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# Orbital mechanics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. 

114 relations: Aerodynamics, Aerospace engineering, Algebraic function, Analytic function, Apsis, Astrophysics, Ballistics, Bi-elliptic transfer, Binary star, Calculus, Canonical units, Carl Friedrich Gauss, Celestial mechanics, Ceres (dwarf planet), Chaos theory, Circular orbit, Classical mechanics, Comet, Conic section, Conservation of energy, Cube (algebra), Declination, Delta-v, Drag (physics), Dwarf planet, Eccentric anomaly, Eccentricity (mathematics), Edmond Halley, Elastic collision, Electrically powered spacecraft propulsion, Ellipse, Escape velocity, Focus (geometry), Force, Gauss' method, General relativity, Genesis (spacecraft), Geocentric orbit, Gravitational constant, Gravity, Gravity assist, Ground track, Hohmann transfer orbit, Hyperbola, Hyperbolic trajectory, Interplanetary Transport Network, Isaac Newton, Johann Heinrich Lambert, Johannes Kepler, Kepler orbit, ... Expand index (64 more) »

## Aerodynamics

Aerodynamics, from Greek ἀήρ aer (air) + δυναμική (dynamics), is the study of the motion of air, particularly its interaction with a solid object, such as an airplane wing.

## Aerospace engineering

Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft.

## Algebraic function

In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation.

## Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

## Apsis

An apsis (ἁψίς; plural apsides, Greek: ἁψῖδες) is an extreme point in the orbit of an object.

## Astrophysics

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the astronomical objects, rather than their positions or motions in space".

## Ballistics

Ballistics is the field of mechanics that deals with the launching, flight, behavior, and effects of projectiles, especially bullets, unguided bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.

## Bi-elliptic transfer

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 certain situations, require less delta-v than a Hohmann transfer maneuver.

## Binary star

A binary star is a star system consisting of two stars orbiting around their common barycenter.

## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

## Canonical units

A canonical unit is a unit of measurement agreed upon as default in a certain context.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

## Ceres (dwarf planet)

Ceres (minor-planet designation: 1 Ceres) is the largest object in the asteroid belt that lies between the orbits of Mars and Jupiter, slightly closer to Mars' orbit.

## Chaos theory

Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.

## Circular orbit

A circular orbit is the orbit with a fixed distance around the barycenter, that is, in the shape of a circle.

## Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## Comet

A comet is an icy small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process called outgassing.

## Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

## Conservation of energy

In physics, the law of conservation of energy states that the total energy of an isolated system remains constant, it is said to be ''conserved'' over time.

## Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.

## Declination

In astronomy, declination (abbreviated dec; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle.

## Delta-v

Delta-v (literally "change in velocity"), symbolised as ∆v and pronounced delta-vee, as used in spacecraft flight dynamics, is a measure of the impulse that is needed to perform a maneuver such as launch from, or landing on a planet or moon, or in-space orbital maneuver.

## Drag (physics)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

## Dwarf planet

A dwarf planet is a planetary-mass object that is neither a planet nor a natural satellite.

## Eccentric anomaly

In orbital mechanics, eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.

## Eccentricity (mathematics)

In mathematics, the eccentricity, denoted e or \varepsilon, is a parameter associated with every conic section.

## Edmond Halley

Edmond (or Edmund) Halley, FRS (–) was an English astronomer, geophysicist, mathematician, meteorologist, and physicist.

## Elastic collision

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter.

## Electrically powered spacecraft propulsion

An electrically-powered spacecraft propulsion system uses electrical energy to change the velocity of a spacecraft.

## Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

## Escape velocity

In physics, escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.

## Focus (geometry)

In geometry, focuses or foci, singular focus, are special points with reference to which any of a variety of curves is constructed.

## Force

In physics, a force is any interaction that, when unopposed, will change the motion of an object.

## Gauss' method

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.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## Genesis (spacecraft)

Genesis was a NASA sample-return probe that collected a sample of solar wind particles and returned them to Earth for analysis.

## Geocentric orbit

A geocentric orbit or Earth orbit involves any object orbiting Planet Earth, such as the Moon or artificial satellites.

## Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

## Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

## Gravity assist

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.

## Ground track

A ground track or ground trace is the path on the surface of the Earth directly below an aircraft or satellite.

## Hohmann transfer orbit

In orbital mechanics, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

## Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

## Hyperbolic trajectory

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.

## Interplanetary Transport Network

The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow.

## Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

## Johann Heinrich Lambert

Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.

## Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

## Kepler orbit

In celestial mechanics, a Kepler orbit (or Keplerian orbit) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space.

## Kepler problem

In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them.

## Kepler's equation

In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force.

## Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

## Kinetic energy

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.

## Lagrangian point

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies, wherein a small object, affected only by the gravitational forces from the two larger objects, will maintain its position relative to them.

## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

## Mass ratio

In aerospace engineering, mass ratio is a measure of the efficiency of a rocket.

## Mean anomaly

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem.

## Mechanical engineering

Mechanical engineering is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.

## Minor planet

A minor planet is an astronomical object in direct orbit around the Sun (or more broadly, any star with a planetary system) that is neither a planet nor exclusively classified as a comet.

## Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

## N-body problem

In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.

## Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

## Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.

## Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

## Oberth effect

In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well, and then accelerates when its fall reaches maximum speed.

## Orbit

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.

## Orbital eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle.

## Orbital elements

Orbital elements are the parameters required to uniquely identify a specific orbit.

## Orbital inclination change

Orbital inclination change is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit.

## Orbital maneuver

In spaceflight, an orbital maneuver (otherwise known as a burn) is the use of propulsion systems to change the orbit of a spacecraft.

## Orbital period

The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.

## Orbital speed

In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if the object is much less massive than the largest body in the system, its speed relative to that largest body.

## Orbital station-keeping

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.

## Orbiting body

In astrodynamics, an orbiting body (m_2) is a body that orbits a primary body (m_1).

## Order of approximation

In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth.

## Orders of magnitude (speed)

To help compare different orders of magnitude, the following list describes various speed levels between approximately 2.2 m/s and 3.0 m/s.

## Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

## Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy), often referred to as simply the Principia, is a work in three books by Isaac Newton, in Latin, first published 5 July 1687.

## Planet

A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

## Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

## Potential energy

In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

## Precession

Precession is a change in the orientation of the rotational axis of a rotating body.

## Primary (astronomy)

A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system.

## Proportionality (mathematics)

In mathematics, two variables are proportional if there is always a constant ratio between them.

## Right ascension

Right ascension (abbreviated RA; symbol) is the angular distance measured only eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point above the earth in question.

## Roche limit

In celestial mechanics, the Roche limit, also called Roche radius, is the distance in which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.

## Rocket

A rocket (from Italian rocchetto "bobbin") is a missile, spacecraft, aircraft or other vehicle that obtains thrust from a rocket engine.

## Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

## Solar System

The Solar SystemCapitalization of the name varies.

## Space rendezvous

A space rendezvous is an orbital maneuver during which two spacecraft, one of which is often a space station, arrive at the same orbit and approach to a very close distance (e.g. within visual contact).

## Spacecraft

A spacecraft is a vehicle or machine designed to fly in outer space.

## Spacecraft propulsion

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites.

## Spaceflight

Spaceflight (also written space flight) is ballistic flight into or through outer space.

## Specific energy

Specific energy is energy per unit mass.

## Specific kinetic energy

Specific kinetic energy is kinetic energy of an object per unit of mass.

## Specific orbital energy

In the gravitational two-body problem, the specific orbital energy \epsilon\,\! (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (\epsilon_p\,\!) and their total kinetic energy (\epsilon_k\,\!), divided by the reduced mass.

## Specific relative angular momentum

In celestial mechanics the specific relative angular momentum \vec plays a pivotal role in the analysis of the two-body problem.

## Sphere of influence (astrodynamics)

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.

## Sputnik 1

Sputnik 1 (or; "Satellite-1", or "PS-1", Простейший Спутник-1 or Prosteyshiy Sputnik-1, "Elementary Satellite 1") was the first artificial Earth satellite.

## Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

## Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

## Standard gravitational parameter

In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.

## Sun

The Sun is the star at the center of the Solar System.

## Trajectory

A trajectory or flight path is the path that a massive object in motion follows through space as a function of time.

## Transcendental function

A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.

## Trojan (astronomy)

In astronomy, a trojan is a minor planet or moon that shares the orbit of a planet or larger moon, wherein the trojan remains in the same, stable position relative to the larger object.

## True anomaly

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit.

## Tsiolkovsky rocket equation

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and thereby move due to the conservation of momentum.

## Universal variable formulation

In orbital mechanics, the universal variable formulation is a method used to solve the two-body Kepler problem.

## Virial theorem

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, \left\langle T \right\rangle, of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, \left\langle V_\text \right\rangle, where angle brackets represent the average over time of the enclosed quantity.

## Vis-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.

## References

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