:: wikimiki.org ::

Interplanetary Superhighway

Interplanetary Superhighway

The Interplanetary Superhighway has come to denote a set of transfer orbits between various planets and moons in the solar system. These transfers have particularly low delta-v requirements, and appear to be the lowest energy transfers, even lower than the common Hohmann transfer orbit that has dominated orbital dynamics in the past. The Interplanetary Superhighway is based around a series of orbital paths predicted by chaos theory, leading to and from the unstable orbits around the Lagrange points — points in space where the gravity between various bodies balances out. There are a number of these around the Earth, created by the balance of forces between the Earth, Moon and Sun. For instance, the L1 point lies at the point between the Earth and Moon where forces between the two balance. Although the forces balance at these points, they are not stable equilibrium points. If a spacecraft placed at the L1 point is given even a slight nudge towards the Moon, for instance, the Moon's gravity will now be greater and the spacecraft will be pulled away from the L1 point. The entire system is in motion, so the spacecraft will not actually hit the Moon, but will travel in a winding path off into space. There is, however, a semi-stable orbit around each of these points. The orbits for two of the points, L4 and L5, are stable, but the orbits for L1 through L3 are stable only on the order of months. The key to the Interplanetary Superhighway was investigating the exact nature of these winding paths near the points. They were first investigated by Jules-Henri Poincaré in the 1890s, and he noticed that the paths leading to and from any of these points would almost always settle, for a time, on the orbit around it. There are in fact an infinite number of paths taking you to the point and back away from it, and all of them require no energy to reach. When plotted, they form a tube with the orbit around the point at one end. As it turns out, it is very easy to transit from a path leading to the point to one leading back out. This makes sense, since the orbit is unstable which implies you'll eventually end up on one of the outbound paths after spending no energy at all. However, with careful calculation you can pick which outbound path you want. This turned out to be quite exciting, because many of these paths lead right by some interesting points in space, like Mars. That means that for the cost of getting to the Earth-Sun L2 point (Lagrange points exist for all bodies in orbit of each other, Earth-Moon, Earth-Sun, Mars-Sun etc.) which is rather low, one can travel to a huge number of very interesting points, almost for free. The transfers are so low-energy that they make travel to almost any point in the solar system possible. On the downside, these transfers are very slow, and only useful for automated probes. Nevertheless, they have already been used to transfer spacecraft out of the Earth-Sun L1 point, a useful point for studying the Sun that was used in a number of recent missions, including the Genesis mission. The Solar and Heliospheric Observatory is here. The Interplanetary Superhighway is also relevant to understanding solar system dynamics; Comet Shoemaker-Levy 9 followed such a trajectory to collide with Jupiter. Mathematics Unites the Heavens and the Atom Furthermore, in recent years, mathematicians have discovered an almost perfect parallel between the motion of spacecraft through the solar system and the motion of atoms in a chemical reaction. The celestial half of this unity arises from the theory of dynamical systems, which describes how a group of celestial bodies such as the Sun, the Earth and a spacecraft will move under the influence of their mutual gravity. It turns out that the tangle of gravitational forces creates tubular "highways" in the space between the bodies; if the spacecraft enters one of the highways, it will be whisked along without the need to use much propellant of its own. The atomic half, meanwhile, arises from the theory of "transition states," which describes how atoms are transferred from one molecule to another during the course of a chemical reaction. The unity exists because the same mathematical equations apply in both cases -which means that insights gained from analyzing one class of problems can help analyze the other.

External links

- [http://www.cds.caltech.edu/~shane/ Shane Ross's] [http://www.cds.caltech.edu/~shane/talks/index.html#els-2004 Superhighway talk], [http://www.cds.caltech.edu/~shane/papers papers], [http://www.cds.caltech.edu/~shane/talks talks], [http://www.cds.caltech.edu/~shane/movies movies], [http://etd.caltech.edu/etd/available/etd-05182004-154045/ thesis], [http://www.cds.caltech.edu/~shane/superhighway/ links], and [http://www.cds.caltech.edu/~shane/superhighway/description.html description]
- [http://www.spacedaily.com/news/cosmology-05z.html "Mathematics Unites The Heavens And The Atom" Space Daily, Sep 28 2005]
- [http://nsf.gov/news/news_summ.jsp?cntn_id=104423&org=olpa&from=news "Math Unites the Heavens and the Atom" Science Daily, Sep 28 2005]
- [http://www.techno-science.net/?onglet=news&news=1845 "Les mathematiques unifient la dynamique interplanetaire et l'atome" Techno Science (French)]
- [http://www.tendencias21.net/Las-matematicas-celestes-son-equivalentes-a-las-de-la-fisica-atomica_a755.html "Las matematicas celestes son equivalentes a las de la fisica atomica" Tendencias 21 (Spanish)]
- [http://sciencenews.org/articles/20050416/bob9.asp "Navigating Celestial Currents" Science News, April 18, 2005]
- [http://pr.caltech.edu/periodicals/EandS/articles/LXV4/exit.html "Next Exit 0.5 Million Kilometers" Engineering and Science, 2002 ]
- [http://www.gg.caltech.edu/~mwl/ Martin Lo's] [http://www.gg.caltech.edu/~mwl/publications/publications2.htm publications] and [http://www.gg.caltech.edu/~mwl/communications/communications2.htm communications]
- [http://www.cds.caltech.edu/~shane/papers/gomez-et-al-2004.pdf "Connecting orbits and invariant manifolds in the spatial restricted three-body problem"]
- [http://www.cds.caltech.edu/~shane/papers/dellnitz-et-al-2005.pdf "Transport in dynamical astronomy and multibody problems"]
- [http://www.cds.caltech.edu/~shane/papers/mars-xrs-04-09-30.pdf "Transport of Mars-crossers from the quasi-Hilda region"]
- [http://focus.aps.org/story/v9/st31 "Asteroids lost in space (Physical Review Focus Article)"]
- [http://www.cds.caltech.edu/~shane/papers/jaffe-ross-et-al-2002.pdf "Statistical theory of asteroid escape rates"]
- [http://www.cds.caltech.edu/~shane/papers/ross-barcelona-2002.pdf "Statistical theory of interior-exterior transition and collision probabilities for minor bodies in the solar system"]
- [http://www.cds.caltech.edu/~shane/papers/low_energy_jovian_2002.pdf "Constructing a low energy transfer between Jovian moons"]
- [http://www.cds.caltech.edu/~shane/papers/NPO-20936.pdf "Low-Energy Transfer from Near-Earth to Near-Moon Orbit"]
- [http://www.cds.caltech.edu/~shane/papers/lo_ross_2001.pdf "The Lunar L1 Gateway: Portal to the Stars and Beyond"]
- [http://www.gg.caltech.edu/~mwl/publications/papers/IPSAndOrigins.pdf "The InterPlanetary Superhighway and the Origins Program"]
- [http://www.maa.org/editorial/mathgames/mathgames_09_07_04.html "Math Games: Manifolds in the Genesis mission"] Category:Spacecraft propulsion Category:Celestial mechanics Category:Dynamical systems

