Citizendia
Your Ad Here

For other uses, see Orbit (disambiguation).
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. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The sizes, and this particular type of orbit are similar to the Pluto-Charon system. Charon (ˈʃærən; also, as in Χάρων) discovered in 1978 is either the largest Moon of Pluto or the smaller member of a double

In physics, an orbit is the path of one object around a point or another body. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Orbits are explained and calculated by Newton's law of universal gravitation and Kepler's laws of planetary motion. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. [1][2]

Contents

History

In the geocentric model of the solar system, mechanisms such as the deferent and epicycle were supposed to explain the motion of the planets in terms of perfect spheres or rings. In Astronomy, the geocentric model of the Universe is the superseded theory that the Earth is the center of the universe and other In the Ptolemaic system of Astronomy, the epicycle (literally on the circle in Greek) was a geometric model used to explain the variations in

The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarized in his three laws of planetary motion. Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. 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. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is The Solar System consists of the Sun and those celestial objects bound to it by Gravity. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the In the Ptolemaic system of Astronomy, the epicycle (literally on the circle in Greek) was a geometric model used to explain the variations in In Geometry, the foci (singular focus) are a pair of special points used in describing Conic sections The four types of conic sections are the Circle [3] 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. The astronomical unit ( AU or au or au or sometimes ua) is a unit of Length based on the distance from the Earth to the 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.

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. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Gravitation is a natural Phenomenon by which objects with Mass attract one another In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface 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. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object 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.

Planetary orbits

Within a planetary system; planets, dwarf planets, asteroids (a. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is A dwarf planet, as defined by the International Astronomical Union (IAU is a Celestial body Orbiting the Sun that is massive enough to be rounded Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but k. a. minor planets), comets, and space debris orbit the central star in elliptical orbits. A comet is a small Solar System body that orbits the Sun and when close enough to the Sun exhibits a visible coma (atmosphere or a tail — Space debris or orbital debris, also called space junk and space waste are the objects in Orbit around Earth created by humans that no A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 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. In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1 To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about that planet. A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. This article is about artificial satellites For natural satellites also known as moons see Natural satellite.

Owing to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape 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. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System.

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. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an Earth orbit, respectively. )

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. In Geometry, the foci (singular focus) are a pair of special points used in describing Conic sections The four types of conic sections are the Circle As a planet approaches periapsis, the planet will increase in speed, or velocity. In Physics, velocity is defined as the rate of change of Position. As a planet approaches apoapsis, the planet will decrease in velocity.

See also:

Understanding orbits

There are a few common ways of understanding orbits. In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. The Secular Variations of the Planetary Orbits (French Variations Séculaires des Orbites Planétaires, abbreviated as VSOP) is a semi-analytic theory describing

As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). Newton's cannonball was a Thought experiment Isaac Newton used to hypothesize that the force of Gravity was universal and it was the key force for 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 cannonball.

The Newton Cannon, an illustration of how objects can "fall" in a curve.
The Newton Cannon, an illustration of how objects can "fall" in a curve.

If the cannon fires its ball with a low initial velocity, the trajectory of the ball curves downward 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 planet, there is one specific firing velocity that produces a circular orbit, as shown in (C). For other meanings of the term "orbit" see Orbit (disambiguation In Astrodynamics or Celestial mechanics a circular

As the firing velocity is increased beyond this, a range of elliptic orbits are produced; one is shown in (D). In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 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 at the point half an orbit beyond, and directly opposite, the firing point.

At a specific velocity called escape velocity, again dependent on the firing height and mass of the planet, an infinite orbit such as (E) is produced — a parabolic trajectory. In Physics, escape velocity is the speed where the Kinetic energy of an object is equal to the magnitude of its Gravitational potential energy In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 At even faster velocities the object will follow a range of hyperbolic trajectories. In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1 In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space".

