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Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. In astrodynamics or celestial mechanics an elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. Image File history File links Two bodies with similar mass orbiting around a common barycenter (red cross) with elliptic orbits. ...
Image File history File links Two bodies with similar mass orbiting around a common barycenter (red cross) with elliptic orbits. ...
In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it was concentrated. ...
Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ...
Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ...
Two bodies with a slight difference in mass orbiting around a common barycenter. ...
In astrodynamics, under standard assumptions any orbit must be of conic section shape. ...
Specific energy of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit and tundra orbit. In astrodynamics the specific orbital energy (or visviva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ...
In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ...
In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses. ...
Molniya orbit is a class of a highly elliptic orbit with inclination of +/63. ...
Tundra orbit is a class of a highly elliptic orbit with inclination of 63. ...
Velocity
Under standard assumptions the orbital speed () of a body traveling along elliptic orbit can be computed from the Visviva equation as: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ...
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. ...
In astrodynamics, the visviva equation, also referred to as orbital energy conservation equation, is one of the fundamental and useful equations that govern the motion of orbiting bodies. ...
where: Conclusion: In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...
In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics: it is orders of magnitude lighter than central body (i. ...
In astrodynamics a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ...
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
 Velocity does not depend on eccentricity but is determined by length of semimajor axis (),
 Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, is positive.
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. ...
Orbital period Under standard assumptions the orbital period () of a body traveling along an elliptic orbit can be computed as: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ...
The orbital period is the time it takes a planet (or another object) to make one full orbit. ...
where: Conclusions: In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
 The orbital period is equal to a circular orbit with the orbit radius equal to the semimajor axis (),
 The orbital period does not depend on the eccentricity (See also: Kepler's third law).
In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ...
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ...
Energy Under standard assumptions, specific orbital energy () of elliptic orbit is negative and the orbital energy conservation equation (the Visviva equation) for this orbit can take the form: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ...
In astrodynamics the specific orbital energy (or visviva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ...
In astrodynamics, the visviva equation, also referred to as orbital energy conservation equation, is one of the fundamental and useful equations that govern the motion of orbiting bodies. ...
where: Conclusions: The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. ...
In astrodynamics a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ...
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : The units of the standard gravitational parameter are km3s2 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...
 Specific energy for elliptic orbits is independent of eccentricity and is determined only by semimajor axis of the ellipse.
Using the virial theorem we find: In astrodynamics the specific orbital energy (or visviva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ...
The semimajor axis of an ellipse In geometry, the term semimajor axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...
In mechanics, the virial theorem provides a general equation relating the average total kinetic energy of a system with its average total potential energy , where angle brackets represent the average of the enclosed quantity. ...
 the timeaverage of the specific potential energy is equal to 2ε
 the timeaverage of r^{1} is a^{1}
 the timeaverage of the specific kinetic energy is equal to ε
Flight path angle Equation of motion  See orbit equation
In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ...
Orbital parameters The state of an orbiting body at any given time is defined by the orbiting body's position and velocity with respect to the central body, which can be represented by the threedimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with less degrees of freedom are the circular and parabolic orbit. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time (epoch) () uniquely determine the state of an orbiting body. ...
Because at least six variables are absolutely required to completely represent an elliptic orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements. The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inversesquare law of gravitational attraction. ...
Solar system In the Solar System, planets, asteroids, comets and space debris have elliptical orbits around the Sun, relative to the Sun. The eight planets and three dwarf planets of the Solar System. ...
253 Mathilde, a Ctype asteroid. ...
Comet HaleBopp Comet West For other uses, see Comet (disambiguation). ...
Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by man that no longer serve any useful purpose. ...
Moons have an elliptic orbit around their planet. Many artificial satellites have various elliptic orbits around the Earth.
See also In astrodynamics a characteristic energy () is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity over an escape velocity required for additional orbital maneuvers. ...
The following is a list of types of orbits: // Box orbit Circular orbit Ecliptic orbit Elliptic orbit Highly Elliptical Orbit Graveyard orbit Hohmann transfer orbit Hyperbolic trajectory Inclined orbit Osculating orbit Parabolic trajectory Capture orbit Escape orbit Semisynchronous orbit Subsynchronous orbit Synchronous orbit Geocentric orbit Geosynchronous orbit Geostationary orbit...
In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ...
In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ...
External links  Apogee  Perigee Lunar photographic comparison
 Aphelion  Perihelion Solar photographic comparison