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

-
-
-
-
-
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 more volatile materials evaporated, leaving only those with high melting points, such as silicates, which form the planets' solid crusts and semi-liquid mantles, and iron, which forms their cores. All have impact craters and many possess tectonic surface features, such as rift valleys and volcanoes. The four inner planets are: volcanoes
- Mercury (0.39 AU from the Sun): The closest planet to the Sun is also the smallest and most atypical of the inner planets, having no atmosphere and, to date, no observed geological activity save that produced by impacts. Its relatively large iron core suggests that it was once a much larger world whose outer mantle was sheared off in early formation by the Sun’s gravity.
- Venus (0.72 AU): The first truly terrestrial planet, Venus, like the Earth, possesses a thick silicate mantle around an iron core, as well as a substantial atmosphere and evidence of one-time internal geological activity, such as volcanoes. It is much drier than Earth, and its atmosphere is 90 times as dense as Earth’s, however, and composed overwhelmingly of carbon dioxide with traces of sulfuric acid.
- Earth/Moon (1 AU): The largest of the inner planets, Earth is also the only one to demonstrate unequivocal evidence of ongoing geological activity. Its liquid hydrosphere, unique among the terrestrials, is probably the reason why Earth is also the only planet where multi-plate tectonics has been observed, since water acts as a lubricant for subduction. Its atmosphere is radically different from the other terrestrials, having been altered by the presence of life to contain 21 percent free oxygen. Its satellite, the Moon, is sometimes considered a terrestrial planet in a co-orbit with its partner, since its orbit around the Sun never actually loops back on itself when observed from above. The Moon possesses many of the features in common with other terrestrial planets, though it lacks an iron core.
- Mars (1.5 AU): Smaller than the Earth or Venus, Mars possesses a tenuous atmosphere of carbon dioxide. Its surface, peppered with vast volcanoes and rift valleys such as Valles Marineris, shows that it was once geologically active and [http://www.universetoday.com/am/publish/mars_volcanoes_active.html recent evidence] suggests it may have continued to be so until very recently. Mars possesses two tiny moons thought to be captured asteroids.

The asteroid belt

Asteroids are objects smaller than planets that mostly occupy the orbit between Mars and Jupiter, between 2.3 and 3.3 AU from the Sun, and are composed in significant part of non-volatile minerals. The main belt contains tens of thousands (possibly millions) over 1 km across, though they can be as small as dust. Despite their large numbers, the total mass of the main asteroid belt is unlikely to be more than a thousandth that of the Earth. Asteroids with a diameter of less than 50 m are called meteoroids. The largest asteroid, Ceres, has a diameter of roughly 1000 km; large enough to be spherical, which would make it a planet by some definitions of the word. The asteroids are thought to be the remnants of a small terrestrial planet that failed to coalesce due to the gravitational interference of Jupiter. They are subdivided into asteroid groups and families based on their specific orbital characteristics. Asteroid moons are asteroids that orbit larger asteroids. They are not as clearly distinguished as planetary moons, sometimes being almost as large as their partners. Trojan asteroids are located in either of Jupiter's L₄ or L₅ points, though the term is also sometimes used for asteroids in any other planetary Lagrange point as well. The inner solar system is dusted with rogue asteroids, many of which cross the orbits of the inner planets.

The outer planets

The four outer planets, or gas giants, (sometimes called Jovian planets) are so large they collectively make up 99 percent of the mass known to orbit the Sun. Their large sizes and distance from the Sun meant they could hold on to much of the hydrogen and helium too light for the smaller and hotter terrestrial planets to retain.
- Jupiter (5.2 AU), at 318 Earth masses, is 2.5 times the mass of all the other planets put together. Its composition of largely hydrogen and helium is not very different from that of the Sun. Three of its 63 satellites, Ganymede, Io and Europa, share elements in common with the terrestrial planets, such as volcanism and internal heating. Jupiter has a faint, smoky ring.
- Saturn (9.5 AU), famous for its extensive ring system, shares many qualities in common with Jupiter, including its atmospheric composition, though it is far less massive, being only 95 Earth masses. Two of its 49 moons, Titan and Enceladus, show signs of geological activity, though they are largely made of ice. Titan is the only satellite in the solar system with a substantial atmosphere.
- Uranus (19.6 AU) and Neptune (30 AU), while having many characteristics in common with the other gas giants, are nonetheless more similar to each other than they are to Jupiter or Saturn. They are both substantially smaller, being only 14 and 17 Earth masses, respectively. Their atmospheres contain a smaller percentage of hydrogen and helium, and a higher percentage of “ices”, such as water, ammonia and methane. For this reason some astronomers suggested that they belong in their own category, “Uranian planets,” or “ice giants.” Both planets possess dark, insubstantial ring systems. Neptune’s largest moon Triton is geologically active. Centaurs are icy comet-like bodies that have less-eccentric orbits so that they remain in the region between Jupiter and Neptune. The first centaur to be discovered, 2060 Chiron, has been called a comet since it has been shown to develop a tail, or coma, just as comets do when they approach the sun.

