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Orbit

Orbit

.]] :For other meanings of the term "orbit", see orbit (disambiguation) 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.

History

Orbits were first analysed mathematically by Johannes Kepler who formulated his results in his laws of planetary motion. He found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed. 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.

Planetary orbits

Within a planetary system, planets, asteroids, comets and space debris orbit the central star in elliptical orbits. Any comet in a parabolic or hyperbolic orbit about the 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. Due to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. Pluto and Mercury have the most eccentric orbits. At the present epoch, Mars has the next largest eccentricity while the smallest eccentricities are those of the orbits of Venus and Neptune. As an object orbits another, 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 the elliptical orbit, the centre 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. See also: Kepler's laws of planetary motion

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 the orbit around a planet (eg Earth), the much-used cannon model may prove useful (see image below). Imagine a cannon sitting on top of a (very) 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. 300px If the cannon fires its ball with a low initial velocity, the trajectory of the ball will curve downwards and hit the ground (A). As the firing velocity is increased, the cannonball will hit the ground further (B) and further (C) away from the cannon, because while the ball is still falling towards the ground, the ground is curving away from it (see first point, above). If the cannonball is fired with sufficient velocity, the ground will curve away from the ball at the same rate as the ball falls - it is now in orbit (D). The orbit may be circular like (D) or if the firing velocity is increased even more, the orbit may become more (E) and more (F) elliptical. At a certain even faster velocity (called the escape velocity) the motion changes from an elliptical orbit to a parabola.

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. 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. An unmoving body that's far from a large object has more energy than one that's close. This is because it can fall farther. This is called "potential energy" because it is not yet actual. With two bodies, an orbit is a flat curve. 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. The path of a free-falling (orbiting) body is always a conic section. An open orbit has the shape of a hyperbola (or in the limiting case, a parabola); 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 is often the case with comets that occasionally approach the Sun. A closed orbit has the shape of an ellipse (or in the limiting case, a circle). 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. 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: # 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 # 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." # 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, K. F. Sundman developed a converging infinite series that solves the 3-body problem, however it converges too slowly to be of much use. 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. 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. 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 analyse 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 centre of force. In such coordinates the radial and transverse components of the acceleration are, respectively: :

\frac - r\left( \frac \right)^2

and :

\frac\frac\left( r^2\frac \right)

. Since the force is always radial, the transverse acceleration is zero, and it follows that: :

\frac = hu^2

, where h is a constant of integration and we have introduced the auxiliary variable u defined as 1/r. If magnitude of the radial force is f(r) per unit mass of the orbiting body, then the elimination of the time variable from the radial component of the equation of motion yields: :

\frac + u = \frac

. In the case of an 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). The equation of the orbit described by the particle is thus: :

r = \frac = \frac

, where φ and e are constants of integration and L is the Semi-latus rectum. This can be recognised as the equation of a conic section in polar coordinates.

Orbital parameters

See: Orbital elements For a general elliptic orbit, the relations between the axis, eccentricity, and least and largest distance are: :Semimajor axis = (periapsis + apoapsis)/2 = mean of the extreme radii :Periapsis = semimajor axis × (1 - eccentricity) = least distance :Apoapsis = semimajor axis × (1 + eccentricity) = largest distance Note that there are alternative definitions for a "mean radius" or "average distance": if you average the radius over time for one orbit (mean anomaly), or over the orbital angle as observed by the primary (true anomaly), then you get a different result. See here for details.

Orbital period

See: orbital period

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. Eventually, the orbit circularises and then the object spirals into the atmosphere. 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. 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. 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, and so can be used indefinitely. See statite for one such proposed use. 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. 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.

Earth orbits

See Earth orbit for more details.
- Low Earth orbit
- High Earth Orbit
- Intermediate circular orbit
- Geostationary orbit
- Geosynchronous orbit
- Geostationary transfer orbit
- Molniya orbit
- Polar orbit
- Polar Sun Synchronous Orbit (this is not a complete list).

Scaling in gravity

The gravitational constant G is defined to be:
- 6.6742 × 10⁻¹¹ N·m²/kg²
- 6.6742 × 10⁻¹¹ m³/(kg·s²)
- 6.6742 × 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. 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 \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.

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.

External links

- An on-line orbit plotter: http://www.bridgewater.edu/departments/physics/ISAW/PlanetOrbit.html
- [http://www.braeunig.us/space/orbmech.htm Orbital Mechanics] (Rocket and Space Technology) Category:Celestial mechanics Category:Solar System als:Umlaufbahn ja:軌道 (力学) simple:Orbit th:วงโคจร

Orbit (disambiguation)

The word orbit can mean more than one thing:
- Planetary orbit
- Orbit (anatomy) - the socket in the skull which accommodates an eye
- In computing:
- ORBit - an object request broker (ORB) for CORBA
- ORBit2 - an object request broker (ORB) for CORBA
- In mathematics:
- Orbit (dynamics)
- Orbit (group theory)
- Wrigley's Orbit, a brand of chewing gum.
- Orbit (band)
- Orbit (irrigation)
- Orbit (magazine) a science fiction magazine

Centripetal force

Centripetal force is the force accelerating an object toward the center of a circular path as the object goes around the circle. An object can travel in a circle only if there is a centripetal force on it. In the case of an orbiting satellite the centripetal force is its weight and acts toward the satellite's primary; in the case of an object at the end of a rope, the centripetal force is the tension of the rope and acts towards whatever the rope is anchored to. In the case of a spinning object, internal tensile stress provides the centripetal force that keeps the object together. Centripetal force must not be confused with centrifugal force. In an inertial reference frame (not rotating or accelerating), the centripetal force accelerates a particle in such a way that it moves along a circular path. In a corotating reference frame, a particle in circular motion has zero velocity. In this case, the centripetal force appears to be exactly cancelled by a pseudo-force, the centrifugal force. Centripetal forces are true forces, appearing in inertial reference frames; centrifugal forces appear only in rotating frames. Centripetal force must not be confused with central force either. Objects moving in a straight line with constant speed also have constant velocity. However, an object moving in an arc with constant speed has a changing direction of motion. As velocity is a vector of speed and direction, a changing direction implies a changing velocity. The rate of this change in velocity is the centripetal acceleration. Differentiating the velocity vector gives the direction of this acceleration towards the center of the circle. In the plane of motion we have: :

\mathbf = - \frac \hat = - \frac \frac = - \omega^2 \mathbf

By Newton's second law of motion, as there is an acceleration there has to be a force in the direction of the acceleration. This is the centripetal force, and is in the plane of motion equal to: :

\mathbf = - \frac \hat = - \frac \frac = - m \omega^2 \mathbf

(where m is mass, v is velocity, r is radius of the circle, and the minus sign denotes that the vector points to the center of the circle and ω = v / r is the angular velocity) In 3D notation we can write: :

\boldsymbol F_c = m \boldsymbol\omega \times   (\boldsymbol\omega \times   \boldsymbol r )

, where

\boldsymbol\omega

is the vector angular velocity of the rotation and

\boldsymbol r

is a vector from an arbitrary point on the rotation axis to the body (with mass

m

). Centripetal means towards the center.

Proof of law

Simply use a polar coordinate system, assume a constant radius, and take two derivatives. Let r(t) be a vector that describes the position of a point mass as a function of time. Since we are assuming uniform circular motion, let r(t) = R·u_r, where R is a constant (the radius of the circle) and u_r is the unit vector pointing from the origin to the point mass. In terms of Cartesian unit vectors: :

u_r = cos(\theta)u_x + sin(\theta)u_y \,

Note: unlike in cartesian coordinates where the unit vectors are constants, in polar coordinates the direction of the unit vectors depend on the angle between the x_axis and the point being described; the angle θ. So we take the first derivative to find velocity: :

v = R \frac  \,

v = R \frac u_\theta \,

v = R \omega u_\theta \,

where ω is the angular velocity (just a short way of writing dθ/dt), u_θ is the unit vector that is perpendicular to u_r that points in the direction of increasing θ. In cartesian terms: u_θ = -sin(θ) u_x + cos(θ) u_y This result for the velocity is good because it matches our expectation that the velocity should be directed around the circle, and that the magnitude of the velocity should be ωR. Taking another derivative, we find that the acceleration, a is: :

a = R \left( \frac  u_\theta - \omega^2 u_r \right) \,

since the motion is uniform, the magnitude of v is constant, and thus there can be no dv/dt that points in the same direction as v. This fact implies ω is constant which simplifies the equation to: :

a = -R \omega^2 u_r \,

A simple substitution brings us to the equation above.

References

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- Category:Force Category:Mechanics ko:구심력 ja:回転運動

Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630), a key figure in the scientific revolution, was a German mathematician, astronomer and astrologer of famed brilliance. He is best known for his laws of planetary motion, expounded in the two books Astronomia nova and Harmonice Mundi. Kepler was a professor of mathematics at the University of Graz, court mathematician to Emperor Rudolf II, and court astrologer to General Wallenstein. Early in his career, Kepler was an assistant to Tycho Brahe. Kepler's career also coincided with that of Galileo Galilei. He is sometimes referred to as "the first theoretical astrophysicist", although Carl Sagan also referred to him as the last scientific astrologer.

Life

Kepler was born on December 27, 1571 at the Imperial Free City of Weil der Stadt (now part of the Stuttgart Region in the German state of Baden-Württemberg, 30 km west of Stuttgart's center). His grandfather had been Lord Mayor of that town, but by the time Johannes was born, the Kepler family fortunes were in decline. His father earned a precarious living as a mercenary, and abandoned the family when Johannes was 17. His mother, an inn-keeper's daughter, had a reputation for involvement in witchcraft. Born prematurely, Johannes is said to have been a weak and sickly child, but despite his ill health, he was precociously brilliant - he often impressed travelers at the inn [aforementioned] with his phenomenal mathematical faculty as a child. Though he excelled in his schooling, Kepler was frequently bullied, and was plagued by a belief that he was physically repulsive, thoroughly unlikable and, compared to the other pupils, an outsider. This ostracizing probably led him to turn to the world of ideas, as well as an abiding religious conviction, for solace. He was introduced to astronomy/astrology at an early age, and developed a love for that discipline that would span his entire life. At age five, he observed the Comet of 1577, writing that he "...was taken by [his] mother to a high place to look at it." At age nine, he observed another astronomical event, the Lunar eclipse of 1580, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red." In 1587, Kepler began attending the University of Tübingen, where he proved himself to be a superb mathematician. Upon his graduation from that school in 1591, he went on to pursue study in theology, becoming a part of the Tübingen faculty. However, before he took his final exams he was recommended for the vacant post of teacher of mathematics and astronomy at the Protestant school in Graz, Austria. He accepted the position in April of 1594, at the age of 23. In April 1597, Kepler married Barbara Müller. She died in 1611 and was outlived by two children. In December 1599, Tycho Brahe wrote to Kepler, inviting Kepler to assist him at Benátky nad Jizerou outside Prague. After Tycho's death, Kepler was appointed Imperial Mathematician (from November 1601 to 1630) to the Habsburg Emperors. In October 1604, Kepler observed the supernova which was subsequently named Kepler's Star. In January 1612 the Emperor died, and Kepler took the post of provincial mathematician in Linz. In 1611, Kepler published a monograph on the origins of snowflakes, the first known work on the subject. He correctly theorized that their hexagonal nature was due to cold, but did not ascertain a physical cause for this. The question of snowflakes was not resolved until the 20th century. On March 8, 1618 Kepler discovered the third law of planetary motion: distance cubed over time squared. He initially rejected this idea, but later confirmed it on May 15 of the same year. In August of 1620, Katherine, Kepler's mother, was arrested in Leonberg as a witch; she was imprisoned for 14 months. She was released in October 1621 after attempts to convict her failed. Even though she was subjected to torture, she refused to confess to the charges. However, only the courageous personal intervention of Kepler (despite the risk to be arrested as well) and his reputation as the famous Imperial Mathematician rescued her.

Death

On November 15, 1630 Kepler died of a fever in Regensburg. In 1632, only two years after his death, his grave was demolished by the Swedish army in the Thirty Years' War.

Work

Kepler lived in an era when there was no clear distinction between astronomy and astrology, and no consensus on the scientific method as the correct way to decide what was correct or incorrect in science. His ideas are therefore a fascinating mixture of what would today be considered mathematical physics and nonsensical mysticism. Although the subsections below separate the two, Kepler did not see them as separate. Kepler was a Pythagorean numbers mystic. That is, he considered mathematical relationships to be at the base of all nature. Thus all creation was an integrated whole. This may be contrasted with the Platonic and Aristotelian notion that the Earth was fundamentally different from the rest of the universe, being composed of different substances and with different natural laws applying. Thus Kepler was the first to attempt to discover universal laws. This quest led him to apply terrestrial physics to celestial bodies, which produced the three Laws of Planetary Motion. Conversely, he was convinced that celestial bodies influence terrestrial events. One result of this belief was his correct assessment of the Moon's role in generating the tides, years before Galileo's incorrect formulation. Another was his belief that someday it would be possible to develop a "scientific astrology," while not believing that any astrologic rules currently propounded were at all valid.

Scientific work

Kepler's laws

Kepler inherited from Tycho Brahe a wealth of the most accurate raw data ever collected on the positions of the planets. The difficulty was to make sense of it. The orbital motions of the other planets are viewed from the vantage point of the Earth, which is itself orbiting the sun. As shown in the example below, this can cause the other planets to appear to move in strange loops. Kepler concentrated on the orbit of Mars, but he had to know the orbit of the Earth accurately first. In order to do this, he needed a surveyor's baseline. In a stroke of pure genius, he used Mars and the Sun as his baseline, since without knowing the actual orbit of Mars, he knew that it would be in the same place in its orbit at times separated by its orbital period. Thus the orbital positions of the Earth could be computed, and from them the orbit of Mars. He was able to deduce his planetary laws without knowing the exact distances of the planets from the sun, since his geometrical analysis needed only the ratios of their solar distances. Image:Retrograde-motion-of-mars.png Kepler, unlike Brahe, held to the heliocentric model of the solar system, and starting from that framework, he made twenty years of painstaking trial-and-error attempts at making some sense out of the data. He finally arrived at his three laws of planetary motion: three laws of planetary motion 1. Kepler's elliptical orbit law: The planets orbit the sun in elliptical orbits with the sun at one focus. 2. Kepler's equal-area law: The line connecting a planet to the sun sweeps out equal areas in equal amounts of time. 3. Kepler's law of periods: The time required for a planet to orbit the sun, called its period, is proportional to the long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets. Using these laws, he was the first astronomer to successfully predict a transit of Venus (for the year 1631). Kepler's laws were the first clear evidence in favor of the heliocentric model of the solar system, because they only came out to be so simple under the heliocentric assumption. Kepler, however, never discovered the deeper reasons for the laws, despite many years of what would now be considered non-scientific mystical speculation. Isaac Newton eventually showed that the laws were a consequence of his laws of motion and law of universal gravitation. (From the modern vantage point, the equal-area law is more easily understood as arising from conservation of angular momentum.)

1604 supernova

angular momentum On October 17, 1604, Kepler observed that an exceptionally bright star had suddenly appeared in the constellation Ophiuchus. (It was first observed by several others on October 9.) The appearance of the star, which Kepler described in his book De Stella nova in pede Serpentarii ('On the New Star in Ophiuchus's Foot'), provided further evidence that the cosmos was not changeless; this was to influence Galileo in his argument. It has since been determined that the star was a supernova, the second in a generation, later called Kepler's Star or Supernova 1604. No further supernovae have been observed in the Milky Way, though others outside our galaxy have been seen.

Other scientific and mathematical work

Kepler also made fundamental investigations into combinatorics, geometrical optimization, and natural phenomena such as snowflakes, always with an emphasis on form and design. He was also one of the founders of modern optics, defining e.g. antiprisms and the Kepler telescope (see Kepler's books Astronomiae Pars Optica — i.a. theoretical explanation of the camera obscura — and Dioptrice). In addition, since he was the first to recognize the non-convex regular solids (such as the stellated dodecahedra), they are named Kepler solids in his honor.

Mysticism and astrology

Mysticism

Kepler discovered the laws of planetary motion while trying to achieve the Pythagorean purpose of finding the harmony of the celestial spheres. In his cosmologic vision, it was not a coincidence that the number of perfect polyhedra was one less than the number of known planets. Having embraced the Copernican system, he set out to prove that the distances from the planets to the sun were given by spheres inside perfect polyhedra, all of which were nested inside each other. The smallest orbit, that of Mercury, was the innermost sphere. He thereby identified the five Platonic solids with the five intervals between the six known planets — Mercury, Venus, Earth, Mars, Jupiter, Saturn; and the five classical elements. In 1596 Kepler published Mysterium Cosmographicum, or The Cosmic Mystery. Here is a selection explaining the relation between the planets and the Platonic solids: :… Before the universe was created, there were no numbers except the Trinity, which is God himself… For, the line and the plane imply no numbers: here infinitude itself reigns. Let us consider, therefore, the solids. We must first eliminate the irregular solids, because we are only concerned with orderly creation. There remain six bodies, the sphere and the five regular polyhedra. To the sphere corresponds the heaven. On the other hand, the dynamic world is represented by the flat-faces solids. Of these there are five: when viewed as boundaries, however, these five determine six distinct things: hence the six planets that revolve about the sun. This is also the reason why there are but six planets… sphere from Mysterium Cosmographicum (1596)]] sphere :… I have further shown that the regular solids fall into two groups: three in one, and two in the other. To the larger group belongs, first of all, the Cube, then the Pyramid, and finally the Dodecahedron. To the second group belongs, first, the Octahedron, and second, the Icosahedron. That is why the most important portion of the universe, the Earth—where God's image is reflected in man—separates the two groups. For, as I have proved next, the solids of the first group must lie beyond the earth's orbit, and those of the second group within… Thus I was led to assign the Cube to Saturn, the Tetrahedron to Jupiter, the Dodecahedron to Mars, the Icosahedron to Venus, and the Octahedron to Mercury… To emphasize his theory, Kepler envisaged an impressive model of the universe which shows a cube, inside a sphere, with a tetrahedron inscribed in it; another sphere inside it with a dodecahedron inscribed; a sphere with an icosahedron inscribed inside; and finally a sphere with an octahedron inscribed. Each of these celestial spheres had a planet embedded within them, and thus defined the planet's orbit. In his 1619 book, Harmonice Mundi or Harmony of the Worlds, as well as the aforementioned Mysterium Cosmographicum, he also made an association between the Platonic solids with the classical conception of the elements: the tetrahedron was the form of fire, the octahedron was that of air, the cube was earth, the icosahedron was water, and the dodecahedron was the cosmos as a whole or ether. There is some evidence this association was of ancient origin, as Plato tells of one Timaeus of Locri who thought of the Universe as being enveloped by a gigantic dodecahedron while the other four solids represent the "elements" of fire, air, earth, and water. In 1975, nine years after its founding, the College for Social and Economic Sciences Linz (Austria) was renamed Johannes Kepler University Linz in honor of Johannes Kepler, since he wrote his magnum opus harmonice mundi in Linz. To his disappointment, Kepler's attempts to fix the orbits of the planets within a set of polyhedrons never worked out, but it is a testimony to his integrity as a scientist that when the evidence mounted against the cherished theory he worked so hard to prove, he abandoned it. His most significant achievements came from the realization that the planets moved in elliptical, not circular, orbits. This realization was a direct consequence of his failed attempt to fit the planetary orbits within polyhedra. Kepler's willingness to abandon his most cherished theory in the face of precise observational evidence also indicates that he had a very modern attitude to scientific research. Kepler also made great steps in trying to describe the motion of the planets by appealing to a force which resembled magnetism, which he believed emanated from the sun. Although he did not discover gravity, he seems to have attempted to invoke the first empirical example of a universal law to explain the behaviour of both earthly and heavenly bodies.

Astrology

Kepler disdained astrologers who pandered to the tastes of the common man without knowledge of the abstract and general rules, but he saw compiling prognostications as a justified means of supplementing his meagre income. Yet, it would be a mistake to take Kepler's astrological interests as merely pecuniary. As one historian, John North, put it, 'had he not been an astrologer he would very probably have failed to produce his planetary astronomy in the form we have it.' Kepler believed in astrology in the sense that he was convinced that astrological aspects physically and really affected humans as well as the weather on earth. He strove to unravel how and why that was the case and tried to put astrology on a surer footing, which resulted in the On the more certain foundations of astrology (1601), in which, among other technical innovations, he was the first to propose the quincunx aspect. In The Intervening Third Man, or a warning to theologians, physicians and philosophers (1610), posing as a third man between the two extreme positions for and against astrology, Kepler advocated that a definite relationship between heavenly phenomena and earthly events could be established. At least 800 horoscopes and natal charts drawn up by Kepler are still extant, several of himself and his family, accompanied by some unflattering remarks. As part of his duties as district mathematician to Graz, Kepler issued a prognostication for 1595 in which he forecast a peasant uprising, Turkish invasion and bitter cold, all of which happened and brought him renown. Kepler is known to have compiled prognostications for 1595 to 1606, and from 1617 to 1624. As court mathematician, he explained to Rudolf II the horoscopes of the Emperor Augustus and Muhammad, and gave astrological prognosis for the outcome of a war between the Republic of Venice and Paul V. In the On the new star (1606) Kepler explicated the meaning of the new star of 1604 as the conversion of America, downfall of Islam and return of Christ. The De cometis libelli tres (1619) is also replete with astrological predictions.

Kepler on God

"I was merely thinking God's thoughts after him. Since we astronomers are priests of the highest God in regard to the book of nature," wrote Kepler, "it benefits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God."

Writings by Kepler

astrological
- Mysterium cosmographicum (The Cosmic Mystery) (1596)
- Astronomiae Pars Optica (The Optical Part of Astronomy) (1604)
- De Stella nova in pede Serpentarii (On the New Star in Ophiuchus's Foot) (1604)
- Astronomia nova (New Astronomy) (1609)
- Dioptrice (Dioptre) (1611)
- Nova stereometria doliorum vinariorum (New Stereometry of wine barrels) (1615)
- Epitome astronomiae Copernicanae (published in three parts from 1618-1621)
- Harmonice Mundi (Harmony of the Worlds) (1619)
- Tabulae Rudolphinae (1627)
- Somnium (The Dream) (1634) - considered the first precursor of science fiction.

Kepler in fiction

- John Banville: Kepler: a novel. London: Secker & Warburg, 1981 ISBN 0-436-03264-3 (and later eds.). Also published: Boston, MA:Godine, 1983 ISBN 0-87923-438-5. Arthur Koestler : The Sleepwalkers; A History of Man's Changing Vision of the Universe. Publihed by Hutchinson. Synopsis; a profound outline of astrology from Pythagoras to Newton with weight given on Kepler.

Machines named in Kepler's honor

Kepler Space Observatory, a solar-orbiting, planet-hunting telescope due to be launched by NASA in 2008.

External links

- [http://posner.library.cmu.edu/Posner/books/annotation.cgi?call=520_K38PN Annotation: Posner Family Collection in Electronic Format] Harmonices mvndi The Harmony of the Worlds in fulltext facsimile in Latin
- Full text of [http://www.gutenberg.net/etext/12406 Kepler] by Walter W. Bryant, from Project Gutenberg
- [http://www.skyscript.co.uk/kepler.html Kepler and the "Music of the Spheres"]
- [http://www.dmoz.org/Science/Astronomy/History/People/Kepler,_Johannes/ Johannes Kepler Directory]
- [http://www.depauw.edu/sfs/backissues/8/christianson8art.htm Gale E. Christianson- Kepler's Somnium: Science Fiction and the Renaissance Scientist]
- Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes Kepler, Johannes als:Johannes Kepler ko:요하네스 케플러 ja:ヨハネス・ケプラー

Kepler's laws of planetary motion

Johannes Kepler's primary contributions to astronomy/astrophysics were his three laws of planetary motion. Kepler, a nearly blind though brilliant German mathematician, derived these laws, in part, by studying the observations of the keen-sighted Danish astronomer Tycho Brahe. The article on Johannes Kepler gives a less mathematical description of the laws, as well as a treatment of their historical and intellectual context. Sir Isaac Newton's later discovery of the laws of motion and universal gravitation depended strongly on Kepler's work. Although from the modern point of view, Kepler's laws can be seen as a consequence of Newton's laws, historically, it was the other way around: Kepler provided a mathematically distilled description of the empirical observations, which Newton then interpreted.

Kepler's first law

The orbit of a planet about a star is an ellipse with the star at one focus. There is no object at the other focus of a planet's orbit. The semimajor axis, a, is half the major axis of the ellipse. In some sense it can be regarded as the average distance between the planet and its star, but it is not the time average in a strict sense, as more time is spent near apocentre than near pericentre.

Kepler's second law

A line joining a planet and its star sweeps out equal areas during equal intervals of time. This is also known as the law of equal areas. Suppose a planet takes 1 day to travel from points A to B. During this time, an imaginary line, from the Sun to the planet, will sweep out a roughly triangular area. This same amount of area will be swept every day. As a planet travels in its elliptical orbit, its distance from the Sun will vary. As an equal area is swept during any period of time and since the distance from a planet to its orbiting star varies, one can conclude that in order for the area being swept to remain constant, a planet must vary in velocity. The physical meaning of the law is that the planet moves faster when it is closer to the sun. This is because the sun's gravity accelerates the planet as it falls toward the sun, and decelerates it on the way back out.

Kepler's third law

The square of the sidereal period of an orbiting planet is directly proportional to the cube of the orbit's semimajor axis. :

P^2 \propto a^3

:P = object's sidereal period :a = orbit's semimajor axis Thus, not only does the length of the orbit increase with distance, also the orbital speed decreases, so that the increase of the sidereal period is more than proportional. See the actual figures: attributes of major planets. This law is also known as the harmonic law.

Accuracy and limitations

As discussed below, Kepler's third law needs to be modified when the orbiting body's mass is not negligible compared to the mass of the body being orbited. However, the correction is fairly small in the case of the planets orbiting the Sun. A more serious limitation of Kepler's laws is that they assume a two-body system. This is a particularly bad approximation in the case of the Earth-Sun-Moon system, and for calculations of the Moon's orbit, Kepler's laws are far less accurate than the empirical method invented by Ptolemy hundreds of years before. Newton generalized Kepler's first law with the realization that an object moving at greater than escape velocity (e.g., some comets) would have an open parabolic or hyperbolic orbit rather than a closed elliptical one. Thus, all of the conic sections are possible orbits. The second law is still valid for open orbits (since angular momentum is still conserved), but the third law is inapplicable because the motion is not periodic. Because electrical forces also obey an inverse square law, Kepler's laws also apply to bodies interacting electrically. If the interaction is repulsive, as in Rutherford scattering, then the orbit is hyperbolic, with the center of repulsion outside the hyperbola. In the planetary model of the atom, the electrons were imagined to orbit the nucleus exactly like the planets orbiting the Sun, and Niels Bohr even went so far as to attempt to assign specific atomic energy levels to specific elliptical orbits. The Keplerian approximation is successful when the quantum-mechanical wavelengths are small compared to the size of the orbit (as in Rutherford scattering, and in some unusual artificially populated electron orbitals with very high values of the principal quantum number). Kepler's laws do not consider the emission of radiation. The emission of gravitational radiation is negligible in our solar system, but important in some stellar systems containing black holes or neutron stars (any system involving large masses combined with large accelerations). In the planetary model of the atom, the emission of electromagnetic radiation should have led to the collapse of all atoms, and this was a hint that classical physics was in need of modification. Kepler's laws don't incorporate relativity, so, for example, they don't correctly predict the precession of Mercury's orbit. The successful explanation of this non-Keplerian behavior was one of the most dramatic early successes of general relativity. Kepler's laws fail even more dramatically in the case of an object orbiting a black hole; here, general relativity predicts that many orbits —those that pass through the event horizon— are one-way streets to a dead-end region of spacetime.

Connection to Newton's laws and conservation laws

Kepler did not understand why his laws were correct; it was Isaac Newton who discovered the answer to this more than fifty years later. The second law can also be seen as a statement of conservation of angular momentum, which is a logical consequence of Newton's laws in the special case of a force that acts along the line connecting two objects.

Kepler's first law

Newton proposed that "every object in the universe attracts every other object along a line of the centres of the objects, proportional to each object's mass, and inversely proportional to the square of the distance between the objects." The following assumes that acceleration is of the form :

\frac = f(r)\hat

. Recall that in polar coordinates: :

\frac = \dot r\hat + r\dot\theta\hat

\frac = (\ddot r - r\dot\theta^2)\hat + (r\ddot\theta + 2\dot r \dot\theta)\hat

In component form, we have: :

\ddot r - r\dot\theta^2 = f(r)

r\ddot\theta + 2\dot r\dot\theta = 0

Since

\dot r = dr/dt

and

\ddot\theta=/

, the latter equation is equivalent to :

\frac = -2\frac

. When integrated, this yields :

\log\dot\theta = -2\log r + \log\ell

, :

\ell = r^2\dot\theta

, for some constant

\ell

, which can be shown to be the specific angular momentum. Now we substitute. Let: :

r = \frac

\dot r = -\frac\dot u = -\frac\frac\frac= -\ell\frac

\ddot r = -\ell\frac\frac = -\ell\dot\theta\frac= -\ell^2u^2\frac

The equation of motion in the

\hat

direction becomes: :

\frac + u = - \fracf\left(\frac\right)

f(r)=-k/r^2

, as Newton's law of gravitation claims, then: :

\frac + u = \frac

where -k is our proportionality constant. This differential equation has the general solution: :

u = A\cos(\theta-\theta_0) + \frac.

Replacing u with r and letting θ₀=0: :

r = \frac

. This is indeed the equation of a conic section with the origin at one focus. Thus, Kepler's first law is a direct result of Newton's law of gravitation and Newton's second law of motion.

Kepler's second law

Assuming Newton's laws of motion, we can show that Kepler's second law is consistent. By definition, the angular momentum

\mathbf

of a point mass with mass

m

and velocity

\mathbf

is : :

\mathbf \equiv m \mathbf \times \mathbf

. where

\mathbf

is the position vector of the particle. Since

\mathbf = \frac

, we have: :

\mathbf = \mathbf \times m\frac

taking the time derivative of both sides: :

\frac = \mathbf \times \mathbf = 0

since the cross product of parallel vectors is 0. We can now say that

|\mathbf|

is constant. The area swept out by the line joining the planet and the sun is half the area of the parallelogram formed by

\mathbf

and

d\mathbf

. :

dA = \begin\frac\end |\mathbf \times d\mathbf| = \begin\frac\end \left|\mathbf \times \fracdt\right| = \fracdt

Since

|\mathbf|

is constant, the area swept out by is also constant. Q.E.D.

Kepler's third law

Newton used the third law as one of the pieces of evidence used to build the conceptual and mathematical framework supporting his law of gravity. If we take Newton's laws of motion as given, and consider a hypothetical planet that happens to be in a perfectly circular orbit of radius r, then we have

F=mv^2/r

for the sun's force on the planet. The velocity is proportional to r/T, which by Kepler's third law varies as one over the square root of r. Substituting this into the equation for the force, we find that the gravitational force is proportional to one over r squared. (Newton's actual historical chain of reasoning is not known with certainty, because in his writing he tended to erase any traces of how he had reached his conclusions.) Reversing the direction of reasoning, we can consider this as a proof of Kepler's third law based on Newton's of gravity, and taking care of the proportionality factors that were neglected in the argument above, we have: :

T^2 = \frac \cdot r^3

where:
- T = planet's sidereal period
- r = radius of the planet's circular orbit
- G = the gravitational constant
- M = mass of the sun The same arguments can be applied to any object orbiting any other object. This discussion implicitly assumed that the planet orbits around the stationary sun, although in reality both the planet and the sun revolve around their common center of mass. Newton recognized this, and modified this third law, noting that the period is also affected by the orbiting body's mass. However typically the central body is so much more massive that the orbiting body's mass may be ignored. Newton also proved that in the case of an elliptical orbit, the semimajor axis could be substituted for the radius. The most general result is: :

T^2 = \frac \cdot a^3

where:
- T = object's sidereal period
- a = object's semimajor axis
- G = 6.67 × 10⁻¹¹ N · m²/kg² = the gravitational constant
- M = mass of one object
- m = mass of the other object For objects orbiting the sun, it can be convenient to use units of years, AU, and solar masses, so that G, 4π² and the various conversion factors cancel out. Also with m<<M we can set m+M = M, so we have simply

T^2=a^3

Proving Kepler's third law

Define point A to be the periapsis, and point B as the apoapsis of the planet when orbiting the sun. Kepler's second law states that the orbiting body will sweep out equal areas in equal quantities of time. If we now look at a very small periods of time at the moments when the planet is at points A and B, then we can approximate the area swept out as a triangle with an altitude equal to the distance between the planet and the sun, and the base equal to the time times the speed of the planet. :

\frac\cdot(1-\epsilon)a\cdot V_A\,dt=\frac\cdot(1+\epsilon)a\cdot V_B\,dt

(1-\epsilon)\cdot V_A=(1+\epsilon)\cdot V_B

V_A=V_B\cdot\frac

Using the law of conservation of energy for the total energy of the planet at points A and B, :

\frac-\frac=\frac-\frac

\frac-\frac=\frac-\frac

\frac=\frac\cdot \left ( \frac-\frac \right )

\frac=\frac\cdot \left ( \frac \right )

V_B^2 \cdot \left ( \frac\right ) ^2-V_B^2=\frac\cdot \left ( \frac \right )

V_B^2 \cdot \left ( \frac\right )=\frac

V_B^2 \cdot \left ( \frac\right )=\frac

V_B^2 \cdot 4\epsilon=\frac

V_B=\sqrt.

Now that we have

V_B

, we can find the rate at which the planet is sweeping out area in the ellipse. This rate remains constant, so we can derive it from any point we want, specifically from point B. :

\frac=\frac=\frac\cdot(1+\epsilon)a\cdot V_B=\frac\cdot(1+\epsilon)a\cdot\sqrt=
\frac\cdot\sqrt

However, the total area of the ellipse is equal to

\pi a \sqrta

. (That's the same as

\pi a b

, because

b=\sqrta

). The time the planet take out to sweep out the entire area of the ellipse equals the ellipse's area, so, :

T\cdot \frac=\pi a \sqrta

T\cdot \frac\cdot\sqrt=\pi \sqrta^2

T=\frac=\frac=
\frac\sqrt

T^2=\fraca^3.

However, if the mass m is not negligible in relation to M, then the planet will orbit the sun with the exact same velocity and position as a very small body orbiting an object of mass

M+m

(see reduced_mass). To integrate that in the above formula, M must be replaced with

M+m

, to give

T^2=\fraca^3

. Q.E.D.

Solution for the motion as a function of time

The Keplerian problem assumes an orbit with semimajor axis a, semiminor axis b, and eccentricity ε. To convert the laws into predictions, Kepler began by adding the orbit's auxiliary circle (that with the major axis as a diameter) and defined these points:
- c center of auxiliary circle and ellipse
- s sun (at one focus of ellipse);

\mboxcs=a\varepsilon

- p the planet
- z perihelion
- x is the projection of the planet to the auxiliary circle; then

\mboxsxz=\frac ba\mboxspz

- y is a point on the circle such that

\mboxcyz=\mboxsxz=\frac ba\mboxspz

and three angles measured from perihelion:
- true anomaly

T=\angle zsp

, the planet as seen from the sun
- eccentric anomaly

E=\angle zcx

, x as seen from the centre
- mean anomaly

M=\angle zcy

, y as seen from the centre image:kepler's-equation-scheme.png Then :

\mboxcxz=\mboxcxs+\mboxsxz

=\mboxcxs+\mboxcyz

\frac2E=a\varepsilon\frac a2\sin E+\frac2M

giving Kepler's equation :

M=E-\varepsilon\sin E

. To connect E and T, assume

r=\mboxsp

then :

a\varepsilon+r\cos T=a\cos E

and

r\sin T=b\sin E

r=\frac=\frac

\tan T=\frac=\frac ba\frac=\frac

which is ambiguous but useable. A better form follows by some trickery with trigonometric identities: :

\tan\frac T2=\sqrt\frac\tan\frac E2

(So far only laws of geometry have been used.) Note that

\mboxspz

is the area swept since perihelion; by the second law, that is proportional to time since perihelion. But we defined

\mboxspz=\frac ab\mboxcyz=\frac ab\frac2M

and so M is also proportional to time since perihelion—this is why it was introduced. We now have a connection between time and position in the orbit. The catch is that Kepler's equation cannot be rearranged to isolate E; going in the time-to-position direction requires an iteration (such as Newton's method) or an approximate expression, such as :

E\approx M+\left(\varepsilon-\frac18\varepsilon^3\right)\sin M+\frac12\varepsilon^2\sin 2M+\frac38\varepsilon^3\sin 3M

via the Lagrange reversion theorem. For the small ε typical of the planets (except Pluto) such series are quite accurate with only a few terms; one could even develop a series computing T directly from M.[http://info.ifpan.edu.pl/firststep/aw-works/fsII/mul/mueller.html]

External links

- Crowell, Benjamin, Conservation Laws, [http://www.lightandmatter.com/area1book2.html http://www.lightandmatter.com/area1book2.html], an online book that gives a proof of the first law without the use of calculus. Category:Celestial mechanics Category:Equations Category:Eponymous laws ko:케플러 법칙 ja:ケプラーの法則

Planet

A planet is generally considered to be a relatively large mass of accreted matter in orbit around a star that is not a star itself. The name comes from the Greek term πλανήτης, planētēs, meaning "wanderer", as ancient astronomers noted how certain lights moved across the sky in relation to the other stars. Based on historical consensus, the International Astronomical Union (IAU) lists nine planets in our solar system. Since the term "planet" has no precise scientific definition, however, many astronomers contest that figure. Some say it should be lowered to eight by removing Pluto from the list, whilst others claim it should be raised to fifteen, twenty, or even higher.

Planetary formation

It is not known with certainty how planets are formed. The prevailing theory is that they are formed from those remnants of a nebula that don't condense under gravity to form a protostar. Instead, these remnants become a thin disc of dust and gas revolving around the protostar and begin to condense about local concentrations of mass within the disc. These concentrations become ever more dense until they collapse inward under gravity to form protoplanets. When the protostar has grown such that it ignites to form a star, its solar wind blows away most of the disc's remaining material. Thereafter there still may be many protoplanets orbiting the star or each other, but over time many will collide, either to form a single larger planet or release material for other larger protoplanets or planets to absorb. Meanwhile, protoplanets that have avoided collisions may become moons of larger planets. With the discovery and observation of planetary systems around stars other than our own, it is becoming possible to elaborate, revise or even replace this account.

Within our solar system

Main article: Solar system The process of naming planets and their features is known as planetary nomenclature. All the currently accepted planets in the solar system are named after Roman gods, except for Uranus (named after a Greek god) and the Earth, which was not seen as a planet by the ancients but rather the centre of the universe. The designated planetary names are near-universal in the Western world, but some non-European languages, such as Chinese, use their own. Moons are also named after gods and characters from classical mythology, or, in the case of Uranus, after Shakespearean characters. Asteroids can be named after anybody or anything at the discretion of their discoverers, subject to approval by the IAU's nomenclature panel.

Accepted planets

Asteroid According to the authority of the IAU, there are nine planets in our solar system. In increasing distance from the Sun they are: #Mercury (astronomical symbol ) #Venus () #Earth () with one confirmed natural satellite, Luna (the Moon) #Mars () with two confirmed natural satellites, Deimos and Phobos #Jupiter () with sixty-three confirmed natural satellites #Saturn () with forty-six confirmed natural satellites #Uranus (Uranus) with twenty-seven confirmed natural satellites #Neptune () with thirteen confirmed natural satellites #Pluto () with three confirmed natural satellites (Charon, S/2005 P 1, S/2005 P 2) However, there is some pressure for Pluto to be reclassified as a Kuiper Belt object, especially in light of the discovery of . This object, however, has not yet received a definitive classification from the IAU.

Other candidates

When Ceres was found orbiting between Mars and Jupiter in 1801, it was initially touted as a planet, but after many smaller objects were found with a similar orbit, it was classified as an asteroid. However, due to its large size (relative to the other asteroids), and its roughly spherical shape, Ceres would be considered a planet by some astronomers' definitions. Similarly, since 1992 many objects have been found in the predicted Kuiper Belt that exists beyond Neptune. Several of the largest of these have challenged the planetary status quo, as they are both spherical and larger than the bodies in the Mars-Jupiter asteroid belt, and are similar in size, orbit and composition to Pluto. However, as yet none have been accepted as planets by the IAU. The most significant of these are (in order of increasing distance from the Sun) 90482 Orcus, , 50000 Quaoar, , , 28978 Ixion, 20000 Varuna, 19521 Chaos, and 90377 Sedna. (However, it should be noted that Sedna is often considered to be beyond the Kuiper Belt; being either a member of the scattered disc or the inner Oort Cloud). Like Ceres before it, Sedna was widely touted as a planet when it was discovered in 2003, as it was the largest object found since Pluto. However, mainly due to its size still being smaller than Pluto's, it did not achieve planetary status from the IAU. However, the discovery in 2005 of (nicknamed Xena), with a size and mass larger than Pluto seems to have forced the issue. As of September 2005 it has not yet been accepted as a planet, but the IAU is expected to announce a definition of a planet by the end of the year, which will either see become a planet, or have Pluto stripped of its status.

Extrasolar planets

:Main article: Extrasolar planet. Of the 173 extrasolar planets (those outside our solar system) discovered to date (October 2005) most have masses which are about the same or larger than Jupiter's. Exceptions include a number of planets discovered orbiting burned-out star remnants called pulsars, such as PSR B1257+12, the planets orbiting the stars Mu Arae, 55 Cancri and GJ 436 which are approximately Neptune-sized [http://www.eso.org/outreach/press-rel/pr-2004/pr-22-04_pf.html], and a planet orbiting Gliese 876 that is estimated to be about 6 to 8 times as massive as the Earth and is probably rocky in origin. It is far from clear if the newly discovered large planets would resemble the gas giants in our solar system or if they are of an entirely different type as yet unknown, like ammonia giants or carbon planets. In particular, some of the newly discovered planets, known as hot Jupiters, orbit extremely close to their parent stars, in nearly circular orbits. They therefore receive much more stellar radiation than the gas giants in our solar system, which makes it questionable whether they are the same type of planet at all. There is also a class of hot Jupiters that orbit so close to their star that their atmospheres are slowly blown away in a comet-like tail: the Chthonian planets. The National Aeronautics and Space Administration of the United States has a program underway to develop a Terrestrial Planet Finder artificial satellite, which would be capable of detecting the planets with masses comparable to terrestrial planets. The frequency of occurrence of these planets is one of the variables in the Drake equation which estimates the number of intelligent, communicating civilizations that exist in our galaxy. Astronomers have recently [http://www.nature.com/news/2005/050711/full/050711-6.html] [http://www.jpl.nasa.gov/news/news.cfm?release=2005-115] detected a planet in a triple star system, a finding that challenges current theories of planetary formation. The planet, a gas giant slightly larger than Jupiter, orbits the main star of the HD 188753 system, in the constellation Cygnus, and is hence known as HD 188753 Ab. The stellar trio (yellow, orange, and red) is about 149 light-years from Earth. The planet, which is at least 14% larger than Jupiter, orbits the main star (HD 188753 A) once every 80 hours or so (3.3 days), at a distance of about 8 Gm, a twentieth of the distance between Earth and the Sun. The other two stars whirl tightly around each other in 156 days, and circle the main star every 25.7 years at a distance from the main star that would put them between Saturn and Uranus in our own Solar System. The latter stars invalidate the leading hot Jupiter formation theory, which holds these planets form at "normal" distances and then migrate inward through some debatable mechanism. This could not have occurred here, the outer star pair disrupting outer planet formation.

Brown dwarf "planets"

The discovery of a planet-sized satellite of a brown dwarf has blurred the distinction between "planet" and "moon." A brown dwarf, though a star in theory, in practice is often described as in between a planet and a star. It is formally defined by the IAU by its official statement that "Substellar objects with true masses above the limiting mass for thermonuclear fusion of deuterium are "brown dwarfs", no matter how they formed nor where they are located." To the IAU, the question of whether an object in orbit around a brown dwarf is a "planet" or a "moon" was simply not relevant, as it does not use the term "moon," only "satellite" and as yet has no official definition for "planet."

Interstellar planets

Interstellar planets are rogues in interstellar space, not gravitationally linked to any given solar system. No interstellar planet is known to date, but their existence is considered a likely hypothesis based on computer simulations of the origin and evolution of planetary systems, which often include the ejection of bodies of significant mass. Such objects are not formally called planets, however, since the IAU has not defined the term "planet".

Definition and classification of planets

Much like "continent", "planet" is a word without a precise definition, with history and culture playing as much of a role as geology and astrophysics. Recent definitions have been vague and imprecise; The American Heritage Dictionary, for instance, formerly defined a planet as: :A nonluminous celestial body larger than an asteroid or comet, illuminated by light from a star, such as the sun, around which it revolves. In the solar system there are nine known planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.' However, for some time that definition has been viewed by many as inadequate. The eight largest planets (which are also the eight nearest to the Sun) are universally recognised as such, and for this reason are often universally referred to as "major planets", but there is controversy over Pluto and other smaller objects.
Suggested wide definitions
Since the discoveries of many of the objects in the Kuiper belt and around other stars, there has been a concerted push amongst scientists to come up with a precise definition of what constitutes a planet. In 1999, the IAU set up a working group to develop a scientifically plausible recommendation, but as of August, 2005 they had not reached a conclusion. After the discovery of (informally called "Xena"), a member of the committee, Alan Stern, has said that the group wanted "to get something done, pronto". He also informed journalists that a "consensus" in the group was moving towards the following definition: :A planet is a body that directly orbits a star, is large enough to be round because of self gravity, and is not so large that it triggers nuclear fusion in its interior. Note that this definition also covers disputes at the upper end of a planet's size, which provides the extra benefit of forming a barrier between planets and brown dwarfs. Many consider this definition the best option as it sets up divisions based on physical characteristics rather than an arbitrary size limit. It is also somewhat universal in its application where other definitions have been crafted mainly to sort our own solar system into simple categories (such as placing the size limit as just under Mars, Mercury or Pluto). Depending how it is interpreted, objects counted as planets under such a new system would include some or all of the objects listed above, with potentially many more yet to be found. Gibor Basri, head of astronomy at the University of Berkeley, has suggested a similar definition and has also proposed the terms "fusor" (any object that achieves fusion in its core) and "planemo" (an object that is round from self-gravity but not a fusor) to help improve the astronomical nomenclature. Under Basri's definition: :A planet is a planemo orbiting a fusor These definitions have the advantage of creating a group including larger moons (which share many characteristics with the smaller planets) and also covering large free-roaming objects, which some astronomers think should be included in the definition of a planet. Basri has also suggested 'liberal use of adjectives' such as "major", "beltway", "dwarf", "giant", "super" and "historical".[http://astron.berkeley.edu/%7Ebasri/defineplanet/Mercury.htm] Others have suggested categories of planet/planemo based on composition such as "rock" (composed mainly of silicate), "gas" (composed mainly of hydrogen and helium), and "ice" (composed mainly of oxygen and carbon).
Suggested narrow definitions
There are alternate suggestions which would instead reduce the number of planets in the system. Upon his discovery of Sedna, Mike Brown of Caltech suggested a definition which would exclude both Sedna and Pluto from being classified as planets, proposing the following: :A planet is any body in the solar system that is more massive than the total mass of all of the other bodies in a similar orbit [http://www.gps.caltech.edu/~mbrown/sedna/#What%20is%20the%20definition%20of%20a%20planet?] This definition generally plays down the importance of size, but instead focuses on the formation of the proposed planet. Under this definition, no Kuiper Belt objects (including Pluto) would be considered planets. Brown's wish to "demote" Pluto prompted many to criticize him for setting out to create a purely scientific definition for a term which had an existing popular (albeit 'flawed') application. Upon his discovery of , Brown indicated he had become a convert to this way of thinking, and proposed that whatever definition of planet be adopted, it should include both Pluto and any Kuiper Belt object found to be larger than Pluto. [http://www.gps.caltech.edu/~mbrown/planetlila/index.html]
Further classification
Astronomers distinguish between minor planets, such as asteroids, comets, and trans-Neptunian objects; and major (or true) planets. Planets within Earth's solar system can be divided into categories according to composition.
- Terrestrial or rocky: Planets that are similar to Earth — with bodies largely composed of rock: Mercury, Venus, Earth, Mars
- Jovian or gas giant: Those with a composition largely made up of gaseous material: Jupiter, Saturn, Uranus, Neptune. Uranian planets, or ice giants, are a sub-class of gas giants, distinguished from true Jovians by their depletion in hydrogen and helium and a significant composition of rock and ice.
- Icy: Sometimes a third category is added to include bodies like Pluto, whose composition is primarily ice; this category of "icy" bodies also includes many non-planetary bodies such as the icy moons of the outer planets of our solar system (e.g. Triton). Many consider the Earth and its Moon to be a double planet, for several reasons:
- The Moon, as measured by its diameter, is 1.5 times larger than Pluto.
- The gravitational force of the Sun on the Moon is larger than the gravitational force of the Earth on the Moon by a factor of approx. 2.2. (This is not a unique situation in the solar system. The Sun's gravity is also stronger than the primary's on Jupiter's moon S/2003 J 2; Uranus' moon S/2001 U 2; Neptune's moons S/2002 N 4 and Psamathe; and several asteroid moons. However, Luna is the sole case of this phenomenon affecting an object of planetary mass.)
See also

- Definition of planet
- Planetary habitability
- Planetary science
- Planemo
- Planetoid
- Brown Dwarf
- Planets in science fiction
- Prograde and retrograde motion
- Skies of other planets
References