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

1. No orbit

2. Interrupted orbits

3. Circumnavigating orbits

4. Infinite orbits

Newton's laws of motion

In many situations relativistic effects can be neglected, and Newton's laws give a highly accurate description of the motion. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Then the acceleration of each body is equal to the sum of the gravitational forces on it, divided by its mass, and the gravitational force between each pair of bodies is proportional to the product of their masses and decreases inversely with the square of the distance between them. To this Newtonian approximation, for a system of two point masses or spherical bodies, only influenced by their mutual gravitation (the two-body problem), the orbits can be exactly calculated. In Classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other If the heavier body is much more massive than the smaller, as for a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate and 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. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point (For the case where the masses of two bodies are comparable an exact Newtonian solution is still available, and qualitatively similar to the case of dissimilar masses, by centering the coordinate system on the center of mass of the two. )

Energy is associated with gravitational fields. A stationary body far from another can do external work if it is pulled towards it, and therefore has gravitational potential energy. Potential energy can be thought of as Energy stored within a physical system Since work is required to separate two massive bodies against the pull of gravity, their gravitational potential energy increases as they are separated, and decreases as they approach one another. For point masses the gravitational energy decreases without limit as they approach zero separation, and it is convenient and conventional to take the potential energy as zero when they are an infinite distance apart, and then negative (since it decreases from zero) for smaller finite distances.

With two bodies, an orbit is a conic section. In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system. The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός 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. In Physics, escape velocity is the speed where the Kinetic energy of an object is equal to the magnitude of its Gravitational potential energy Since the kinetic energy is never negative, if the common convention is adopted of taking the potential energy as zero at infinite separation, the bound orbits have negative total energy, parabolic trajectories have zero total energy, and hyperbolic orbits have positive total energy.

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). In Geometry, a hyperbola ( Greek, "over-thrown" has several equivalent definitions In Mathematics, the parabola (pəˈræbələ from the Greek παραβολή) is a Conic section, the intersection of a right circular 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. A comet is a small Solar System body that orbits the Sun and when close enough to the Sun exhibits a visible coma (atmosphere or a tail —

A closed orbit has the shape of an ellipse. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a In the special case that the orbiting body is always the same distance from the center, it is also the shape of a circle. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the 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. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from 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.

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. Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer These can be formulated as follows:

  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. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth
  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 cube of its semi-major axis to the square of its period is the same constant value for all planets.

Note that that while the bound orbits around a point mass, or a spherical body with an ideal Newtonian gravitational field, are all closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects (as caused, for example, by the slight oblateness of the Earth, or by relativistic effects, changing the gravitational field's behavior with distance) will cause the orbit's shape to depart to a greater or lesser extent from the closed ellipses characteristic of Newtonian two body motion. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. The 2-body solutions were published by Newton in Principia in 1687. The Philosophiæ Naturalis Principia Mathematica ( Latin: "mathematical principles of natural philosophy" often Principia 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. Karl Frithiof Sundman (1873 &ndash 1949 was a Finnish Mathematician who used analytic methods to prove the existence of a convergent Infinite series solution Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.

Instead, orbits with many bodies 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. An ephemeris (plural ephemerides; from the Greek word ἐφήμερος ephemeros "daily" is a table of values that gives the positions of Celestial navigation, also known as astronavigation, is a Position fixing technique that was devised to help sailors cross the featureless oceans without having to Still there are secular phenomena that have to be dealt with by post-newtonian methods. In Astronomy, secular phenomena (which repeat too slowly to be observed if at all are contrasted with phenomena observed to repeat periodically Post-Newtonian formalism is a calculational tool that expresses Einstein's (nonlinear equations of gravity in terms of the lowest-order deviations from Newton's theory

The differential equation form is used for scientific or mission-planning purposes. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the 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. In Mathematics, in the field of Differential equations an initial value problem is an Ordinary differential equation together with specified value called 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.

