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Encyclopedia > Orbit
Two bodies with a slight difference in mass orbiting around a common barycenter. The sizes, and this particular type of orbit are similar to the Pluto-Charon system.
Two bodies with a slight difference in mass orbiting around a common barycenter. The sizes, and this particular type of orbit are similar to the Pluto-Charon system.

In physics, an orbit is the path that an object makes around another object while under the influence of a source of centripetal force, such as gravity. Image File history File links Two bodies with a slight difference in mass orbiting around a common barycenter (red cross) with circular orbits. ... Image File history File links Two bodies with a slight difference in mass orbiting around a common barycenter (red cross) with circular orbits. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... It has been suggested that Center of gravity be merged into this article or section. ... Adjectives: Plutonian Atmosphere Surface pressure: 0. ... Charon (shair-ən or kair-ən (key), IPA , Greek Χάρων), discovered in 1978, is, depending on the definition employed, either the largest moon of Pluto or one member of a double dwarf planet with Pluto being the other member. ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and characterization of universal laws which govern matter, energy, space, and time. ... The centripetal force is the external force required to make a body follow a circular path at constant speed. ... Gravity is a force of attraction that acts between bodies that have mass. ...

Contents

History

Orbits were first analyzed mathematically by Johannes Kepler who formulated his results in his three laws of planetary motion. First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed of the planet depends on the planet's distance from the sun. And third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the sun. For each planet, the cube of the planet's distance from the sun, measured in astronomical units (AU), is equal to the square of the planet's orbital period, measured in Earth years. Jupiter, for example, is approximately 5.2 AU from the sun and its orbital period is 11.86 Earth years. So 5.2 cubed equals 11.86 squared, as predicted. Johannes Kepler (December 27, 1571 – November 15, 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... The eight planets and three dwarf planets of the Solar System. ... Major features of the Solar System (not to scale; from left to right): Pluto, Neptune, Uranus, Saturn, Jupiter, the asteroid belt, the Sun, Mercury, Venus, Earth and its Moon, and Mars. ... For other uses, see Ellipse (disambiguation). ... Circle illustration This article is about the shape and mathematical concept of circle. ... In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... In geometry, the focus (pl. ... The astronomical unit (AU or au or a. ...


Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies responding to the force of gravity were conic sections. Newton showed that a pair of bodies follow orbits of dimensions that are in inverse proportion to their masses about their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Sir Isaac Newton, (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. ... “Gravity” redirects here. ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... 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 were concentrated. ...


Planetary orbits

Within a planetary system, planets, dwarf planets, asteroids (a.k.a. minor planets), comets ,and space debris orbit the central star in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a central star is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about that planet. An artists concept of a protoplanetary disc. ... The eight planets and three dwarf planets of the Solar System. ... Artists impression of Pluto (background) and Charon (foreground). ... 253 Mathilde, a C-type asteroid. ... Comet Hale-Bopp 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. ... STAR is an acronym for: Organizations Society of Ticket Agents and Retailers], the self-regulatory body for the entertainment ticket industry in the UK. Society for Telescopy, Astronomy, and Radio, a non-profit New Jersey astronomy club. ... In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... Major features of the Solar System (not to scale; from left to right): Pluto, Neptune, Uranus, Saturn, Jupiter, the asteroid belt, the Sun, Mercury, Venus, Earth and its Moon, and Mars. ... A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... An Earth observation satellite, ERS 2 For other uses, see Satellite (disambiguation). ...


Owing to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest eccentricities are those of the orbits of Venus and Neptune. Perturbation is a term used in astronomy to describe alterations to an objects orbit caused by gravitational interactions with other bodies. ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... This article is about the planet. ... Adjectives: Martian Atmosphere Surface pressure: 0. ... Adjectives: Venusian or (rarely) Cytherean Atmosphere Surface pressure: 9. ... Adjectives: Neptunian Atmosphere Surface pressure: ≫ 100 kPa (cloud level) Composition: 80% ± 3. ...


As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other. This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ...


In the elliptical orbit, the center of mass of the orbiting-orbited system will sit at one focus of both orbits, with nothing present at the other focus. As a planet approaches periapsis, the planet will increase in velocity. As a planet approaches apoapsis, the planet will decrease in velocity. 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 were concentrated. ... In geometry, the focus (pl. ... The velocity of an object is its speed in a particular direction. ...


