the Solar System n-body problem – Problem in physics and celestial
Hill_sphere
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
Girl/Female
Gujarati, Hindu, Indian
Miracle
Surname or Lastname
English
English : variant spelling of Godby.
Boy/Male
French, German, Latin, Swedish
Bean Farmer; A Bean
Boy/Male
Tamil
Full of Joy, Mountain strength, Ireland, Peace, Sun Ray
Girl/Female
Arabic, Muslim
Fruit
Boy/Male
Indian, Sanskrit
Having No Superior
Boy/Male
Latin Polish
Light.
Biblical
Lydia, a standing pool
Boy/Male
Tamil
Balaaditya | பலாதீதà¯à®¯
Young Sun, Young Man, The newly risen Sun
Boy/Male
British, English
Son who Lives in the Swamp
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
HYPERBOLIC TRAJECTORY
n.
One who uses hyperboles.
p. pr. & vb. n.
of Hyperbolize
a.
Having some property that belongs to an hyperboloid or hyperbola.
n.
The use of hyperbole.
n.
A figure of speech in which the expression is an evident exaggeration of the meaning intended to be conveyed, or by which things are represented as much greater or less, better or worse, than they really are; a statement exaggerated fancifully, through excitement, or for effect.
v. i.
To speak or write with exaggeration.
a.
Exaggerated; excessive; hyperbolical.
a.
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.
a.
Belonging to the hyperbola; having the nature of the hyperbola.
adv.
In the form of an hyperbola.
n.
A figure by which a grave and magnificent word is put for the proper word; amplification; hyperbole.
imp. & p. p.
of Hyperbolize
n.
Diminution; a species of hyperbole, representing a thing as being less than it really is.
v. t.
To state or represent hyperbolically.
a.
Alt. of Hyperbolical
n.
A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.
n.
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
a.
Having the form, or nearly the form, of an hyperbola.
n.
The act of exaggerating; the act of doing or representing in an excessive manner; a going beyond the bounds of truth reason, or justice; a hyperbolical representation; hyperbole; overstatement.
a.
Of or pertaining to an hyperbaton; transposed; inverted.