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Radial Trajectory
In astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards or away from each other in a straight line. Classification There are three types of radial trajectories (orbits). * Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. The relative speed of the two objects is less than the escape velocity. This is an elliptic orbit with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1 this is not a parabolic orbit. If the coefficient of restitution of the two bodies is 1 (perfectly elastic) this orbit is periodic. If the coefficient of restitution is less than 1 (inelastic) this orbit is non-periodic. * Radial parabolic trajectory, a non-periodic orbit where the relative speed of the two objects is always equal to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control. 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 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. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. or ... [...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. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the primary body the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''. According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e.g. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbits
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Orbits
Summary A simple list of just the common orbit abbreviations. List of abbreviations of common Earth orbits List of abbreviations of other orbits Classifications The following is a list of types of orbits: Centric classifications * Galactocentric orbit: An orbit about the center of a galaxy. The Sun follows this type of orbit about the Galactic Center of the Milky Way. * Heliocentric orbit: An orbit around the Sun. In the Solar System, all planets, comets, and asteroids are in such orbits, as are many artificial satellites and pieces of space debris. Moons by contrast are not in a heliocentric orbit but rather orbit their parent object. * Geocentric orbit: An orbit around the planet Earth, such as that of the Moon or of artificial satellites. * Lunar orbit (also selenocentric orbit): An orbit around Earth's Moon. * Areocentric orbit: An orbit around the planet Mars, such as that of its moons or artificial satellites. For orbits centered about planets other than Earth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Harmonic Motion
In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position. It results in an oscillation, described by a sinusoid which continues indefinitely, if uninhibited by friction or any other dissipation of energy. Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler's Equation
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was first derived by Johannes Kepler in 1609 in Chapter 60 of his ''Astronomia nova'', and in book V of his '' Epitome of Copernican Astronomy'' (1621) Kepler proposed an iterative solution to the equation. The equation has played an important role in the history of both physics and mathematics, particularly classical celestial mechanics. Equation Kepler's equation is where M is the mean anomaly, E is the eccentric anomaly, and e is the eccentricity. The 'eccentric anomaly' E is useful to compute the position of a point moving in a Keplerian orbit. As for instance, if the body passes the periastron at coordinates x = a(1 - e), y = 0, at time t = t_0, then to find out the position of the body at any time, you first calculate the mean anomaly M from the time and the mean motion n by the formula M = n(t - t_0), then solve the Kepler equation above ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Escape 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 parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of orbiting body from central body, *\mu is the standard gravitational parameter. At any p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. The force may be either attractive or repulsive. The problem is to find the position or speed of the two bodies over time given their masses, positions, and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements. The Kepler problem is named after Johannes Kepler, who proposed Kepler's laws of planetary motion (which are part of classical mechanics and solved the problem for the orbits of the planets) and investigated the types of forces that would result in orbits obeying those laws (called ''Kepler's inverse problem''). For a discussion of the Kepler problem specific to radial orbits, see Radial trajectory. General relativity provides more accurate solutions to the two-body problem, especial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations For A Falling Body
Lection 0 A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions. Assuming constant acceleration ''g'' due to Earth’s gravity, Newton's law of universal gravitation simplifies to ''F'' = ''mg'', where ''F'' is the force exerted on a mass ''m'' by the Earth’s gravitational field of strength ''g''. Assuming constant ''g'' is reasonable for objects falling to Earth over the relatively short vertical distances of our everyday experience, but is not valid for greater distances involved in calculating more distant effects, such as spacecraft trajectories. History Galileo was the first to demonstrate and then formulate these equations. He used a ramp to study rolling balls, the ramp slowing the acceleration enough to measure the time taken for the ball to roll a known distance. He measured elapsed time with a water clock, using an "extremely accurate balance" to measure the amount of water.See the work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler's Equation
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was first derived by Johannes Kepler in 1609 in Chapter 60 of his ''Astronomia nova'', and in book V of his '' Epitome of Copernican Astronomy'' (1621) Kepler proposed an iterative solution to the equation. The equation has played an important role in the history of both physics and mathematics, particularly classical celestial mechanics. Equation Kepler's equation is where M is the mean anomaly, E is the eccentric anomaly, and e is the eccentricity. The 'eccentric anomaly' E is useful to compute the position of a point moving in a Keplerian orbit. As for instance, if the body passes the periastron at coordinates x = a(1 - e), y = 0, at time t = t_0, then to find out the position of the body at any time, you first calculate the mean anomaly M from the time and the mean motion n by the formula M = n(t - t_0), then solve the Kepler equation above ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Trajectory
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 parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of orbiting body from central body, *\mu is the standard gravitational parameter. At any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM when one body is much larger than the other. \mu=GM \ For several objects in the Solar System, the value of ''μ'' is known to greater accuracy than either ''G'' or ''M''. The SI units of the standard gravitational parameter are . However, units of are frequently used in the scientific literature and in spacecraft navigation. Definition Small body orbiting a central body The central body in an orbital system can be defined as the one whose mass (''M'') is much larger than the mass of the orbiting body (''m''), or . This approximation is standard for planets orbiting the Sun or most moons and greatly simplifies equations. Under Newton's law of universal gravitation, if the distance between the bodies is ''r'', the force exerted on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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