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. In Astrodynamics an Orbit equation defines the path of Orbiting body m_2\\! around Central body m_1\\! relative to In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. )

Please note that the following is a classical (Newtonian) analysis of orbital mechanics, which assumes the more subtle effects of general relativity (like frame dragging and gravitational time dilation) are negligible. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging Gravitational time dilation is the effect of time passing at different rates in regions of different Gravitational potential; the higher the local distortion of Spacetime General relativity does, however, need to be considered for some applications such as analysis of extremely massive heavenly bodies, precise prediction of a system's state after a long period of time, and in the case of interplanetary travel, where fuel economy, and thus precision, is paramount.

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 Mathematics, the polar coordinate system is a two-dimensional Coordinate system in which each point on a plane is determined by In such coordinates the radial and transverse components of the acceleration are, respectively:

a_r = \frac{d^2r}{dt^2} - r\left( \frac{d\theta}{dt} \right)^2

and

a_{\theta} = \frac{1}{r}\frac{d}{dt}\left( r^2\frac{d\theta}{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^2\frac{d\theta}{dt} \right) = 0.

After integrating, we have

r^2\frac{d\theta}{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). In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. The constant of integration, h, is the angular momentum per unit mass. In Astrodynamics, the specific relative angular momentum of an Orbiting body with respect to a Central body is the Relative angular momentum It then follows that

\frac{d\theta}{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}{d\theta^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:

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). Gravitation is a natural Phenomenon by which objects with Mass attract one another Gravitation is a natural Phenomenon by which objects with Mass attract one another The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Substituting into the prior equation, we have

\frac{d^2u}{d\theta^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). This article is about the harmonic oscillator in classical mechanics The solution is:

u(\theta) = \frac{ GM }{h^2} + A \cos(\theta-\theta_0)

where A and θ0 are arbitrary constants.

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 e is:

e \equiv \frac{h^2A}{G M}\ .

In general, this can be recognized as the equation of a conic section in polar coordinates (r, θ). In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface In Mathematics, the polar coordinate system is a two-dimensional Coordinate system in which each point on a plane is determined by We can make a further connection with the classic description of conic section with:

\frac{h^2}{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 Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a

Orbital planes

Main article: Orbital plane (astronomy)

The analysis so far has been two dimensional; it turns out that an unperturbed orbit is two dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two dimensional plane into the required angle relative to the poles of the planetary body involved. The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. This article describes perturbation theory as a general mathematical method

The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles.

Orbital period

Main article: Orbital period

The orbital period is simply how long an orbiting body takes to complete one orbit. The orbital period is the time taken for a given object to make one complete Orbit about another object

Specifying orbits

Main article: orbital elements

It turns out that it takes a minimum 6 numbers to specify an orbit about a body, and this can be done in several ways. The elements of an orbit are the parameters needed to specify that Orbit uniquely given a model of two point-masses obeying the Newtonian laws of motion and the For example, specifying the 3 numbers specifying location and 3 specifying the velocity of a body gives a unique orbit that can be calculated forwards (or backwards). In Physics, velocity is defined as the rate of change of Position. However, traditionally the parameters used are slightly different.

The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his Kepler's laws. Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. The Keplerian elements are six:

In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. Inclination in general is the Angle between a Reference plane and another plane or axis of direction The longitude of the ascending node (☊ or Ω is one of the Orbital elements used to specify the Orbit of an object in space The argument of periapsis (or argument of perifocus) ( ω) is the Orbital element describing the Angle of an Orbiting body's periapsis In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In the study of orbital dynamics the mean anomaly of an orbiting body is the Angle the body would have traveled about the center of the orbit's Auxiliary circle In Astronomy, an epoch is a moment in time used as a reference for the Orbital elements of a Celestial body. However, in practice, orbits are affected, perturbed, by forces other than gravity due to the central body and thus the orbital elements change over time.

Orbital perturbations

An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time.

Radial, prograde and tranverse perturbations

It can be shown that a radial impulse given to a body in orbit doesn't change the orbital period (since it doesn't affect the angular momentum), but changes the eccentricity. This means that the orbit still intersects the original orbit in two places.

