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Parameter in the gravitational two-body problem
gravitational two-body problem, the specific orbital energy ε {\displaystyle \varepsilon } (or specific vis-viva energy) of two orbiting bodies is the constant quotient
Specific_orbital_energy
Physical quantity representing energy content per unit mass
Specific energy or massic energy is energy per unit mass. It is also known as gravimetric energy density, which is not to be confused with energy density
Specific_energy
Speed at which a body orbits around the barycenter of a system
instantaneous orbital speed at a given point of the orbit can be computed from its distance to the central body and the object's specific orbital energy, sometimes
Orbital_speed
Field of classical mechanics concerned with the motion of spacecraft
standard assumptions, specific orbital energy ( ϵ {\displaystyle \epsilon } ) of elliptic orbit is negative, and the orbital energy conservation equation
Orbital_mechanics
Aircraft-specific energy is very similar to specific orbital energy except that it is expressed as a positive quantity. A zero value of aircraft-specific energy
Aircraft_specific_energy
Concept in gravitational orbital mechanics
For a given orbital radius, the escape velocity will be 2 {\displaystyle {\sqrt {2}}} times the orbital velocity. Specific total energy, ε = v 2 2 −
Vis-viva_equation
Measure in astrodynamics
orbital inclination) needs about 160–164 km2/s2. Specific orbital energy Orbit Parabolic trajectory Hyperbolic trajectory Wie, Bong (1998). "Orbital Dynamics"
Characteristic_energy
Kepler orbit with an eccentricity of less than one
the specific orbital energy is independent of the eccentricity. Using the virial theorem to find: the time-average of the specific potential energy is
Elliptic_orbit
Transfer manoeuvre between two orbits
astronautics, the Hohmann transfer orbit (/ˈhoʊmən/) is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around
Hohmann_transfer_orbit
Trajectory of Earth around the Sun
center of the orbit is relatively close to the center of the Sun (relative to the size of the orbit). As seen from Earth, the planet's orbital prograde motion
Earth's_orbit
Type of spacecraft maneuver
burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity (and so, its kinetic energy) is greatest. In some cases, it is even
Oberth_effect
Vector quantity in celestial mechanics
semi-major axis and the orbital period of a satellite that can be reduced to a constant of the central body. Specific orbital energy, another conserved quantity
Specific_angular_momentum
Process that leads to gradual decrease of the distance between two orbiting bodies
Orbital decay is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These
Orbital_decay
Concept in astrodynamics
elliptical orbits. The semi major axis is directly linked to the specific orbital energy ( ϵ {\displaystyle \epsilon \,} ) or characteristic energy C 3 {\displaystyle
Hyperbolic_trajectory
Measure of amount of effort to change trajectory
Delta-v budget Gravity drag Orbital maneuver Orbital stationkeeping Spacecraft propulsion Orbital propellant depot Specific impulse Tsiolkovsky rocket
Delta-v
Astrodynamic equation
Kepler's first law Circular orbit Elliptic orbit Parabolic trajectory Hyperbolic trajectory Tsiolkovsky rocket equation Orbital speed Escape velocity Celestial
Orbit_equation
Movement during spaceflight
In spaceflight, an orbital maneuver (otherwise known as a burn) is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far
Orbital_maneuver
Concept in celestial mechanics
kg). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object
Escape_velocity
Periodic, three-dimensional orbit
Halo orbit A halo orbit is a periodic, non-planar orbit associated with one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics
Halo_orbit
Spaceflight operation
acceleration to reach orbital speed. Higher energy orbits like geostationary orbit are often reached via elliptical transfer orbits. One type of orbit insertion is
Orbit_insertion
Curved path of an object around a point
mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Alternatively, it is known as an orbital revolution
Orbit
Amount by which an orbit deviates from a perfect circle
astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another
Orbital_eccentricity
Spacecraft end-of-life orbit
2015-03-07. "FCC Enters Orbital Debris Debate". Space.com. Archived from the original on March 8, 2005. "US Government Orbital Debris Standard Practices"
Graveyard_orbit
Orbit around Earth
to drag from the Earth's atmosphere, which decreases the orbital altitude. The rate of orbital decay depends on the satellite's cross-sectional area and
Geocentric_orbit
Orbit with a fixed distance from the barycenter
a priori clear from dimensional analysis.[citation needed] The specific orbital energy ( ϵ {\displaystyle \epsilon \,} ) is negative, and ϵ = − v 2 2
Circular_orbit