See also:

Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... The Secular Variations of the Planetary Orbits (French: Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) is a theory describing the long-term changes (secular variation) in the orbits of the planets Mercury to Neptune to the highest accuracy astronomy can muster nowadays. ...

Understanding orbits

There are a few common ways of understanding orbits.

  • As the object moves sideways, it falls toward the orbited object. However it moves so quickly that the curvature of the orbited object will fall away beneath it.
  • A force, such as gravity, pulls the object into a curved path as it attempts to fly off in a straight line.
  • As the object falls, it moves sideways fast enough (has enough tangential velocity) to miss the orbited object. This understanding is particularly useful for mathematical analysis, because the object's motion can be described as the sum of the three one-dimensional coordinates oscillating around a gravitational center.

As an illustration of an orbit around a planet, the much-used cannon model may prove useful (see image below). Imagine a cannon sitting on top of a tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so that the cannon will be above the Earth's atmosphere and we can ignore the effects of air friction on the cannon ball. Look up path in Wiktionary, the free dictionary. ... Newtons cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. ...


Image File history File links No higher resolution available. ...


If the cannon fires its ball with a low initial velocity, the trajectory of the ball curves downwards and hits the ground (A). As the firing velocity is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense — they are describing a portion of an elliptical path around the center of gravity — but the orbits are of course interrupted by striking the earth.


If the cannonball is fired with sufficient velocity, the ground curves away from the ball at least as much as the ball falls — so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity, and mass of the object being fired, there is one specific firing velocity that produces a circular orbit, as shown in (C).


As the firing velocity is increased beyond this, a range of elliptical orbits are produced; one is shown in (D). If the initial firing is above the surface of the earth as shown, there will also be elliptical orbits at slower velocities; these will come closest to the earth opposite the firing the point. For other uses, see Ellipse (disambiguation). ...


At a faster velocity called escape velocity, again dependent on the firing height and mass of the object, an infinite orbit such as (E) is produced — first a range of parabolic orbits, and at even faster velocities a range of hyperbolic orbits. In a practical sense, both of these infinite orbit types mean the object is "breaking free" of the planet's gravity, and "going off into space". Space Shuttle Atlantis launches on mission STS-71. ... A parabola A parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a cone, and a plane tangent to the cone or parallel to some plane tangent to the cone. ... For hyperbole, the figure of speech, see hyperbole. ...


The velocity relationship of two objects with mass can thus be considered in four practical classes, with subtypes:


1. No orbit


2. Interrupted orbits

  • Range of interrupted elliptical paths

3. Circumnavigating orbits

  • Range of elliptical paths with closest point opposite firing point
  • Circular path
  • Range of elliptical paths with closest point at firing point

4. Infinite orbits

  • Parabolic paths
  • Hyperbolic paths

Newton's laws of motion

For a system of only two bodies that are only influenced by their mutual gravity, their orbits can be exactly calculated by Newton's laws of motion and gravity. Briefly, the sum of the forces will equal the mass times its acceleration. Gravity is proportional to mass, and falls off proportionally to the square of distance. Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... Isaac Newtons theory of universal gravitation (part of classical mechanics) states the following: Every single point mass attracts every other point mass by a force pointing along the line combining the two. ...


To calculate, it is convenient to describe the motion in a coordinate system that is centered on the heavier body, and we can say that the lighter body is in orbit around the heavier body. In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ...


An unmoving body that's far from a large object has more gravitational potential energy than one that's close, because it can fall farther. Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ...


With two bodies, an orbit is a conic section. The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less. Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... Space Shuttle Atlantis launches on mission STS-71. ...


An open orbit has the shape of a hyperbola (when the velocity is greater than the escape velocity), or a parabola (when the velocity is exactly the escape velocity). The bodies approach each other for a while, curve around each other around the time of their closest approach, and then separate again forever. This may be the case with some comets if they come from outside the solar system. In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... Comet Hale-Bopp Comet West For other uses, see Comet (disambiguation). ...


