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Topic: Horseshoe orbit

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Orbit

3753 Cruithne

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	CalendarHome.com - - Calendar Encyclopedia (Site not responding. Last check: 2007-10-16)
		Such an orbit also has a velocity equal to the escape velocity and therefore will escape the gravitational pull of the planet and travel until its velocity relative to the planet is 0.
		Synchronous Orbit - An orbit where the satellite has an orbital period equal to the average rotational period (earth's is: 23 hours, 56 minutes, 4.091 seconds) of the body being orbited and in the same direction of rotation as that body.
		Horseshoe Orbit - An orbit that appears to a ground observer to be orbiting a certain planet but is actually in co-orbit with the planet.
	encyclopedia.calendarhome.com /cgi-bin/encyclopedia.pl?p=Satellite (3299 words)

	Horseshoe orbit - Wikipedia, the free encyclopedia
		A horseshoe orbit is the type of orbit you get when you observe an object from another nearly co-orbital object, such as a planet.
		For example, if an object orbits the Sun in slightly less or more than a year, and if its orbit is a little more eccentric than Earth's, every year it will appear to trace a kidney-bean shape around a point on Earth's orbit.
		The moons of Saturn Epimetheus and Janus occupy horseshoe orbits with respect to each other (in their case, there is no repeated looping: each one traces a full horseshoe with respect to the other).
	en.wikipedia.org /wiki/Horseshoe_orbit (572 words)

	Horseshoe map - Wikipedia, the free encyclopedia
		The horseshoe map f is a diffeomorphism defined from a region S of the plane into itself.
		The horseshoe map is an Anosov diffeomorphism that serves as a model for general behavior at transverse homoclinic points.
		The horseshoe map was designed to reproduce the chaotic dynamics of a flow in the neighborhood of a given periodic orbit.
	en.wikipedia.org /wiki/Horseshoe_map (1578 words)

	The SPSU Mathematics Colloquium (Site not responding. Last check: 2007-10-16)
		Some interesting stable or unstable orbits are known in the general three-body case, and several new ones have been discovered just recently, including a remarkable figure-8 orbit.
		Some of these orbits are remarkable, such as a horseshoe orbit, which is actually followed by an asteroid (Cruithne), occupying almost the same orbit as the Earth, and which can be called a second moon of the Earth.
		Orbits around the Earth-Sun L1 - L5 points are just now being used as parking orbits for special-purpose satellites such as the solar observer SOHO and the cosmic microwave background mapper WMAP.
	www2.spsu.edu /math/pacecolloquium.htm (291 words)

	Three-Body Problem
		The saddle points on either side of m are unstable for all mass ratios, but the one to the left of M is the horseshoe orbit for the sun/Jupiter and sun/earth systems (the other two saddle points are not plotted for these systems because the scale is not suitable).
		The Trojan and horseshoe orbits are closely-related examples of a stable orbit: a closed curve that rotates about the center of mass in sync with m.
		Horseshoe orbits can be generated for both the sun/Jupiter and sun/earth systems with a d/400 y-displacement from the left saddle point.
	www.kw.igs.net /~jackord/bp/f8.html (931 words)

	3753 Cruithne - Wikipedia, the free encyclopedia
		It was not until 1997 that its unusual orbit was determined by Paul Wiegert and Kimmo Innanen, working at York University in Canada, and Seppo Mikkola, working at the University of Turku in Finland.
		Cruithne's horseshoe orbit and the orbit of the Earth
		Other examples of natural bodies known to be in horseshoe orbits at the time of writing include Janus and Epimetheus, natural satellites of Saturn.
	www.wikipedia.com /wiki/3753_Cruithne (696 words)

	Smale Horseshoe (Site not responding. Last check: 2007-10-16)
		Remnants of a horseshoe (sometimes called the proto-horseshoe [11]) are buried within a chaotic attractor.
		The horseshoe (or some other variant of a hyperbolic invariant set) acts as the skeleton on which chaotic and periodic orbits are organized.
		To quote Holmes , ``Horseshoes in a sense provide the `backbone' for the attractors [12].'' Therefore, horseshoes are essential to both the mathematical and physical analysis of a chaotic system.
	cnls.lanl.gov /~nbt/Book/node126.html (292 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		However, its unusual orbit was not determined until 1997 by Paul Wiegert and Kimmo Innanen, working at York University in Canada, and Seppo Mikkola, working at the University of Turku in Finland.
		Instead, it follows a spiralling path that moves along the Earth's orbit in a horseshoe shape, the two ends of the horseshoe approaching either side of Earth but not quite reaching it.
		There is only one other known example of natural bodies in a horseshoe orbit at the time of writing, the natural satellites of Saturn named Janus and Epimetheus.
	www.online-encyclopedia.info /encyclopedia/3/37/3753_cruithne.html (416 words)