Type of orbit
of the orbiting body, μ {\displaystyle \mu \,} is the standard gravitational parameter. Under standard assumptions, the specific orbital energy ( ϵ {\displaystyle
Parabolic_trajectory
Term in geometry; longest and shortest semidiameters of an ellipse
total specific orbital energy is always the same. This statement will always be true under any given conditions.[citation needed] Planet orbits are always
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Concept in celestial mechanics
hyperbolic orbits, μ is twice the semi-major axis times the negative of the specific orbital energy, where the latter is defined as the total energy of the
Standard gravitational parameter
Standard_gravitational_parameter
Orbit around Earth between 160 and 2000 km
elliptical orbit (HEO) List of orbits Medium Earth orbit (MEO) Medium-lift launch vehicle Specific orbital energy examples Suborbital spaceflight Space domain
Low_Earth_orbit
Orbit around the barycenter of the Sun
Mars orbit. Every two years, low-energy transfer windows open up, which allow movement between the two planets with the lowest possible energy requirements
Heliocentric_orbit
Orbit keeping the satellite at a fixed longitude above the equator
A geosynchronous orbit (sometimes abbreviated GEO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours
Geosynchronous_orbit
Angle between a reference plane and the plane of an orbit
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital
Orbital_inclination
Spaceflight where the spacecraft does not go into orbit
will fail to complete an orbit. The major axis is vertical, the semi-major axis a is more than R/2. The specific orbital energy ϵ {\displaystyle \epsilon
Sub-orbital_spaceflight
Mathematical equation describing the motion of a rocket
applied to orbital maneuvers in order to determine how much propellant is needed to change to a particular new orbit, or to find the new orbit as the result
Tsiolkovsky_rocket_equation
Time an astronomical object takes to complete one orbit around another object
reciprocal is the orbital frequency, a kind of revolution frequency, in units of hertz. According to Kepler's Third Law, the orbital period T of two point
Orbital_period
Orbit of an object around the Moon
that make most unstable, and leave only a few orbital trajectories possible for indefinite frozen orbits. These would be useful for long-term stays in
Lunar_orbit
The Moon's circuit around Earth
needed][relevant?] However, because the orbital velocity of the Moon around Earth (1 km/s) is small compared to the orbital velocity of Earth about the Sun (30 km/s)
Orbit_of_the_Moon
Quasi-periodic orbital trajectory
trajectory In orbital mechanics, a Lissajous orbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that
Lissajous_orbit
and V2R = GM, where R = radius of orbit in metres, T = orbital period in seconds, V = orbital speed in m/s, G = gravitational constant ≈ 6.673×10−11 Nm2/kg2
List_of_orbits
Transfer orbit used to reach geosynchronous or geostationary orbit
cost to send a spacecraft to such orbits is very high due to their high orbital radius. A GTO is an intermediary orbit used to make this process more efficient
Geostationary_transfer_orbit
Classical approach to the many-body problem of astronomy
is frequently perturbed Osculating orbit Orbit modeling Orbital resonance Perturbation theory Proper orbital elements Stability of the Solar System Footnotes
Perturbation_(astronomy)
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
horseshoe orbit of (419624) 2010 SO16 around the Earth-Sun system over 900 years In celestial mechanics, a horseshoe orbit is a type of co-orbital motion
Horseshoe_orbit
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
Earth orbit) can take less than 90 minutes. So, for satellites that need to orbit quickly, HEO is not a good fit. Second, HEOs take far more energy to place
High_Earth_orbit
Type of high-latitude satellite orbit
It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270 degrees, and an orbital period of about half a sidereal
Molniya_orbit
Earth-centered orbit above low Earth orbit and below geostationary orbit
where R is the radius of orbit in metres; T is the orbital period in seconds; V is the orbital speed in m/s; G is the gravitational constant, approximately
Medium_Earth_orbit
Spaceflight where spacecraft orbits an astronomical body
An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least
Orbital_spaceflight
Type of geocentric orbit
surface. Even if an orbit remains Sun-synchronous, however, other orbital parameters such as argument of periapsis and the orbital eccentricity evolve
Sun-synchronous_orbit
Movement around a celestial body that remains below its Karman line
causing rapid orbital decay if left unchecked. A number of artificial satellites have been placed into transatmospheric Earth orbits, usually due to
Transatmospheric_orbit
Equilibrium points near two orbiting bodies