A closed orbit has the shape of an ellipse. In the special case that the orbiting body is always the same distance from the center, it is also the shape of a circle. Otherwise, the point where the orbiting body is closest to Earth is the perigee, called periapsis (less properly, "perifocus" or "pericentron") when the orbit is around a body other than Earth. The point where the satellite is farthest from Earth is called apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part. For other uses, see Ellipse (disambiguation). ... Circle illustration This article is about the shape and mathematical concept of circle. ... Perigee is the point at which an object in orbit around the Earth makes its closest approach to the Earth. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ...


Orbiting bodies in closed orbits repeat their path after a constant period of time. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows: Johannes Kepler (December 27, 1571 – November 15, 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. ...

  1. The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of the ellipse. Therefore the orbit lies in a plane, called the orbital plane. The point on the orbit closest to the attracting body is the periapsis. The point farthest from the attracting body is called the apoapsis. There are also specific terms for orbits around particular bodies; things orbiting the Sun have a perihelion and aphelion, things orbiting the Earth have a perigee and apogee, and things orbiting the Moon have a perilune and apolune (or, synonymously, periselene and aposelene). An orbit around any star, not just the Sun, has a periastron and an apastron
  2. As the planet moves around its orbit during a fixed amount of time, the line from Sun to planet sweeps a constant area of the orbital plane, regardless of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time."
  3. For each planet, the ratio of the 3rd power of its semi-major axis to the 2nd power of its period is the same constant value for all planets.

Except for special cases like Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies. The 2-body solutions were published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a converging infinite series that solves the 3-body problem, however it converges too slowly to be of much use. Apparent magnitude: up to -12. ... STAR is an acronym for: Organizations Society of Ticket Agents and Retailers], the self-regulatory body for the entertainment ticket industry in the UK. Society for Telescopy, Astronomy, and Radio, a non-profit New Jersey astronomy club. ... A contour plot of the effective potential (the Hills Surfaces) of a two-body system (the Sun and Earth here), showing the five Lagrange points. ... Newtons own copy of his Principia, with hand written corrections for the second edition. ... Karl Fritiof Sundman (1873 – 1949), Finnish mathematician who used analytic methods to prove the existence of an infinite series solution to the three-body problem in 1906 and 1909. ...


Instead, orbits can be approximated with arbitrarily high accuracy. These approximations take two forms.


One form takes the pure elliptic motion as a basis, and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moon, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. Still there are secular phenomena that have to be dealt with by post-newtonian methods. Perturbation is a term used in astronomy to describe alterations to an objects orbit caused by gravitational interactions with other bodies. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros = daily) was, traditionally, a table providing the positions (given in a Cartesian coordinate system, or in right ascension and declination or, for astrologers, in longitude along the zodiacal ecliptic), of the Sun, the Moon, the planets, asteroids or comets in the... Celestial Navigation is the 15th episode of The West Wing. ... In astronomy, secular phenomena (which repeat too slowly to be observed, if at all) are contrasted with phenomena observed to repeat periodically. ... The parameterized post-Newtonian formalism or PPN formalism is a tool used to compare classical theories of gravitation in the limit most important for everyday gravitational experiments: the limit in which the gravitational field is weak and generated by objects moving slowly compared to the speed of light. ...


The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces will equal the mass times its acceleration (F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial ones corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a tiny time in the future, then repeat this. However, tiny arithmetic errors from the limited accuracy of a computer's math accumulate, limiting the accuracy of this approach. A simulation of airflow into a duct using the Navier-Stokes equations A differential equation is a mathematical equation for an unknown function of one or several variables which relates the values of the function itself and of its derivatives of various orders. ... In mathematics, an initial value problem is a statement of a differential equation together with specified value of the unknown function at a given point in the domain of the solution. ...


Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large objects have been simulated.


Analysis of orbital motion

(See also orbit equation and Kepler's first law.)

To analyze the motion of a body moving under the influence of a force which is always directed towards a fixed point, it is convenient to use polar coordinates with the origin coinciding with the center of force. In such coordinates the radial and transverse components of the acceleration are, respectively: In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point basicly. ...

a_r = frac{d^2r}{dt^2} - rleft( frac{dtheta}{dt} right)^2

and

a_{theta} = frac{1}{r}frac{d}{dt}left( r^2frac{dtheta}{dt} right).

