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Tisserand's Criterion
Tisserand's criterion is used to determine whether or not an observed orbiting body, such as a comet or an asteroid, is the same as a previously observed orbiting body. While all the orbital parameters of an object orbiting the Sun during the close encounter with another massive body (e.g. Jupiter) can be changed dramatically, the value of a function of these parameters, called Tisserand's relation (due to Félix Tisserand) is approximately conserved, making it possible to recognize the orbit after the encounter. Definition Tisserand's criterion is computed in a circular restricted three-body system. In a circular restricted three-body system, one of the masses is assumed to be much smaller than the other two. The other two masses are assumed to be in a circular orbit about the system's center of mass. In addition, Tisserand's criterion also relies on the assumptions that a) one of the two larger masses is much smaller than the other large mass and b) the comet or asteroid has not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena are due to the effects of solar radiation and the solar wind acting upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. The coma may be up to 15 times Earth's diameter, while the tail may stretch beyond one astronomical unit. If sufficiently bright, a comet may be seen from Earth without the aid of a telescope and may subtend an arc of 30° (60 Moons) across the sky. Comets have been observed and recorded since ancient times by many cultures and religions. Comets usually have highly eccentric elliptical orbits, and they have a wide range of orbital periods, ranging from several years to potentially several mill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. Of the roughly one million known asteroids the greatest number are located between the orbits of Mars and Jupiter, approximately 2 to 4 AU from the Sun, in the main asteroid belt. Asteroids are generally classified to be of three types: C-type, M-type, and S-type. These were named after and are generally identified with carbonaceous, metallic, and silicaceous compositions, respectively. The size of asteroids varies greatly; the largest, Ceres, is almost across and qualifies as a dwarf planet. The total mass of all the asteroids combined is only 3% that of Earth's Moon. The majority of main belt asteroids follow slightly elliptical, stable orbits, revolving in the same direction as the Earth and taking from three to six years to comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Félix Tisserand
François Félix Tisserand (13 January 1845 – 20 October 1896) was a French astronomer. Life Tisserand was born at Nuits-Saint-Georges, Côte-d'Or. In 1863 he entered the École Normale Supérieure, and on leaving he went for a month as professor at the lycée at Metz. Urbain Le Verrier offered him a post in the Paris Observatory, which he entered as astronome adjoint in September 1866. In 1868 he took his doctor's degree with a thesis on Delaunay's Method, which he showed to be of much wider scope than had been contemplated by its inventor. Shortly afterwards he went out to Kra Isthmus to observe the 1868 solar eclipse. He was part of a French expedition together with the Édouard Stephan and Georges Rayet. The French astronomers were accompanied by Mongkut, the King of Siam who had calculated the location and the date of the eclipse by himself two years before and prepared a comfortable watching place for the scientists. In 1873 he was appointed director of the observatory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semimajor Axis
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 two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the center t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (orbit)
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy. Definition In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: * circular orbit: ''e'' = 0 * elliptic orbit: 0 < ''e'' < 1 * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a Plane of reference, reference plane and the orbital plane or Axis of rotation, axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°. Orbits The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the orbital plane and the plane of reference, normally stated in degree (angle), degrees. For a satellite orbiting a planet, the plane of reference is usually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler 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. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. Keplerian elements The traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the traj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tisserand's Parameter
Tisserand's parameter (or Tisserand's invariant) is a value calculated from several orbital elements (semi-major axis, orbital eccentricity and inclination) of a relatively small object and a larger " perturbing body". It is used to distinguish different kinds of orbits. The term is named after French astronomer Félix Tisserand, and applies to restricted three-body problems in which the three objects all differ greatly in mass. Definition For a small body with semi-major axis a\,\!, orbital eccentricity e\,\!, and orbital inclination i\,\!, relative to the orbit of a perturbing larger body with semimajor axis a_P, the parameter is defined as follows: :T_P\ = \frac + 2\cos i\sqrt The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation. Applications * TJ, Tisserand's parameter with respect to Jupiter as perturbing body, is frequently used to distinguish asteroids (typically T_J > 3) from Jupiter-family comets (typically 2< T_J < 3).< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Integral
In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem.Bibliothèque nationale de France Unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases. It was named after German mathematician . Definition Synodic system One of the suitable coordinate systems used is the so-called ''syn ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight. ''Vis viva'' (Latin for "living force") is a term from the history of mechanics, and it survives in this sole context. It represents the principle that the difference between the total work of the accelerating forces of a system and that of the retarding forces is equal to one half the ''vis viva'' accumulated or lost in the system while the work is being done. Equation For any Keplerian orbit (elliptic, parabolic, hyperbolic, or radial), the ''vis-viva'' equation is as follows: :v^2 = GM \left( - \right) where: * ''v'' is the relative speed of the two bodies * ''r'' is the distance between the two bodies centers of mass * ''a'' is the length of the semi-major axis ('' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its momentum vector; the latter is in Newtonian mechanics. Unlike linear momentum, angular m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler 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. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. Keplerian elements The traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the traj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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