For a prograde or retrograde impulse (i. e. an impulse applied along the orbital motion), this changes both the eccentricity as well as the orbital period, but any closed orbit will still intersect the perturbation point. Notably, a prograde impulse given at periapsis raises the altitude at apoapsis, and vice versa, and a retrograde impulse does the opposite. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from

A transverse force out of the orbital plane causes rotation of the orbital plane.

Orbital decay

Main article: Orbital decay

If some part of a body's orbit enters an atmosphere, its orbit can decay because of drag. Orbital decay is the process of prolonged reduction in the height of a satellite's Orbit. In Fluid dynamics, drag (sometimes called fluid resistance) is the force that resists the movement of a Solid object through a Fluid (a Particularly 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.

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 minima. 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. Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see 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.

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. Solar sails (also called light sails or photon sails, especially when they use Light sources other than the Sun) are a proposed form of A magnetic sail or magsail is a proposed method of Spacecraft propulsion which would use a static magnetic field to deflect charged particles radiated by the 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. A statite (a Portmanteau of static and satellite) is a hypothetical type of artificial Satellite that employs a Solar sail to

Orbital decay can also occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced 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 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 tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced 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. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about 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.

Finally, orbits can decay via the emission of gravitational waves. In Physics, a gravitational wave is a Fluctuation in the Curvature of Spacetime which propagates as a wave, traveling outward from 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. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type

Oblateness

The standard analysis of orbiting bodies assumes that all bodies consist of uniform spheres, or more generally, concentric shells each of uniform density. It can be shown that such bodies are gravitationally equivalent to point sources.

However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body. Ellipticity redirects here For the mathematical topic of ellipticity see Elliptic operator. A quadrupole or quadrapole is one of a sequence of configurations of — for example — electric charge or current or gravitational mass that can exist in ideal form but it

The general effect of this is to change the orbital parameters over time; predominantly this gives a rotation of the orbital plane around the rotational pole of a central planet (it perturbs the argument of perigee) in a way that is dependent on the angle of orbital plane to the equator as well as altitude at perigee. The argument of periapsis (or argument of perifocus) ( ω) is the Orbital element describing the Angle of an Orbiting body's periapsis

Other gravitating bodies

The effects of other gravitating bodies can be very large. For example, the orbit of the Moon cannot be in any way accurately described without allowing for the action of the Sun's gravity as well as the Earth's.

Earth orbits

Main article: Geocentric orbit

Scaling in gravity

The gravitational constant G is measured to be:

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. A scale factor is a number which scales, or multiplies some quantity 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.

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 = 3\pi \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. In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae

Role in 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. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form 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. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J

See also

References

  1. ^ Stern, David (3-24-05). (20) Newton's theory of "Universal Gravitation" (en). Retrieved on 2008-06-01. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 193 - Roman Emperor Didius Julianus is Assassinated 987 - Hugh Capet is elected
  2. ^ Stern, David (3-21-05). Kepler's Three Laws of Planetary Motion: An Overview for Science teachers (en). Retrieved on 2008-06-01. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 193 - Roman Emperor Didius Julianus is Assassinated 987 - Hugh Capet is elected
  3. ^ Jones, Andrew. Kepler's Laws of Planetary Motion (en). about.com. Aboutcom is an online source for original information and advice and is among the top 15 US Websites ( Nielsen Online Spring 2008 Retrieved on 2008-06-01. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 193 - Roman Emperor Didius Julianus is Assassinated 987 - Hugh Capet is elected
  4. ^ Basics of Spaceflight a JPL primer used by its employees.

External links

Dictionary

orbit

-noun

  1. A circular or elliptical path of one object around another object.
  2. A sphere of influence; an area of control.
  3. The course of one's usual progression, or the extent of one's typical range.
  4. (anatomy) The bony cavity containing the eyeball; the eye socket.
  5. (physics) The path an electron takes around an atom's nucleus
  6. (mathematics) A collection of points related by the evolution function of a dynamical system.

-verb

  1. To circle or revolve around another object.
  2. To move around the general vicinity of something.
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic