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Orbital Energy
In the gravitational two-body problem, the specific orbital energy \varepsilon (or specific ''vis-viva'' energy) of two orbiting bodies is the constant quotient of their mechanical energy (the sum of their mutual potential energy, \varepsilon_p, and their kinetic energy, \varepsilon_k) to their reduced mass. According to the orbital energy conservation equation (also referred to as ''vis-viva'' equation), it does not vary with time: \begin \varepsilon &= \varepsilon_k + \varepsilon_p \\ &= \frac - \frac = -\frac \frac \left(1 - e^2\right) = -\frac \end where *v is the relative orbital speed; *r is the orbital distance between the bodies; *\mu = (m_1 + m_2) is the sum of the standard gravitational parameters of the bodies; *h is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass; *e is the orbital eccentricity; *a is the semi-major axis. It is a kind of specific energy, typically e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Two-body Problem
In classical mechanics, the two-body problem is to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two bodies are point particles that interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions. A simpler "one body" model, the " central-force problem", treats one object as the immobile source of a force acting on the other. One then seeks to predict the motion of the single remaining mobile object. Such an approximation can give useful results when one object is much m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Escape Velocity
In celestial mechanics, escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body, assuming: * Ballistic trajectory – no other forces are acting on the object, such as propulsion and friction * No other gravity-producing objects exist. Although the term ''escape velocity'' is common, it is more accurately described as a speed than as a velocity because it is independent of direction. Because gravitational force between two objects depends on their combined mass, the escape speed also depends on mass. For artificial satellites and small natural objects, the mass of the object makes a negligible contribution to the combined mass, and so is often ignored. Escape speed varies with distance from the center of the primary body, as does the velocity of an object traveling under the gravitational influence of the primary. If an object is in a circular or elliptical orbit, its speed is always less than the es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periapsis Distance
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the ''apogee'', and at the nearest point the ''perigee'', like with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named ''aphelion'' for the farthest and ''perihelion'' for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Velocity Vector
In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position (\mathbf) and velocity (\mathbf) that together with their time (epoch) (t) uniquely determine the trajectory of the orbiting body in space. Orbital state vectors come in many forms including the traditional Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance Matrix (VCM). Frame of reference State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. One of the more popular reference frames for the state vectors of bodies moving near Earth is the Earth-centered inertial (ECI) system defined as follows: *The origin is Earth's center of mass; *The Z axis is coincident with Earth's rotational axis, positive northward; *The X/Y plane coincides with Earth's equatorial plane, with the +X axis pointing toward the vernal equinox and the Y axis completing a right-hand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Excess Velocity
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one. Under simplistic assumptions a body traveling along this trajectory will coast towards infinity, settling to a final excess velocity relative to the central body. Similarly to parabolic trajectories, all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive. Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories. Parameters describing a hyperbolic trajectory Like an elliptical orbit, a hyperbo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Orbit
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits. Velocity The orbital velocity (v) of a body travelling along a parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of the orbiting body from the central body, *\mu is the standard gravitational parameter. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the ''apogee'', and at the nearest point the ''perigee'', like with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named ''aphelion'' for the farthest and ''perihelion'' for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Angular Momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. "Specific" in this context indicates angular momentum per unit mass. The SI unit for specific relative angular momentum is square meter per second. Definition The specific relative angular momentum is defined as the cross product of the relative position vector \mathbf and the relative velocity vector \mathbf . \mathbf = \mathbf\times \mathbf = \frac where \mathbf is the angular momentum vector, defined as \mathbf \times m \mathbf. The \mathbf vector is always perpendicular to the instantaneo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Institute Of Aeronautics And Astronautics
The American Institute of Aeronautics and Astronautics (AIAA) is a professional society for the field of aerospace engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is s .... The AIAA is the U.S. representative on the International Astronautical Federation and the International Council of the Aeronautical Sciences. In 2015, it had more than 30,000 members among aerospace professionals worldwide (a majority are American or live in the United States). History The AIAA was founded in 1963 from the merger of two earlier societies: the American Rocket Society (ARS), founded in 1930 as the American Interplanetary Society (AIS), and the Institute of the Aerospace Sciences (IAS), founded in 1932 as the Institute of the Aeronautical Sciences. Paul Johnston was the first executive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the ''apogee'', and at the nearest point the ''perigee'', like with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named ''aphelion'' for the farthest and ''perihelion'' for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Relative Angular Momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. " Specific" in this context indicates angular momentum per unit mass. The SI unit for specific relative angular momentum is square meter per second. Definition The specific relative angular momentum is defined as the cross product of the relative position vector \mathbf and the relative velocity vector \mathbf . \mathbf = \mathbf\times \mathbf = \frac where \mathbf is the angular momentum vector, defined as \mathbf \times m \mathbf. The \mathbf vector is always perpendicular to the instant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