The trans-Neptunian region

The area beyond Neptune, often referred to as the outer solar system or simply the "trans-Neptunian region", is still largely unexplored.

The Kuiper belt

This region's first formation, which actually begins inside the orbit of Neptune, is the Kuiper belt, a great ring of debris, similar to the asteroid belt but composed mainly of ice and far greater in extent, which lies between 30 to 50 AU from the Sun. This region is thought to be the place of origin for short-period comets, such as Halley's comet. Though there are estimated to be over 70,000 Kuiper belt objects with a diameter greater than 100 km, the total mass of the Kuiper belt is relatively low, perhaps equalling or just exceeding the mass of the Earth. Many Kuiper belt objects have orbits that take them outside the plane of the ecliptic.
- Pluto, the solar system's smallest planet, is considered to be part of the Kuiper Belt population. Like others in the belt, it has a relatively eccentric orbit inclined 17 degrees to the ecliptic and ranging from 29.7 AU from the Sun at perihelion to 49.5 AU at aphelion. It has a large moon (the largest in the solar system relative to its own size), called Charon, and, new observations suggest, two other, much smaller moons. Like the Earth/Moon, Pluto and Charon are often considered a double planet. A member of the traditional nine planets, Pluto's tiny mass (less than 1% of Earth's) and diameter have called this status into question. Kuiper belt objects with Pluto-like orbits are called Plutinos. Other Kuiper belt objects have resonant orbits and are grouped accordingly. The remaining Kuiper belt objects, in more "classical" orbits, are classified as Cubewanos. The Kuiper Belt has a very sharply defined edge. At around 49 AU, a sharp dropoff occurs in the number of objects observed. This dropoff is known as the "Kuiper Cliff", and as yet its cause is unknown. Some speculate that something must exist beyond the belt large enough to sweep up the remaining debris, perhaps as large as Earth or Mars. This view is still controversial, however.

The scattered disc

Overlapping the Kuiper belt but extending much further outwards is the scattered disc. Scattered disc objects are believed to have been originally native to the Kuiper belt, but were ejected into erratic orbits in the outer fringes. One particular scattered disc object, originally found in 2003 but confirmed two years later by Mike Brown, has renewed the old debate about what constitutes a planet since, though its size is not yet known, it is almost certainly larger than Pluto. It currently has no name, but has been given the provisional designation , and has been nicknamed "Xena" by its discoverers, after the television character. It has many similarities with Pluto: its orbit is highly eccentric, with a perihelion of 38.2 AU (roughly Pluto's distance from the Sun) and an aphelion of 97.6 AU, and is steeply inclined to the ecliptic plane, indeed, at 44 degrees, more so than any known object in the solar system. Like Pluto, it is believed to consist largely of rock and ice, and has a [http://www.gps.caltech.edu/%7Embrown/planetlila/moon/index.html moon]. Whether it and the largest Kuiper belt objects should be considered planets or whether instead Pluto should be reclassified as a minor planet has not yet been resolved.

A new region?

Sedna, the newly discovered Pluto-like object with a gigantic, highly elliptical 10,500-year orbit that takes it from about 76 to 928 AU, has too distant a perihelion to be a scattered member of the Kuiper Belt and could be the first in an entirely new population. is also believed to be a member of this population.

Comets

Comets are composed largely of volatile ices and have highly eccentric orbits, generally having a perihelion within the orbit of the inner planets and an aphelion far beyond Pluto. Short-period comets exist with apoapses closer than this, however, and old comets that have had most of their volatiles driven out by solar warming are often categorized as asteroids. Long period comets have orbits lasting thousands of years. Some comets with hyperbolic orbits may originate outside the solar system.

And beyond

The point at which the solar system ends and interstellar space begins is not precisely defined, since its outer boundaries are delineated by two separate forces: the solar wind and the Sun's gravity. gravity The heliosphere expands outward in a great bubble to about 95 AU, or three times the orbit of Pluto. The edge of this bubble is known as the termination shock; the point at which the solar wind collides with the opposing winds of the interstellar medium. Here the wind slows, condenses and becomes more turbulent, forming a great oval structure known as the heliosheath that looks and behaves very much like a comet's tail; extending outward for a further 40 AU at its stellar-windward side, but tailing many times that distance in the opposite direction. The outer boundary of the sheath, the heliopause, is the point at which the solar wind finally terminates, and one enters the environment of interstellar space. Beyond the heliopause, at around 230 AU, lies the bow shock, a plasma "wake" left by the Sun as it travels through the Milky Way. But even at this point, we could not be said to have left the solar system, for the Sun's gravity will still hold sway even up to the Oort cloud, the great mass of icy objects, currently hypothetical, believed to be the source for all long-period comets and to surround our solar system like a shell from 50,000 to 100,000 AU beyond the Sun, or almost halfway to the next star system. The vast majority of the solar system, therefore, is completely unknown.

Age of the solar system

Scientists estimate that the solar system is 4.6 billion years old. To calculate this figure, they examine an unstable element, which is subject to radioactive decay. By observing how much this element has decayed, they can calculate how old this element is. The oldest rocks on earth are approximately 3.9 billion years old, however it is hard to find these rocks as the earth has been thoroughly resurfaced. To estimate the age of the solar system, scientists must find rocks from space, such as meteorites – which are formed during the early condensation of the solar nebula. The oldest meteorite was found to have an age of 4.6 billion years, hence the solar system must be around 4.6 billion years old.

Galactic orbit of the solar system

The solar system is part of the Milky Way galaxy, a spiral galaxy with a diameter of about 100,000 light years containing approximately 200 billion stars, of which our Sun is rather large and bright. (The vast majority of stars are red dwarfs; our Sun is placed near the middle of the Hertzsprung-Russell diagram, but stars larger and hotter than it are rare, whereas stars dimmer and cooler than it are very common, although we can observe only those few other red dwarfs that are very near our Sun in space). Estimates place the solar system at between 25,000 and 28,000 light years from the galactic center in the Orion Arm. Its speed is about 220 kilometres per second, and it completes one revolution every 226 million years. At the galactic location of the solar system, the escape velocity with regard to the gravity of the Milky Way is about 1000 km/s. The solar system appears to have a very unusual orbit. It is both extremely close to being circular, and at nearly the exact distance at which the orbital speed matches the speed of the compression waves that form the spiral arms. The solar system appears to have remained between spiral arms for most of the existence of life on Earth. The radiation from supernovae in spiral arms could theoretically sterilize planetary surfaces, preventing the formation of large animal life on land. By remaining out of the spiral arms, Earth may be unusually free to form large animal life on its surface.

Planetary system formation

For many years, our solar system had the only planetary system known, and so theories of planetary formation only had to explain one system to be plausible. The discovery in recent years of many extrasolar planets has uncovered systems very different to our own, and theories have had to be revised accordingly. Exoplanets have not been seen by astronomers yet, however we know they exist because of the gravitational tug the planets induce on the star, and hence making the star ‘wobble’. Astronomers can calculate how massive the planets are by observing how much the star wobbles. Exoplanets can also be observed more directly by their occultation of the stars' discs, which dims them slightly. In October, 1995, astronomers Michel Mayor and Didier Queloz announced the discovery of a massive planet orbiting 51 Pegasi – a Sun-like star in the constellation Pegasus. This planet is about half as massive as Jupiter, and had an orbital period of 4.2 Earth days, due to its closeness to the star (0.05 AU). Since then, over 160 more planets have been identified. Many extrasolar planetary systems contain such a “hot Jupiter”: a planet comparable to or larger than Jupiter orbiting very close to the parent star, perhaps orbiting it in a matter of days. It has been hypothesised that while the giant planets in these systems formed in the same place as the gas giants in our system did, some sort of migration took place which resulted in the giant planet spiralling in towards the parent star. Any terrestrial planets which had previously existed would presumably either be destroyed or ejected from the system. There has also been some photographic evidence to suggest that regions in the Orion Nebula, which is 1500 light years from Earth, have star systems forming.

Discovery of the solar system

The planets out to Saturn were known to ancient astronomers, who observed the wandering of these objects against the apparently fixed pattern of stars. Venus and Mercury were each identified as single objects despite the difficulty of connecting "evening" and "morning stars". It was also identified that the two non-pointlike objects, the sun and the Moon, moved across the same fixed background. However knowledge of the nature of these celestial drifters was entirely speculative and largely incorrect. The nature and structure of the solar system were long misperceived, for at least two reasons:
- The Earth was considered stationary, and the motion of objects in the sky was therefore taken at face value: the sun was thought to orbit the Earth, for example (This conception of the universe, in which the Earth is at the center, is called the Geocentric model; geos means "Earth" in Greek).
- Many solar system objects and phenomena cannot be perceived at all without technical aid. Over the last several hundred years, conceptual and technological advances have helped us understand the solar system much better. The first and most fundamental of the conceptual advances was the Copernican Revolution, which proposed that the planets orbit the sun—models of the solar system with the sun in the center are called heliocentric (helios meaning "Sun" in Greek). Despite the name, the most striking (and then-controversial) Copernican realization was not that the sun was central but that the Earth was peripheral, orbital: planets had been considered merely points in the sky, but if the Earth itself was a planet, perhaps the other planets were, like Earth, huge solid spheres. Philosophically, there were a number of objections to heliocentrism:
- If the Earth is moving, what force keeps the air from flying off into space?
- The Earth is made of heavy rock. Heavy rock moves down. Down in a sphere means the centre. The planets are ephemeral and light, so they are above. How can Earth be a planet?
- If the Earth is mobile, then why do we not observe parallax in the stars (the stars appearing to shift in relation to further objects due to the change in position)? The subsequent invention of the telescope gave the principal technological advance on discovering the solar system, with Galileo's improved version of the telescope rapidly giving benefit in terms of discovering satellites of other planets, especially Jupiter's four major satellites. This showed that all objects in the universe did not orbit the Earth. However, perhaps Galileo's most important discovery was that the planet Venus has phases like the Moon, proving that it must orbit the Sun. Then, in 1687, Isaac Newton devised his law of universal gravitation which explained the force that both kept the Earth moving through the heavens and also kept the air from flying away. Finally, in 1838, astronomer Friedrich Wilhelm Bessel successfully measured the parallax of the star 61 Cygni, proving conclusively that the Earth was in motion.

Exploration of the solar system

Since the start of the space age, a great deal of exploration has been performed by unmanned space missions that have been organized and executed by various space agencies. The first probe to land on another solar system body was the Soviet Union's Luna 2 probe, which impacted on the Moon in 1959. Since then, increasingly distant planets have been reached, with probes landing on Venus in 1965, Mars in 1976, the asteroid 433 Eros in 2001, and Saturn's moon Titan in 2005. Spacecraft have also made close approaches to other planets: Mariner 10 passed Mercury in 1973. The first probe to explore the outer planets was Pioneer 10, which flew by Jupiter in 1973. Pioneer 11 was the first to visit Saturn, in 1979. The Voyager probes performed a grand tour of the outer planets following their launch in 1977, with both probes passing Jupiter in 1979 and Saturn in 1980–1981. Voyager 2 then went on to make close approaches to Uranus in 1986 and Neptune in 1989. The Voyager probes are now far beyond Pluto's orbit, and astronomers anticipate that they will encounter the heliopause which defines the outer edge of the solar system in the next few years. Pluto remains the only planet not having been visited by a man-made spacecraft, though that will change with the launching of New Horizons by NASA in January 2006. It is scheduled to fly by Pluto in July 2015 and then make an extensive study of as many Kuiper Belt objects as it can. Through these unmanned missions, we have been able to get close-up photographs of most of the planets and, in the case of landers, perform tests of their soils and atmospheres. Manned exploration, meanwhile, has only taken human beings as far as the Moon, in the Apollo program. The last manned landing on the Moon took place in 1972, but the recent discovery of ice in deep craters in the polar regions of the Moon has prompted speculation that mankind may return to the Moon in the next decade or so. Manned missions to Mars have been eagerly anticipated by generations of space enthusiasts, and it was hoped that the first manned interplanetary flights would take place in the 1980s, after the successful Apollo program. Europe (ESA and EU) now plans manned Lunar and Mars missions as part of Aurora Exploration Programme endorsed in 2001. United States followed with similar programme called Vision for Space Exploration in 2004.

Attributes of major planets

All attributes below are measured relative to the Earth: Of the other objects, Ganymede has the largest mass (0.02). Note: Although is a minor planet, it is being considered as possibly being a major planet (the tenth in the solar system). See Planet (Table) for a more comprehensive table.

Attributes of the largest minor planets

The largest minor planets are smoothly rounded, like planets, because their gravity overcomes material strength that keeps smaller bodies in non-spherical shapes. Before the discovery of 2060 Chiron and the trans-Neptunian objects, the term "minor planet" was a synonym for asteroid, but many people now prefer to restrict the use of "asteroid" to refer to rocky bodies of the inner solar system. Most trans-Neptunian objects are icy, like comets, although those we can detect at that distance are much larger than comets. Several asteroids, in the strict sense, are large enough to be spherical. The largest known trans-Neptunian objects are much larger than the large asteroids. (Natural satellites of major planets also range smoothly from small non-spherical objects to large spherical ones, and the largest are larger than 1 Ceres, the largest asteroid). All attributes below are measured relative to the Earth:

Other facts

The total surface area of the solar system's objects that have solid surfaces and a diameter greater than 1 km is ~1.7 km² —about 11 times the area of the Earth's land masses. It has been suggested that the Sun may be part of a binary star system, with a distant companion named Nemesis. Nemesis was proposed to explain some timing regularities of the great extinctions of life on Earth. The hypothesis says that Nemesis creates periodical perturbations in the Oort cloud of comets surrounding the solar system, causing a "comet shower". Some of them hit Earth, causing destruction of life. This hypothesis is no longer taken seriously by most scientists, mostly because infrared surveys failed to spot any such object, which should have been very conspicuous at those wavelengths. The concept of the tenth planet has frequently been explored in science fiction works and conspiracy theories (see also Planet X, and hypothetical planet).

The solar system in small scales

Scaling down the size of the solar system makes it easier for students to grasp the relative distances. The enormous ratio of interplanetary distances to planetary diameters makes constructing a scale model of the solar system a challenging task. (For example, the distance between the Earth and the Sun is almost 12,000 times the diameter of the Earth.) Several places have built such models.

The solar system in astrology

External links

- [http://solarsystem.nasa.gov/index.cfm NASA's Solar System Exploration site]
- [http://space.jpl.nasa.gov NASA's Solar System Simulator]
- [http://www.jpl.nasa.gov/solar_system NASA/JPL Solar System main page]
- [http://members.aol.com/astroequation/ Astronomical Enigma] Mathematical Order in the orbits of the solar system.
- [http://www.solarviews.com Solarviews]
- [http://celestia.sourceforge.net Celestia] Free 3D realtime space-simulation (OpenGL)
- [http://www.nineplanets.org/ The Nine Planets] Comprehensive solar system site by Bill Arnett
- [http://www.krysstal.com/solarsys_planets.html Planetary data]
- [http://www.solstation.com/habitable.htm Stars and Habitable Planets]
- [http://www.michaelschultz.de/index_en.html Solar System] An interactive planets animation (145 zoom steps and time effects)
- [http://my.execpc.com/~culp/space/timeline.html Timeline of solar system exploration]
- [http://www.anzwers.org/free/universe/index.html An Atlas of the Universe]
- mirror matter [http://uk.arxiv.org/abs/astro-ph/0104251 planets] and other [http://uk.arxiv.org/abs/astro-ph/0110161 mirror objects] in the solar system?
- [http://www.solarsystem.org.uk/ The Virtual Solar System, including a scale model of the system]
- ko:태양계 ms:Sistem suria ja:太陽系 simple:Solar system th:ระบบสุริยะ zh-min-nan:Thài-iông-hē

Hohmann transfer orbit

In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that moves a spacecraft from one orbit to another using a fairly low delta-v. It was named after Walter Hohmann, the German scientist who published it in 1925. (See also interplanetary travel.) A Hohmann transfer orbit will take a spacecraft from low Earth orbit (LEO) to geosynchronous orbit (GEO) in just over five hours (geostationary transfer orbit), from LEO to the Moon in about 5 days and from the Earth to Mars in about 260 days. However, Hohmann transfers are very slow for trips to more distant points, so when visiting the outer planets it is common to use a gravitational slingshot to increase speed in-flight. gravitational slingshot The Hohmann transfer orbit is one half of an elliptic orbit that touches both the orbit that one wishes to leave (labelled 1 on diagram) and the orbit that one wishes to reach (3 on diagram). The transfer (2 on diagram) is initiated by firing the spacecraft's engine in order to accelerate it so that it will follow the elliptical orbit. When the spacecraft has reached its destination orbit, it has slowed down to a speed not only lower than the speed in the original circular orbit, but even lower than required for the new circular orbit; the engine is fired again to accelerate it again, to that required speed. Since this transfer requires two powerful bursts, it can not be applied with a low-thrust engine. With that, the circular orbit can be gradually enlarged. Together this requires a delta-v that is up to 141% more (see also below), and, of course, the lower the thrust the longer it takes. When used to move a spacecraft from orbiting one planet to orbiting another, the situation becomes somewhat more complex. For example, consider a spacecraft travelling from the Earth to Mars. At the beginning of its journey, the spacecraft will already have a certain velocity associated with its orbit around Earth – this is velocity that will not need to be found when the spacecraft enters the transfer orbit (around the Sun). At the other end, the spacecraft will need a certain velocity to orbit Mars, which will actually be less than the velocity needed to continue orbiting the Sun in the transfer orbit, let alone attempting to orbit the Sun in an Mars-like orbit. Therefore, the spacecraft will have to decelerate and allow Mars' gravity to capture it. Therefore, relatively small amounts of thrust at either end of the trip are all that are needed to arrange the transfer. Note, however, that the alignment of the two planets in their orbits is crucial – the destination planet and the spacecraft must arrive at the same point in their respective orbits around the Sun at the same time, see launch window. Hohmann transfer orbits also work to bring a spacecraft from a higher orbit into a lower one – in this case, the spacecraft's engine is fired in the opposite direction to its current path, causing it to drop into the elliptical transfer orbit, and fired again in the lower orbit to brake it to the correct speed for that lower orbit. In certain situations where the semimajor axis of the final orbit is much greater then the semimajor axis of the initial orbit (usually by a factor of 12), it may be more advantageous to use a bi-elliptic transfer.