Since the force is entirely radial, and since acceleration is proportional to force, it follows that the transverse acceleration is zero. As a result,

frac{d}{dt}left( r^2frac{dtheta}{dt} right) = 0.

After integrating, we have

r^2frac{dtheta}{dt} = {rm const.} which is actually the theoretical proof of Kepler's 2nd law (A line joining a planet and the sun sweeps out equal areas during equal intervals of time)

The constant of integration h is the angular momentum per unit mass. It then follows that Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ...

frac{dtheta}{dt} = { h over r^2 } = hu^2

where we have introduced the auxiliary variable

u = { 1 over r }.

The radial force is f(r) per unit is ar, then the elimination of the time variable from the radial component of the equation of motion yields:

frac{d^2u}{dtheta^2} + u = -frac{f(1 / u)}{h^2u^2}.

In the case of gravity, Newton's law of universal gravitation states that the force is proportional to the inverse square of the distance: Gravity is a force of attraction that acts between bodies that have mass. ... Gravity is a force of attraction that acts between bodies that have mass. ...

f(1/u) = a_r = { -GM over r^2 } = -GM u^2

where G is the constant of universal gravitation, m is the mass of the orbiting body (planet), and M is the mass of the central body (the Sun). Substituting into the prior equation, we have According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

frac{d^2u}{dtheta^2} + u = frac{ GM }{h^2}.

So for the gravitational force – or, more generally, for any inverse square force law – the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ...


The equation of the orbit described by the particle is thus:

r = frac{1}{u} = frac{ h^2 / GM }{1 + e cos (theta - theta_0)},

where p, e and θ0are constants of integration,

p = { h^2 over GM } = a(1-e^2)

If parameter e is smaller than one, e is the eccentricity and a the semi-major axis of an ellipse. In general, this can be recognized as the equation of a conic section in polar coordinates (r,θ). In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... For other uses, see Ellipse (disambiguation). ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ...


Orbital period

Main article: Orbital period

The orbital period is the time it takes a planet (or another object) to make one full orbit. ...

Orbital decay

Main article: Orbital decay

If some part of a body's orbit enters an atmosphere, its orbit can decay because of drag. At each periapsis, the object scrapes the air, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body. Orbital decay is the process of prolonged reduction in the height of a satellite’s orbit due to drag produced by an atmosphere. ... An object falling through a gas or liquid experiences a force in direction opposite to its motion. ...


The bounds of an atmosphere vary wildly. During solar maxima, the Earth's atmosphere causes drag up to a hundred kilometres higher than during solar minimums. Solar maximum or solar max is the period of greatest solar activity in the solar cycle of the sun. ...


Some satellites with long conductive tethers can also decay because of electromagnetic drag from the Earth's magnetic field. Basically, the wire cuts the magnetic field, and acts as a generator. The wire moves electrons from the near vacuum on one end to the near-vacuum on the other end. The orbital energy is converted to heat in the wire. The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ...


Orbits can be artificially influenced through the use of rocket motors which change the kinetic energy of the body at some point in its path. This is the conversion of chemical or electrical energy to kinetic energy. In this way changes in the orbit shape or orientation can be facilitated.


Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input other than that of the sun, and so can be used indefinitely. See statite for one such proposed use. Concept image of a solar sail spacecraft in the process of unfurling sails. ... A magnetic sail or magsail is a proposed method of spacecraft propulsion. ... A statite is a hypothetical type of artificial satellite that employs a solar sail to continuously modify its orbit in ways that gravity alone would not allow. ...


Orbital decay can also occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years. Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... A synchronous orbit is an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body. ... The tidal force is a secondary effect of the force of gravity and is responsible for the tides. ... Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ... Phobos (IPA or , Greek Φόβος: Fright), is the larger and innermost of Mars two moons (the other being Deimos), and is named after Phobos, son of Ares (Mars) from Greek Mythology. ...


Finally, orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely. In physics, a gravitational wave is a fluctuation in the curvature of spacetime which propagates as a wave, traveling outward from a moving object or system of objects. ... Simulated view of a black hole in front of the Milky Way. ... A neutron star is one of the few possible endpoints of stellar evolution. ...