	Orbital Mechanics I
		The point in an orbit where the engines are fired becomes a point in a new orbit.
		The basic principle behind all circular orbits is that the the centripetal force needed to keep the planet in orbit is supplied by an inverse-square gravitational force.
		Spacecraft in extreme near earth orbit are subject to small but (in the long run) non-negligible amounts of aerodynamic drag from the upper regions of the earth's atmosphere.
	www.hypertextbook.com /physics/mechanics/orbital-mechanics-1 (2919 words)

	Horseshoe orbit Definition / Horseshoe orbit Research (Site not responding. Last check: 2007-10-16)
		A horseshoe orbit is the type of orbit In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity.
		History Orbits were first analysed mathematically by Kepler who formulated his results in his laws of planetary motion.
		He located that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed....
	www.elresearch.com /Horseshoe_orbit (337 words)

	orbits
		Orbits of planets in our solar system are ellipses with the sun at one focus.
		The period of a planets orbit squared is proportional to the radius of the orbit cubed.
		Balls rolling inside a sphere travel so slowly as they near the bottom of the sphere that the orbital period remains the same even though the circumference of their orbit is small.
	www.exo.net /~pauld/workshops/orbits.html (639 words)

	Gravity Simulator
		A horseshoe orbit is an orbit where 2 objects share a similar orbit.
		The simulation Horseshoe.gsim uses a rotating frame to simulate a test particle in a horseshoe orbit around a hypothetical planet.
		Every time the object is traveling faster than the planet, as it approaches the planet, the planet's gravity pulls on the object causing it to speed up.
	www.orbitsimulator.com /gravity/articles/horseshoe.html (165 words)

	Horseshoe orbit - Result for Horseshoe orbit - Meaning of Horseshoe orbit - Definition of Horseshoe orbit - Dictionary ...
		For example, if an object orbits the Sun in slightly less or more than a year, and if its orbit is a little more eccentricity (orbit) eccentric than Earth's, every year it will appear to trace a kidney-bean shape around a point on Earth's orbit.
		The moons of Saturn (planet) Saturn Epimetheus (moon) Epimetheus and Janus (moon) Janus occupy horseshoe orbits with respect to each other (in their case, there is no repeated looping: each one traces a full horseshoe with respect to the other).
		There you find a list of all editors and the possibility to edit the original text of the article Horseshoe orbit.
	www.mauspfeil.net /Horseshoe_orbit.html (299 words)

	[6.0] Advanced Concepts In Orbital Mechanics
		To visualize the simplest form of a horseshoe orbit, imagine an asteroid that is orbiting slightly inside the orbit of the Earth.
		If the velocity of the stars in their mutual orbit is known and the period of the orbit is known, then the length of the circumference of the orbit can be determined by multiplying the velocity times the period, giving the length of the circumference of the orbit.
		These little "nudges" on the orbit of an asteroid don't amount to much at any one time, but over a long period they can modify the asteroid's orbit to the point where it is "lost" and has to be "discovered" again.
	www.vectorsite.net /tpecp_06.html (5013 words)

	Near-Earth Asteroid 3753 Cruithne
		The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth, one which is known in the lingo of celestial mechanics as being co-orbital with the Earth (meaning it shares the Earth's orbit with it) and, more particularly, as being of the "horseshoe" type.
		Horseshoe orbits are named because of their shape in a reference frame which corotates with their accompanying planet, and have been known theoretically for many years.
		Though the asteroid thus appears to orbit the Earth, this is a result of the frame of reference we are using.
	www.light1998.com /Lilith-Lilim/Cruithne.htm (1876 words)

	Augusta Georgia: technology@ugusta: Tiny dancer in the sky follows Earth's lead around sun 6/12/97
		Since objects orbiting far from the sun orbit more slowly than objects nearby - just as an ice skater spins more slowly when she extends her arms - the asteroid slows down.
		Called a ``horseshoe'' orbit because the asteroid appears to shift direction in mid-swing, it is a phenomenon seen only in one other place in the solar system - on two moons of Saturn.
		Since asteroids orbiting near Earth usually hang around for no longer than 100 million years, it is hard to imagine how 3753 could have formed with the Earth at the birth of the solar system almost 5 billion years ago.
	www.augustachronicle.com /stories/061397/tech_asteroid.html (937 words)

	Horseshoe Example (Site not responding. Last check: 2007-10-16)
		That is, it amounts to a choice of ``phase'' for the periodic orbit.
		This is illustrated for the period three orbit 110 and the period one orbit 000 in Figure 5.33(a).
		The case of the period two orbit in the horseshoe template is illustrated in Figure 5.33(c,d).
	cnls.lanl.gov /People/nbt/Book/node157.html (205 words)