Calculation

Ignoring the delta-v needed to get to/from orbits around planets at either end of the journey, and just calculating the delta-v needed to get from one circular orbit to another coplanar circular orbit around a primary body, e.g. the Sun, the vis viva equation says, :

v^2 = \mu \left( \frac - \frac \right)

where:
-

v \,\!

is the speed of an orbiting body
-

\mu = GM\,\!

is the standard gravitational parameter of the primary body
-

r \,\!

is the distance of the orbiting body from the primary
-

a \,\!

is the semi-major axis of the body's orbit Therefore the Delta-v required for the Hohmann transfer can be computed as follows: :

\Delta v_P 
= \sqrt
  \left( \sqrt - 1 \right)

, Delta-v required at periapsis. :

\Delta v_A 
= \sqrt
  \left( 1 - \sqrt\,\! \right)

, Delta-v required at apoapsis. where:
-

r_1\,\!

is radius of lower orbit, and periapsis distance of Hohmann transfer orbit,
-

r_2\,\!

is radius of higher orbit, and apoapsis distance of Hohmann transfer orbit. Whether moving into a higher or lower orbit, by Kepler's third law, the time taken to transfer between the orbits is: :

t_H 
= \begin\frac12\end \sqrt
= \pi \sqrt

(one half of the orbital period for the whole ellipse) where:
-

a_H\,\!

is length of semi-major axis of the Hohmann transfer orbit.

Example; maximum delta-v

For the geostationary transfer orbit we have

r_2

= 42,164 km and e.g.

r_1

= 6,678 km (altitude 300 km). In the smaller circular orbit the speed is 7.73 km/s, in the larger one 3.07 km/s. In the elliptical orbit in between the speed varies from 10.15 km/s at the perigee to 1.61 km/s at the apogee. The delta-v's are 10.15 − 7.73 = 2.42 and 3.07 − 1.61 = 1.46 km/s, together 3.88 km/s. [http://www.google.com/search?num=100&hl=en&lr=&newwindow=1&safe=off&q=sqrt%28398600%2F6678%29
- sqrt%282%2F%286678%2F42164%2B1%29%29] Compare with the delta-v for an escape orbit: 10.93 − 7.73 = 3.20 km/s. Applying a delta-v at the LEO of only 0.78 km/s more would give the rocket the escape speed, while at the geostationary orbit a delta-v of 1.46 km/s is needed for reaching the sub-escape speed of this circular orbit. This illustrates that at large speeds the same delta-v provides more specific orbital energy, and, as explained in gravity drag, energy increase is maximized if one spends the delta-v as soon as possible, rather than spending some, being decelerated by gravity, and then spending some more (of course, the objective of a Hohmann transfer orbit is different). A Hohmann transfer orbit from a given circular orbit to a larger circular orbit, in the case of a single central body, costs the largest delta-v (53.6 % of the original orbital speed) if the radius of the target circle is 15.5 times as large as that of the original circle. For larger target circles the delta-v decreases again, and tends to

\sqrt-1

times the original orbital speed (41.4%). (The first burst tends to acceleration to the escape speed, the second tends to zero.)

Low-thrust transfer

It can be derived that going from one circular orbit to another by gradually changing the radius costs a delta-v of simply the absolute value of the difference between the two speeds. Thus for the geostationary transfer orbit 7.73 - 3.07 = 4.66 km/s, the same as, in the absence of gravity, the deceleration would cost. In fact, acceleration is applied to compensate half of the deceleration due to moving outward. Therefore the acceleration due to thrust is equal to the deceleration due to the combined effect of thrust and gravity. For escaping the Earth from LEO the required delta-v is 7.73 km/s, compare with the 3.20 km/s in the case of a single burst.

Interplanetary Superhighway

In 1997, a set of orbits known as the Interplanetary Superhighway was published, providing even lower-energy (though much slower) paths between different orbits than Hohmann transfer orbits.

External links

- http://www.pma.caltech.edu/~chirata/deltav.html
- [http://www.braeunig.us/space/orbmech.htm ORBITAL MECHANICS] (Rocket and Space Technology) Category:Astrodynamics Category:Spacecraft propulsion Category:Celestial mechanics

Chaos theory

:For the album by Jumpsteady, see Chaos Theory (album). : For the video game, see Splinter Cell: Chaos Theory. In mathematics and physics, chaos theory deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions (see butterfly effect). As a result of this sensitivity, the observed behavior of physical systems that exhibit chaos appears to be random, even though the model of the system is 'deterministic' in the sense that it is well defined and contains no random parameters. Examples of such systems include the atmosphere, the solar system, plate tectonics, turbulent fluids, economies, and population growth. turbulent Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. See the article on chaos for a discussion of the origin of the word in mythology, and other uses. When it is said that chaos theory studies deterministic systems, it is necessary to mention a related field of physics called quantum chaos theory which studies non-deterministic systems following the laws of quantum mechanics.

Description of the theory

A non-linear dynamical system can, in general, exhibit one or more of the following types of behavior:
- forever at rest
- forever expanding (only for unbounded systems)
- periodic motion
- quasi-periodic motion
- chaotic motion The type of behavior a system may exhibit depends on the initial state of the system and the values of its parameters, if any. The most difficult type of behavior to characterize and predict is chaotic motion, a non-periodic complex motion which has given name to the theory.

