# Orbital mechanics

astrodynamicsastrodynamicistorbital dynamicsfuzzy orbital transfersApollo-typeastrodynamicastrodynamicalcomputeddynamicaldynamical astronomy
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.wikipedia
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### Spaceflight

space travelspace flightspace transport
Until the rise of space travel in the twentieth century, there was little distinction between orbital and celestial mechanics.
Once in space, the motion of a spacecraft – both when unpropelled and when under propulsion – is covered by the area of study called astrodynamics.

### Gauss's method

efficient method
Gauss's method was able to use just three observations (in the form of pairs of right ascension and declination), to find the six orbital elements that completely describe an orbit.
In orbital mechanics (subfield of celestial mechanics), Gauss's method is used for preliminary orbit determination from at least three observations (more observations increases the accuracy of the determined orbit) of the orbiting body of interest at three different times.

### Orbital elements

orbital parametersorbital elementKeplerian elements
Gauss's method was able to use just three observations (in the form of pairs of right ascension and declination), to find the six orbital elements that completely describe an orbit.
There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics.

### Orbital maneuver

orbit raisingmaneuvermaneuvers
Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers.
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement and gravity of a planet or other celestial body to alter the path and speed of a spacecraft, typically in order to save propellant, time, and expense.

### Space rendezvous

rendezvousorbital rendezvousrendezvoused
The space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods requiring hours or even days to complete.
In 1963 Buzz Aldrin submitted his doctoral thesis titled, Line-Of-Sight Guidance Techniques For Manned Orbital Rendezvous. As a NASA astronaut, Aldrin worked to "translate complex orbital mechanics into relatively simple flight plans for my colleagues."

### Orbit

orbitsorbital motionplanetary motion
Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.
The above classical (Newtonian) analysis of orbital mechanics assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible.

### Rocket

rocketsrocketryrocket scientist
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.
Spacecraft are further studied in the subfield of astrodynamics.

### Celestial mechanics

celestialcelestial dynamicscelestial mechanician
Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.

### Space exploration

space missionexplorationspace missions
Orbital mechanics is a core discipline within space-mission design and control.
Once in space, the motion of a spacecraft—both when unpropelled and when under propulsion—is covered by the area of study called astrodynamics.

### Hyperbolic trajectory

hyperbolichyperbolic orbithyperbolic excess velocity
The velocity equation for a hyperbolic trajectory has either + {1\over{a}}, or it is the same with the convention that in that case a is negative.
In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull.

### Circular orbit

circularcircular orbitscircular Keplerian orbits
Below we consider a circular orbit in astrodynamics or celestial mechanics under standard assumptions.

### Vis-viva equation

orbital energy conservation equationvis viva'' equationvis-viva'' equation
In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies.

### Orbiting body

astronomical bodyorbiting bodiessecondary body
In astrodynamics, an orbiting body is any physical body that orbits a more massive one, called the primary body.

### Kepler's equation

formula for this inverseinverse radial Kepler equationradial Kepler equation
One approach to calculating orbits (mainly used historically) is to use Kepler's equation:
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force.

### Robert H. Goddard

Robert GoddardRobert Hutchings GoddardDr. Robert H. Goddard
He consulted the rocket scientist Robert Goddard and was encouraged to continue his work on space navigation techniques as Goddard believed they would be needed in the future.
Herrick began corresponding with Goddard in 1931 and asked if he should work in this new field, which he named astrodynamics.

### Eccentric anomaly

where M is the mean anomaly, E is the eccentric anomaly, and is the eccentricity.
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.

### Johann Heinrich Lambert

LambertJohann LambertJohann H. Lambert
Newton's method of successive approximation was formalised into an analytic method by Euler in 1744, whose work was in turn generalised to elliptical and hyperbolic orbits by Lambert in 1761-1777.
In astrodynamics he also solved the problem of determination of time of flight along a section of orbit, known now as Lambert's problem.

### Hohmann transfer orbit

Hohmann transfertransfer orbitsHohmann orbit
The Hohmann transfer orbit alone is a poor approximation for interplanetary trajectories because it neglects the planets' own gravity.
In orbital mechanics, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii around the same body in the same plane.

### Universal variable formulation

These difficulties are what led to the development of the universal variable formulation, described below.
In orbital mechanics, the universal variable formulation is a method used to solve the two-body Kepler problem.

### Apsis

perigeeperihelionapogee
In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body.

### Sphere of influence (astrodynamics)

sphere of influencecapturedgravitational influence
The size of the "neighborhoods" (or spheres of influence) vary with radius r_{SOI}:
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body.

### Orbital station-keeping

station keepingstation-keepingstationkeeping
On the other hand, the various perturbations can be orchestrated by clever astrodynamicists to assist with orbit maintenance tasks, such as station-keeping, ground track maintenance or adjustment, or phasing of perigee to cover selected targets at low altitude.
In astrodynamics, the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit are called orbital station-keeping.

### Gravity assist

gravitational slingshotgravitational assistslingshot
In a gravity assist, a spacecraft swings by a planet and leaves in a different direction, at a different speed.
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.

### Gravitational constant

Newton's constantGuniversal gravitational constant
where G is the gravitational constant, equal to
:In orbital mechanics, the period

### Specific energy

Orders of magnitude (specific energy density)Energy densityspecific energies
The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy.
Specific mechanical energy, rather than simply energy, is often used in astrodynamics, because gravity changes the kinetic and potential specific energies of a vehicle in ways that are independent of the mass of the vehicle, consistent with the conservation of energy in a Newtonian gravitational system.