	Near-Earth Asteroid 3753 Cruithne
		The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth, one which is known in the lingo of celestial mechanics as being co-orbital with the Earth (meaning it shares the Earth's orbit with it) and, more particularly, as being of the "horseshoe" type.
		Horseshoe orbits are named because of their shape in a reference frame which corotates with their accompanying planet, and have been known theoretically for many years.
		The high inclination of Cruithne's orbit relative to that of the other planets is clear from these vantage points, and is what causes it to avoid collisions.
	www.astro.uwo.ca /~wiegert/3753/3753.html (2233 words)

	ESA Science & Technology: Asteroid Encounters
		Some of them are thought to be burnt-out comets that have lost much of their water ice after numerous close flybys of the Sun.
		At least one small object, 3753 Cruithne, is known to travel in a strange horseshoe-shaped orbit around the Earth.
		The main groups are the Amors, which travel between the Earth and Mars; the Apollos, which cross Earth's orbit; and the Atens, which stay mainly inside Earth's orbit.
	sci.esa.int /science-e/www/object/index.cfm?fobjectid=34094&fbodylongid=1518 (250 words)

	Orbital Mechanics I
		The point in an orbit where the engines are fired becomes a point in a new orbit.
		The basic principle behind all circular orbits is that the the centripetal force needed to keep the planet in orbit is supplied by an inverse-square gravitational force.
		Spacecraft in extreme near earth orbit are subject to small but (in the long run) non-negligible amounts of aerodynamic drag from the upper regions of the earth's atmosphere.
	hypertextbook.com /physics/mechanics/orbital-mechanics-1 (3199 words)

	Tadpole & Horseshoe Orbits — Newton's Great... Oversight — Science — PAIAS
		They tend to orbit the Trojan point in an orbit that is elongated, non-elliptical, and not even symmetrical.
		Although it is possible that we might someday find one in a horseshoe orbit, all the known Trojan asteroids of Jupiter are found in the tadpoles, but with more found in the leading tadpole around L4.
		This atmosphere and this space debris is also in some orbit or other, so it may in fact be traveling with a Trojan body and not affecting it viscously, but there will tend to be much more in some other orbit that does.
	paias.org /Science/Newton/Newt4Orbits.htm (1103 words)

	Astronomy - March 23 1999
		Aristotle's ideas that the stars are lights fixed in a huge sphere orbiting the Earth, or that stones can't fall from the skies, have been discarded, although it should be noted that recent large impacts on the Earth were barely acknowledged until 1960.
		Estimates of the number and size of unknown objects are based on the number of known craters on Earth, and are diminished by the assumption that the number of objects was much higher near the beginning of the solar system and has been reduced by impacts and not increased by any unusual events.
		Asteroid Cruithne 3753, a mere 5 kilometers across, is in a 20 degree inclination and 0.51 eccentricity, in a horseshoe orbit.
	www.geocities.com /Athens/Aegean/7551/astronomy.html (2924 words)

	Does Earth have a Second Moon? - Unexplained Mysteries Discussion Forums
		Petit found that the orbit was elliptical, with a period of 2 hours 44 minutes 59 seconds, an apogee at 3570 km above the Earth's surface and perigee at just 11.4 km (!) above the Earth's surface.
		Pickering devoted his attention to the theory of the subject: if the satellite orbited 320 km above the surface and if its diameter was 0.3 meters, with the same reflecting power as the Moon, it should be visible in a 3-inch telescope.
		A moon typically is defined as an object whose orbit encompasses a planet, say, the Earth, rather than the sun, said Carl Murray, who worked with Namouni and Christou on the research.
	www.unexplained-mysteries.com /forum/index.php?showtopic=87698 (2539 words)

	Cruithne, Earths "second moon"
		That means Neptune makes 3 orbits for every 2 of Pluto.) Cruithne's nearest pass to Earth is.1 AU (40 moon lengths), although right now it never comes closer than.3 AU.
		Cruithne also has an orbit of almost one year, that's why consecutive purple dots are close to one another.
		Cruithne has an orbit slightly less than a year at first, then when it approaches Earth it slows down to slightly more than a year, and back and forth and back and forth.
	burtleburtle.net /bob/physics/cruithne.html (597 words)

	Cruithne earths second moon
		Cruithne, discovered in 1986, and then found in 1997 to have a highly eccentric orbit, cannot be seen by the naked eye, but scientists working at Queen Mary and Westfield College in London were intrigued enough with its peregrinations to come up with mathematical models to describe its path.
		Namouni and his colleagues latched on to Cruithnes orbit and worked out models built on Lagranges work to explain its eccentric orbit and then theorized that such "co-orbital dynamics" could explain the strange movement of other objects at the Lagrangian points.
		In his view, there are three classes of moons large moons in near-circular orbits around a planet, having formed soon after the planet; smaller fragments that are the products of collisions; and outer, irregular moons in odd orbits, or captured asteroids like Cruithne.
	www.fuchsiashockz.co.uk /articles/science/cruithne_earths_second_moon.php (1009 words)

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