Chaotic motion

In order to classify the behavior of a system as chaotic, the system must exhibit the following properties:
- it must be sensitive to initial conditions
- it must be topologically transitive
- its periodic orbits must be dense Sensitivity to initial conditions means that two points in such a system may move in vastly different trajectories in their phase space even if the difference in their initial configurations is very small. The systems behave identically only if their initial configurations were exactly the same. An example of such sensitivity is the so-called "butterfly effect", whereby the flapping of a butterfly's wings is imagined to create tiny changes in the atmosphere which over the course of time cause it to diverge from what it would have been and potentially cause something as dramatic as a tornado to occur. The butterfly flapping its wings represents a small change in the initial condition of the system which causes a chain of events leading to large-scale phenomena like tornadoes. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. Other commonly-known examples of chaotic motion are the mixing of colored dyes and airflow turbulence. Sensitivity to initial conditions is related to the Lyapunov exponent. Transitivity means that application of the transformation on any given Interval

I_1

stretches it until it overlaps with any other given Interval

I_2

. Transitivity, dense periodic points, and sensitivity to initial conditions can all be extended to an arbitrary metric space. J. Banks and colleagues showed in 1992 that in the setting of a general metric space, transitivity and dense periodic points together imply sensitivity to initial conditions. This elementary but unexpected fact prompted Bau-Sen Du, of the Institute of Mathematics, Academia Sinica, Taiwan to define a stronger version of sensitive dependence - extreme sensitive dependence - which is not a consequence of transitivity and dense periodic points. Extreme sensitive dependence means, roughly, that points close together separate and converge infinitely often, as is often the case in examples of chaotic dynamical systems.

Attractors

One way of visualizing chaotic motion, or indeed any type of motion, is to make a phase diagram of the motion. In such a diagram time is implicit and each axis represents one dimension of the state. For instance, one might plot the position of a pendulum against its velocity. A pendulum at rest will be plotted as a point and a one in periodic motion will be plotted as a simple closed curve. When such a plot forms a closed curve, the curve is called an orbit. Our pendulum has an infinite number of such orbits, forming a pencil of nested ellipses about the origin. Often phase diagrams reveal that most state trajectories wind up approaching some common limit. The system ends up doing the same motion for all initial states in a region around the motion, almost as though the system is attracted to that motion. Such attractive motion is fittingly called an attractor for the system and is very common for forced dissipative systems. For instance, if we attach a damper to our pendulum, no matter what its initial position and velocity it will wind up being at rest - or more correctly: it will reach rest at the limit. The trajectories on the phase diagram will all spiral in towards the middle, rather than forming sets of ovals. This point in the middle - the state when the pendulum is at rest - is called an "attractor". Attractors are often associated with dissipative systems like this, where some element (the damper) dissipates energy. Such an attractor may be called a "point attractor". Not all attractors are points. Some are simple loops, or more complex doubled loops (for which you need more than two degrees of freedom). And some are actually fractals: the so called "strange attractors". Systems with loop attractors exhibit periodic motion. Those with more complex split loops tend to exhibit quasiperiodic motion. And systems with strange attractors tend to exhibit chaotic behavior. At any point on the phase diagram, the system will tend to evolve to another neighbouring state in some sort of deterministic way. If our pendulum is at a particular position and travelling with a particular velocity, we can calculate what its (infinitesimally) "next" position and velocity will be. That is, we can treat our phase diagram as being a vector field, and use vector calculus to understand it. Attractors in our phase diagram are simply those regions with a negative divergence.

Strange attractors

While most of the motion types mentioned above give rise to very simple attractors, such as points and circle-like curves called limit cycles, chaotic motion gives rise to what are known as strange attractors, attractors that can have great detail and complexity. For instance, a simple three-dimensional model of the Lorenz weather system gives rise to the famous Lorenz attractor. The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because not only was it one of the first, but it is one of the most complex and as such gives rise to a very interesting pattern which looks like the wings of a butterfly. Another such attractor is the Rössler Map, which experiences period-two doubling route to chaos, like the logistic map. Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set which forms at the boundary between basins of attraction of fixed points - Julia sets can be thought of as strange repellers. Both strange attractors and Julia sets typically have a fractal structure. The Poincaré-Bendixson theorem shows that a strange attractor can only arise in a continuous dynamical system if it has three or more dimensions. However, no such restriction applies to discrete systems, which can exhibit strange attractors in two or even one dimensional systems.

History

The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff, A.N. Kolmogorov, M.L. Cartwright, J.E. Littlewood, and Stephen Smale. Except for Smale, who was perhaps the first pure mathematician to study nonlinear dynamics, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing. Chaos theory progressed more rapidly after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map. The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical. One of the earliest electronic digital computers, ENIAC, was used to run simple weather forecasting models. An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961. Lorenz was using a basic computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course. He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time. To his surprise the weather that the machine began to predict was completely different to the weather calculated before. Lorenz tracked this down to the computer printout. The printout rounded variables off to a 3-digit number, but the computer worked with 6-digit numbers. This difference is tiny and the consensus at the time would have been that it should have had practically no effect. However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome. The term chaos as used in mathematics was coined by the applied mathematician James A. Yorke. The availability of cheaper, more powerful computers broadens the applicability of chaos theory. Currently, chaos theory continues to be a very active area of research.

Mathematical theory

Mathematicians have devised many additional ways to make quantitative statements about chaotic systems. These include:
- fractal dimension of the attractor
- Lyapunov exponents
- recurrence plots
- Poincaré maps
- bifurcation diagrams
- Transfer operator

Minimum complexity of a chaotic system

Many simple systems can also produce chaos without relying on differential equations, such as the logistic map, which is a difference equation (recurrence relation) that describes population growth over time. Even discrete systems, such as cellular automata, can heavily depend on initial conditions. Stephen Wolfram has investigated a cellular automaton with this property, termed by him rule 30.