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External links

- [http://www.nineplanets.org/ NinePlanets.org] - tour of the solar system
- [http://www.iau.org International Astronomical Union]
- [http://www.fourmilab.ch/cgi-bin/uncgi/Solar/ Solar System Live] (an interactive orrery)
- [http://janus.astro.umd.edu/javadir/orbits/ssv.html Solar System Viewer] (animation)
- [http://www.sky-pics.net/ Pictures of the solar system]
- [http://gw.marketingden.com/planets/sun.html Renderings of the planets]
- [http://planetquest.jpl.nasa.gov/ NASA Planet Quest]
- [http://www.ciw.edu/IAU/div3/wgesp/definition.html Working definition of "planet"] from IAU WGESP — the lower bound remained a matter of consensus in February 2003
- Dan Green's page on [http://cfa-www.harvard.edu/cfa/ps/icq/ICQPluto.html planet classification]
- [http://www.spacedaily.com/news/outerplanets-04b.html Gravity Rules: The Nature and Meaning of Planethood]; S. Alan Stern; March 22, 2004
- [http://www.iau.org/IAU/FAQ/PlutoPR.html On the status of Pluto]; IAU, February 3, 1999
- als:Planet ko:행성 ms:Planet ja:惑星 simple:Planet th:ดาวเคราะห์ zh-min-nan:He̍k-chheⁿ

Solar system

The solar system comprises our Sun and the retinue of celestial objects gravitationally bound to it. Traditionally, this is said to consist of the Sun, nine planets and their 158 currently known moons; however, a large number of other objects, including asteroids, meteoroids, planetoids, comets, and interplanetary dust, orbit the Sun as well. Although the term "solar system" is frequently applied to other star systems and the planetary systems which may comprise them, it should strictly refer to our system specifically: the word "solar" is derived from the Sun's Latin name, Sol (and the term sometimes appears as Solar System). When talking about another stellar system (or planetary system), including the star(s) and bodies associated with them through gravity, it is usual to shorten it to "the system" (e.g. "the Alpha Centauri system" or "the 51 Pegasi system").

Structure and layout of the solar system

The Sun (astronomical symbol ☉) is a main sequence G2 star that contains 99.86% of the system's known mass. Its two largest orbiting bodies, Jupiter and Saturn, account for 91% of the remainder (The Oort Cloud might hold a substantial percentage, but as yet its existence is unconfirmed). In broad terms, the charted regions of our solar system consist of the Sun and its planetary system: the eight bodies in relatively unique orbits (commonly called planets or major planets) and two belts of smaller objects (which can be called minor planets, planetoids, meteoroids, planetesimals or, in the case of Pluto, planets). Objects in orbit round the Sun all lie within the same shallow plane, called the ecliptic, and all orbit in the same direction. Many are in turn orbited by moons, and the largest are encircled by planetary rings of dust and other particles. The major planets are, in order, Mercury (☿), Venus (♀), Earth (♁), Mars (♂), Jupiter (♃), Saturn (♄), Uranus (♅/10px), Neptune (♆), and Pluto (♇), though Pluto's status has been thrown into question by the discovery of (see below). Eight of the nine planets are named after or derived from gods and goddesses from Greco-Roman mythology; Earth, a Germanic word, is known in many Romance languages as Terra, the Roman goddess of the Earth. Distances within the solar system are measured most often in astronomical units, or AU. 1 AU is the distance between the Earth and the Sun, or 149 598 000 kilometers. Pluto is roughly 38 AU from the Sun, while Jupiter lies at roughly 5.2 AU. For very large distances within the solar system, such as regions beyond Pluto or the orbital circumferences of planets, the terameter (Tm, one milliard kilometers) is sometimes used. Despite the fact that many diagrams (like the image at the top of this article), for practicality's sake, represent the solar system as having each orbit the same distance apart, in actuality the orbits are largely arranged geometrically, that is, each is roughly double the distance from the Sun as the one before it. Venus’s distance from the Sun is roughly double that of Mercury, Earth’s distance is roughly double that of Venus, Mars’s double that of Earth and so on. This relationship is roughly expressed in the Titius-Bode law, a mathematical formula for predicting the semi-major axes of planets in AU. In its simplest form, it is written :

a= 0.4 + 0.3\times k

where k=0,1,2,4,8,16,32,64,128. By this formulation, we would expect Mercury's orbit (k=0) to be 0.4 AU, and Mars's orbit (k=4) to be at 1.6 AU. In fact their orbits are 0.38 and 1.52 AU.Ceres, the largest asteroid, lies at k=8. This law is only a rough guide, and doesn't fit all of the planets (Neptune is far closer than predicted, though Pluto lies at Neptune's predicted orbit). As of now, there is no scientific explanation for why this law "works," and many claim it is merely a coincidence. Pluto

Origin and evolution of the solar system

The current hypothesis of solar system formation is the nebular hypothesis, first proposed in 1755 by Immanuel Kant. It states the solar system was formed from a gaseous cloud called the solar nebula. It had a diameter of 100 AU and was 2-3 times the mass of the Sun. Over time, the nebula began to collapse, possiby due to disturbance by a nearby supernova. This explosion sent shock waves into space, which squeezed the nebula, pushing more and more matter inward until gravitational forces overcame its internal gas pressure and it also began to collapse. As the nebula collapsed, it decreased in size, which in turn caused it to spin faster to conserve angular momentum. And as the competing forces associated with gravity, gas pressure, magnetic fields, and rotation acted on it, the contracting nebula began to flatten into a spinning pancake shape with a bulge at the center. When the nebula further condensed, a protostar was formed in the middle. This system was heated by the friction of the rocks colliding into each other. Lighter elements such as hydrogen and helium evaporated out of the centre and migrated to the edges of the disc, thus concentrating the heavier elements to form dust and rocks in the centre. These heavier elements clumped together to form planetesimals and protoplanets. In the outer regions of this solar nebula, ice and volatile gases were able to survive, and as a result, the inner planets are rocky and the outer planets were massive enough to capture large amounts of lighter gases, such as hydrogen and helium. After 100 million years, the pressures and densities of hydrogen in the centre of the collapsed nebula became great enough for the protosun to sustain thermonuclear fusion reactions. As a result of this, hydrogen was converted to helium, and a great amount of heat was released. 4×¹H → ⁴He + neutrinos + photons During that time, the protostar turned into the Sun and the protoplanets and planetesimals were transformed into planets. All of the planets formed in a relatively short time of a few million years.

Regions of the solar system

protostar's rotating magnetic field on the plasma in the interplanetary medium (Solar Wind) [http://quake.stanford.edu/~wso/gifs/HCS.html]. (click to enlarge) ]] According to their location, the objects in the solar system are divided into three zones: Zone I or the inner solar system, including terrestrial planets and the Main belt of asteroids; Zone II, including the giant planets, their satellites and the centaurs, and Zone III, or the outer solar system, comprising the area of the Trans-Neptunian objects including the Kuiper Belt, the Oort cloud, and the vast region in between.

Interplanetary medium

The environment in which the solar system resides is called the interplanetary medium. The Sun radiates a continuous stream of charged particles, a plasma known as solar wind, which forms a very tenuous "atmosphere" (the heliosphere), permeating the interplanetary medium in all directions for at least ten billion (10) miles (16 Tm or 16 km) into space. Small quantities of dust are also present in the interplanetary medium and are responsible for the phenomenon of zodiacal light. Some of the dust is likely interstellar dust from outside the solar system. The influence of the Sun's rotating magnetic field on the interplanetary medium creates the largest structure in the Solar System, the heliospheric current sheet.

The inner planets

The four inner or terrestrial planets are characterised by their dense, rocky makeup. They formed in the hotter regions close to the Sun, where lighter and m