Earth orbits

Main article: Geocentric orbit

Geocentric orbit refers to the orbit of any object orbiting the Earth, such as the Moon or artificial satellites. ...

Scaling in gravity

The gravitational constant G is measured to be: According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

  • (6.6742 ± 0.001) × 10−11 N·m2/kg2
  • (6.6742 ± 0.001) × 10−11 m3/(kg·s2)
  • (6.6742 ± 0.001) × 10−11 (kg/m3)-1s-2.

Thus the constant has dimension density-1 time-2. This corresponds to the following properties.


Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the earth. A scale factor is a number which scales some quantity. ... Several equivalence relations in mathematics are called similarity. ...


When all densities are multiplied by four, orbits are the same, but with orbital velocities doubled.


When all densities are multiplied by four, and all sizes are halved, orbits are similar, with the same orbital velocities.


These properties are illustrated in the formula

GT^2 sigma = 3pi left( frac{a}{r} right)^3,

for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period. The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...


Role in the evolution of atomic theory

When atomic structure was first probed experimentally early in the twentieth century, an early picture of the atom portrayed it as a miniature solar system bound by the coulomb force rather than by gravity. This was inconsistent with electrodynamics and the model was progressively refined as quantum theory evolved, but there is a legacy of the picture in the term orbital for the wave function of an energetically bound electron state. Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Fig. ... e- redirects here. ...


See also

An artificial satellite orbit is a path that an artificial satellite makes around another object with sufficient mass to have a gravitational effect on it. ... Reentry redirects here. ... In stellar dynamics a box orbit refers to a particular type of orbit which can be seen in triaxial systems, that is, systems which do not possess a symmetry around any of its axes. ... In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ... A geostationary orbit (abbreviated GEO) is a circular orbit in the Earths equatorial plane, any point on which revolves about the Earth in the same direction and with the same period as the Earths rotation. ... Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. ... Space Shuttle Atlantis launches on mission STS-71. ... A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earths equator (0º latitude). ... Gravity is a force of attraction that acts between bodies that have mass. ... It has been suggested that sling effect be merged into this article or section. ... A halo orbit is an orbit around a Lagrange point between two larger bodies. ... 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. ... In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. ... Artists concept of the Interplanetary Transport Network. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ... In orbital mechanics, a Lissajous orbit is a quasi-periodic orbital trajectory an object can follow around a colinear libration point of a two-body system without requiring any propulsion. ... In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. ... Milankovitch cycles are the collective effect of changes in the Earths movements upon its climate, named after Serbian civil engineer and mathematician Milutin Milanković. The eccentricity, axial tilt, and precession of the Earths orbit vary in several patterns, resulting in 100,000 year ice age cycles of the... This article is about the n-body problem in classical mechanics. ... In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... An orbital maneuver is a change from one orbit to another, accomplished by applying thrust. ... The orbit of the Moon around the Earth is completed in approximately 27. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... An orbital spaceflight (or orbital flight) in the general sense is a spaceflight where the trajectory of a spacecraft reaches the height of, and through having an appropriate velocity enters into, orbit around an astronomical body. ... 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. ... Perigee is the point at which an object in orbit around the Earth makes its closest approach to the Earth. ... In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ... This article is about retrograde motion. ... Rosetta Orbit (image courtesy NASA) A Rosetta orbit is a complex type of orbit. ... In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ... A sub-orbital spaceflight (or sub-orbital flight) is a spaceflight that does not involve putting a vehicle into orbit. ... Mathematically the term trajectory refers to the ordered set of states which are assumed by a dynamical system over time (see e. ...

References

  • Abell, Morrison, and Wolff (1987). Exploration of the Universe, fifth edition, Saunders College Publishing. 

External links


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Orbit :: Wrigley (171 words)
Orbit is available in seven great flavors including Original Peppermint, Spearmint, Wintermint, Bubblemint, Cinnamint and two fabulous new flavors: Citrusmint and Sweet Mint.
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The size of the orbit is given by the periapsis distance (SP) and the elongation of the orbit is given by the eccentricity (e).
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The argument of the periapsis measures the angular displacement in the plane of the orbit between the ascending node and the line that passes through the center of the orbit (C) and the periapsis (P).
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