increasing the object's orbital period. The closer to Earth the object is, the greater this effect is. At the L1 point, the object's orbital period becomes exactly
Lagrange_point
Either of two extreme points in a celestial object's orbit
2 ) μ a {\displaystyle h={\sqrt {\left(1-e^{2}\right)\mu a}}} Specific orbital energy ε = − μ 2 a {\displaystyle \varepsilon =-{\frac {\mu }{2a}}} where:
Apsis
Specific mechanical energy is the mechanical energy of an object per unit of mass. Similar to mechanical energy, the specific mechanical energy of an
Specific_mechanical_energy
Fuel-efficient orbital maneuver
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional
Low-energy_transfer
Range of low orbital altitudes
highly elliptical orbit around Earth with a perigee as low as 80 to 90 km (50 to 56 mi), surviving for multiple orbits. Sub-orbital flight and near space
Very_low_Earth_orbit
Cartesian vectors of position and velocity of an orbiting body in space
In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle
Orbital_state_vectors
Horizontal angle from north or other reference cardinal direction
azimuth of the Sun or a star given its declination and hour angle at a specific location, modify the formula for a spherical Earth. Replace φ2 with declination
Azimuth
periapsis ω (measured on orbital plane): ϖ = Ω + ω {\displaystyle \varpi =\Omega +\omega } which are derived from the orbital state vectors. Define the
Longitude_of_periapsis
Celestial orbit whose trajectory is a conic section in the orbital plane
parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also tend toward a straight line. It considers
Kepler_orbit
Table of positions of astronomical objects at given times
Concerning the size and shape of an orbit Nautical almanac – Publication on celestial body positions Osculating orbit – Orbital perturbations Ptolemy's table
Ephemeris
Center of mass of multiple bodies orbiting each other
the mass of the secondary in Earth masses (M🜨) a (km) is the average orbital distance between the centers of the two bodies r1 (km) is the distance
Barycenter_(astronomy)
Problem in physics and celestial mechanics
predict a planet's motion; i.e., to give its orbital properties: position, orbital diameter, period and orbital velocity. Having done so, he and others soon
N-body_problem
Periodic, three-dimensional orbit
In orbital mechanics a near-rectilinear halo orbit (NRHO) is a halo orbit that passes close to the smaller of two bodies and has nearly stable behavior
Near-rectilinear_halo_orbit
Kind of planetary orbit
synchronous orbit has a period equal to the rotational period of the body which contains the barycenter of the orbit. One particular supersynchronous orbital regime
Supersynchronous_orbit
Orbital data format
three-line element set (3LE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the epoch. Using a suitable
Two-line_element_set
Maintenance of a particular orbit
astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers
Orbital_station-keeping
Quotient of a quantity by mass
density of a material Specific orbital energy, orbital energy per unit mass Specific power, per unit of mass (or volume or area) Specific relative angular
Specific_quantity
Wave-like behavior of an electron in a molecule
in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions
Molecular_orbital
Flight into or through outer space
insufficient specific orbital energy, in which case a suborbital flight will last only a few minutes, but it is also possible for an object with enough energy for
Spaceflight
Circular orbit above Earth's Equator and following the direction of Earth's rotation
following the direction of Earth's rotation. An object in such an orbit has an orbital period equal to Earth's rotational period, one sidereal day, and
Geostationary_orbit
Type of orbital maneuver
aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require
Bi-elliptic_transfer
Branch of engineering
lift and aeronautics). Astrodynamics – the study of orbital mechanics including prediction of orbital elements when given a select few variables. While
Aerospace_engineering
Satellite orbit with high inclination
orbit to provide telecommunications services. Near-polar orbiting satellites commonly choose a sun-synchronous orbit, where each successive orbital pass
Polar_orbit
Laws describing planetary orbits
square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. The elliptical orbits of planets were indicated
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Function describing an electron in an atom
electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with
Atomic_orbital
Defining the orbit of an object in space
towards the positive x-axis. Equinox Kepler orbits List of orbits Orbital node Perturbation of the orbital plane can cause precession of the ascending
Longitude of the ascending node
Longitude_of_the_ascending_node
Parameter of Keplerian orbits
ν by 2π − ν) 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
True_anomaly
Space navigation technique
gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity
Gravity_assist
Parameters that define a specific orbit
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems
Orbital_elements
Region in which an astronomical body dominates the attraction of satellites
for orbital stability), this expression reduces to the one presented above.[citation needed] In the Earth-Sun example, the Earth (5.97×1024 kg) orbits the
Hill_sphere
Time period during which a rocket must launch to reach its target
would require an orbital plane change maneuver which would require a large amount of propellant. For launches above low Earth orbit (LEO), the actual
Launch_window
Propulsive maneuver used to arrive at the Moon
Comparison of all orbital launch systemsPages displaying short descriptions of redirect targets Low energy transfer – Fuel-efficient orbital maneuverPages
Trans-lunar_injection
This is an extended version of the energy density table from the main Energy density page. Prelas, Mark (2015). Nuclear-Pumped Lasers. Springer. p. 135
Energy density extended reference table
Energy_density_extended_reference_table
Estimate of total change in velocity of a space mission
energy/high speed multiplies the effect of a burn. Thus for example the delta-v for a Hohmann transfer from Earth's orbital radius to Mars's orbital radius
Delta-v_budget
Specifies the orbit of an object in space
equal to the time of its periastron. Apsidal precession Kepler orbit Orbital mechanics Orbital node Iglesias-Marzoa, Ramón; López-Morales, Mercedes; Jesús
Argument_of_periapsis
Point where an orbit crosses a plane of reference to which it is inclined
An orbital node is either of the two points where an orbiting object intersects a plane of reference inclined with respect to the orbital plane. A non-inclined
Orbital_node
Chart used to plan spacecraft launches
In orbital mechanics, a porkchop plot (also pork-chop plot) is a chart that shows level curves of equal characteristic energy (C3) against combinations
Porkchop_plot
Type of spacecraft orbit
In orbital mechanics, a distant retrograde orbit (DRO) is a highly stable retrograde orbit around the smaller of two bodies, passing outside the system's
Distant_retrograde_orbit
Characteristic of conic sections
parabolic and hyperbolic partial differential equations. Kepler orbits Eccentricity vector Orbital eccentricity Roundness (object) Conic constant Thomas, George
Eccentricity_(mathematics)
Type of orbit around an astronomical body
an inclined orbit. A non-inclined orbit is an orbit coplanar with a plane of reference. The orbital inclination is 0° for prograde orbits, and π (180°)
Near-equatorial_orbit
Elliptical orbit used to move a spacecraft from one circular orbit to another
In orbital mechanics, a transfer orbit is an intermediate elliptical orbit that is used to move a spacecraft in an orbital maneuver from one circular
Transfer_orbit
1990 Solar System image by Voyager 1
Dot Family Portrait Related Grand Tour program Gravity assist Specific orbital energy of Voyager 1 Titan IIIE NASA Deep Space Network Antennas Voyager
Family_Portrait_(Voyager)
Event causing release of space debris
different orbital energies complete revolutions at different rates, within days, the cloud is progressively stretched along the parent orbit, eventually
In-orbit_fragmentation
Moment in time used as a reference point in astronomy
the disciplines of celestial mechanics or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational
Epoch_(astronomy)
Orbital mechanics term
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was derived by Johannes
Kepler's_equation
Specifies the orbit of an object in space
if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit. Define T as the time required
Mean_anomaly
Method for describing the electronic structure of molecules using quantum mechanics
electrons moving from one orbital at a lower energy to a higher energy orbital. The molecular orbital diagram for the final state describes the electronic nature
Molecular_orbital_theory
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, the
Eccentric_anomaly
their orbital eccentricity, radial orbits are classified by their specific orbital energy, the constant sum of the total kinetic and potential energy, divided
Radial_trajectory
Region of space gravitationally dominated by a given body
particular celestial body exerts the main gravitational influence on an orbiting object. As such it is the dominating part of a gravitational field. It
Sphere of influence (astrodynamics)
Sphere_of_influence_(astrodynamics)
NASA space probe launched in 1977
to the outer planets Local Interstellar Cloud Space exploration Specific orbital energy of Voyager 1 Timeline of artificial satellites and space probes
Voyager_1
Branch of astronomy
planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary
Celestial_mechanics
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