Other examples of chaotic systems

- Double pendulum
- Logistic map
- Hénon map
- Lorenz model
- Smale horseshoe
- Dynamical billiards

References

Textbooks and technical works

-
-
-
-
-
-
-
-
- "Wave Propagation in Ray-Chaotic Enclosures: Paradigms, Oddities and Examples", Vincenzo Galdi, et. al., IEEE Antennas and Propagation Magazine, February 2005, p. 62

Semitechnical and popular works

- The Beauty of Fractals, by H.-O. Peitgen and P.H. Richter
- Chance and Chaos, by David Ruelle
- Computers, Pattern, Chaos, and Beauty, by Clifford A. Pickover
- Fractals, by Hans Lauwerier
- Fractals Everywhere, by Michael Barnsley
- Order Out of Chaos, by Ilya Prigogine and Isabelle Stengers
- Chaos and Life, by Richard J Bird
- Does God Play Dice?, by Ian Stewart
- The Science of Fractal Images, by Heinz-Otto Peitgen and Dietmar Saupe, Eds.
- Explaining Chaos, by Peter Smith
- Chaos, by James Gleick
- Complexity, by M. Mitchell Waldrop
- Chaos, Fractals and Self-organisation, by Arvind Kumar
- Chaotic Evolution and Strange Attractors, by David Ruelle
- Sync: The emerging science of spontaneous order, by Steven Strogatz
- The Essence of Chaos, by Edward Lorenz
- Deep Simplicity, by John Gribbin

Popular culture

- Ian Malcolm, a character from the movie and book Jurassic Park, was a chaos theory mathematician.

External links

- http://www.nbi.dk/ChaosBook/
- [http://www.libraryreference.org/chaos.html Chaos Theory and Education]
- [http://www.imho.com/grae/chaos/chaos.html Chaos Theory: A Brief Introduction]
- [http://www.ae.uiuc.edu/lndvl Linear and Nonlinear Dynamics and Vibrations Laboratory at the University of Illinois]
- [http://hypertextbook.com/chaos/ The Chaos Hypertextbook]. An introductory primer on chaos and fractals.
- Chaos Theory in the Social Sciences, edited by L Douglas Kiel, Euel W Elliott.
- [http://www.cut-the-knot.org/blue/chaos.shtml Emergence of Chaos] at cut-the-knot
- Category:Non-linear systems ko:혼돈 이론 ja:カオス理論 simple:Chaos theory th:ทฤษฎีความอลวน

Gravity

Gravity is the force of attraction between massive particles. Weight is determined by the mass of an object and its location in a gravitational field. While a great deal is known about the properties of gravity, the ultimate cause of the gravitational force remains an open question. General relativity is the most successful theory of gravitation to date. It postulates that mass and energy curve space-time, resulting in the phenomenon known as gravity. The effect of the bending of spacetime is often misunderstood as most people seem to prefer to think of a falling object as accelerating when the facts do not support that assumption. Skydivers do not feel any acceleration (other than from wind resistance). Gravity is acceleration.

F=\dot=m\dot+\dotv\,\!

means (if the mass is unvarying) that there must be a force that causes a mass to accelerate. For a rocket ship, that is the rocket engine. For the earth, it is the compression of the mass between something on the surface of the earth and the earth's center of mass. The acceleration is in relation to spacetime in that the weight one feels is one's resistance to deviating from one's path in spacetime. The same holds true in the rocket ship except that a rocket engine supplies the force to accelerate an occupant from his spacetime path. There is no difference between the weight he feels because of gravity or the rocket.

Newton's law of universal gravitation

Newton's law of universal gravitation states the following: :Every object in the Universe attracts every other object with a force directed along the line of centers of mass for the two objects. This force is proportional to the product of their masses and inversely proportional to the square of the separation between the centers of mass of the two objects. Given that the force is along the line through the two masses, the law can be stated symbolically as follows. :

F = - G \frac

where: :F is the magnitude of the (repulsive) gravitational force between two objects :G is the gravitational constant, that is approximately : G = 6.67 × 10⁻¹¹ N m² kg^-2 :m₁ is the mass of first object :m₂ is the mass of second object :r is the distance between the objects It can be seen that this repulsive force F is always negative, and this means that the net attractive force is positive. The minus sign is used to hold the same value meaning as in the Coulomb's Law, where a positive force as result means repulsion between two charges. Thus gravity is proportional to the mass of each object, but has an inverse square relationship with the distance between the centres of each mass. Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the force has to be calculated by integrating the force (in vector form, see below) over the extents of the two bodies. It can be shown that for an object with a spherically-symmetric distribution of mass, the integral gives the same gravitational attraction on masses outside it as if the object were a point mass.¹ This law of universal gravitation was originally formulated by Isaac Newton in his work, the Principia Mathematica (1687). Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated: ::The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth. [In A Treasury of Science ed. Harlow Shapley et al, Harper & Bros. NY: 1946] The history of gravitation as a physical concept is considered in more detail below.

Vector form

below Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors. :

\mathbf_ =
 G 
 \, \mathbf_

\mathbf_ =
 - G 
 \, \mathbf_

where :F₁₂ is the force on object 1 due to object 2 :G is the gravitational constant :m₁ and m₂ are the masses of the objects 1 and 2 :r₂₁ = | r₂ − r₁ | is the distance between objects 2 and 1 :

\mathbf_ \equiv \frac

is the unit vector from object 2 to 1 It can be seen, that the vector form of the equation is the same as the scalar form, except for the vector value of F and the unit vector. Also, it can be seen that F₁₂ = − F₂₁. Gravitational acceleration is given by the same formula except for one of the factors m: :

\mathbf =
  G 
  \, \mathbf

Gravitational field

The gravitational field is a vector field that describes the gravitational force an object of given mass experiences in any given place in space. It is a generalization of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 1 is a rocket, object 2 the Earth), we simply write

\mathbf r

instead of

\mathbf r_

and

m

instead of

m_1

and define the gravitational field

\mathbf g(\mathbf r)

as: :

\mathbf g(\mathbf r) =
 G 
 \, \mathbf

so that we can write: :

\mathbf( \mathbf r) = m \mathbf g(\mathbf r)

This formulation is independent of the objects causing the field. The field has units of force divided by mass; in