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Topic: Elliptical orbits

Related Topics

Circular orbit

Orbit equation

Orbit

Hohmann transfer orbit

Standard gravitational parameter

Specific orbital energy

Orbital speed

Argument of the perihelion

Double planet

Astrodynamics

Longitude of the ascending node

Orbital period

Planet

Planet X

Binary star

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	Cosmos4Kids.com: Exploration: Satellites
		Elliptical Orbit: An orbit that is similar to a polar orbit in that the spacecraft moves in a North-South direction.
		The orbit is also similar to a HEO orbit because of the path of the spacecraft.
		An orbit that is not larger than 2,000 kilometers from the surface of the Earth.
	www.cosmos4kids.com /files/explore_satellite.html (471 words)

	Planetary orbit - Wikipedia, the free encyclopedia
		As an object orbits another, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other.
		In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less.
		The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it.
	en.wikipedia.org /wiki/Orbit (2510 words)

	Ellipso: System Overview: Orbital Architecture: Borealis
		The apogees are near the northern extremity of the orbits.
		The Borealis elliptical orbits concentrate satellite coverage from the equator to the North-effectively tailoring capacity to northern latitudes where demand is greatest.
		The elliptical orbits concentrate capacity where it is needed, require less launch energy than comparable circular orbits, and allow batteries to recharge south of the equator, when the satellites are "quiet".
	www.ellipso.com /overview/borealis.html (169 words)

	TRAJECTORIES AND ORBITS
		Orbit is commonly used in connection with natural bodies (planets, moons, etc.) and is often associated with paths that are more or less indefinitely extended or of a repetitive character, like the orbit of the Moon around the Earth.
		The parabolic orbit is the Borderline case between open and closed orbits and therefore identifies the border line condition between space vehicles that are tied to paths (elliptical) in the general vicinity of their parent planet and those that can take up paths (hyperbolic) extending to regions remote from their parent planet.
		The elliptical orbits generated by velocities below escape velocity are the type followed by artificial satellites, as well as by all the planets and moons of the solar system.
	www.hq.nasa.gov /office/pao/History/conghand/traject.htm (1856 words)

	Elliptical Orbits
		I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
		Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.
		As an example of using Kepler's 3rd Law, let's calculate the "radius" of the orbit of Mars (that is, the length of the semi-major axis of the orbit) from the orbital period.
	www.astro-tom.com /technical_data/elliptical_orbits.htm (987 words)

	Tech Museum \| Satellites \| Elliptical Orbits
		A satellite in elliptical orbit follows an oval-shaped path.
		One part of the orbit is closest to the center of Earth (perigee) and the other part is farthest away (apogee).
		So communications satellites in elliptical orbits cover the areas in the high northern and southern hemispheres that are not covered by GEO satellites.
	www.thetech.org /exhibits/online/satellite/4/4d/4d.1.html (88 words)

	Parameters Describing Elliptical Orbits (Site not responding. Last check: 2007-10-27)
		The location of the greatest distance between the orbiting body and the central body when the orbit is an ellipse.
		The angle from the ascending node to the pericenter, measured in the plane of the orbit.
		When the mass of an orbiting body is small enough to ignore, the same value of K can be used for all small objects orbiting around the same central body.
	www.lns.cornell.edu /~seb/celestia/orbital-parameters.html (714 words)

	Orbits (Site not responding. Last check: 2007-10-27)
		In 1684 Wren, Hooke and Halley discussed, at the Royal Society, whether the elliptical shape of planetary orbits was a consequence of an inverse square law of force depending on the distance from the Sun.
		When he computed the orbits for three comets which had appeared in 1537, 1607 and one Halley observed himself in 1682, he found that the characteristics of the orbits were almost identical.
		The elliptical orbit was computed by Lexell who correctly realised that the small elliptical orbit had been produced by perturbations by Jupiter.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Orbits.html (4382 words)

	Celestial Mechanics, Lecture 3: Transfer Orbits (Site not responding. Last check: 2007-10-27)
		Superperiodic elliptical transfer orbits can be either prograde or retrograde, and they provide the spaceship pilot with more opportunities to find a transfer orbit, however at the expense of greatly increasing the transit time (always by a whole multiple of the transfer orbit's period).
		For the hyperbolic orbit and the short-path elliptic orbit, the inclination to the ecliptic is
		For the long-path elliptic orbit, the inclination is
	www.jabpage.org /posts/trans3.html (3670 words)

	The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas (Site not responding. Last check: 2007-10-27)
		The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas
		The velocity in orbit is alway less than that needed to escape from the central object.
		These orbits are useful in describing two objects that pass by each other but are not 'captured' one by the other.
	www.go.ednet.ns.ca /~larry/orbits/ellipse.html (546 words)

	Orbits Explained
		are elliptical or that the force is the inverse square of distance to the Sun.
		represents elliptical orbits and the inverse square relationship of force and distance.
		situated at the center of the elliptical orbit, such as for a mass on a spring.
	www.orbitsexplained.com (1186 words)

	ZetaTalk: Elliptical Orbits (Site not responding. Last check: 2007-10-27)
		Planets that orbit both binary suns do so in a figure 8, pulling toward the second binary at the juncture where the planet is positioned between the binaries, but propelled by momentum to continue its orbital curve while moving toward the second binary.
		Rushing to an attraction causes the orbit to draw long at that point, a factor of momentum on the orbiting planet, which is an influence toward an elliptical orbit.
		Where no apparent gravitational giant exists to explain the elliptical orbit, particle flows other than gravity are the dominant influence on the shape of the orbit.
	www.zetatalk.com /science/s109.htm (308 words)

	Elliptical Orbits - Physics Help and Math Help - Physics Forums
		Your new orbit must go through your new position (close to your old one) while the average distance from the earth is increased- obviously that can't be a circle.
		Elliptical orbits are the general rule (for bound orbits, that is).
		Orbits with an inverse-square law force also have the property that they are closed - the orbit passes through it's starting point.
	www.physicsforums.com /showthread.php?t=41381 (1644 words)

	Johannes Kepler -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-27)
		The smallest orbit, that of Mercury, was the innermost sphere.
		To emphasize his theory, Kepler envisaged an impressive model of the universe which shows a cube, inside a sphere, with a tetrahedron inscribed in it; another sphere inside it with a dodecahedron inscribed; a sphere with an icosahedron inscribed inside; and finally a sphere with an octahedron inscribed.
		To his disappointment, Kepler's attempts to fix the orbits of the planets within a set of polyhedrons never worked out, but it is a testimony to his integrity as a scientist that when the evidence mounted against the cherished theory he worked so hard to prove, he abandoned it.
	www.absoluteastronomy.com /encyclopedia/j/jo/johannes_kepler.htm (2331 words)

	Orbits - Gravitational Assist from Planets (Site not responding. Last check: 2007-10-27)
		Establish the orbit and its parameters for the flight of the space probe from Earth to Jupiter.
		Determine the hyperbolic orbit of the probe near Jupiter.
		Tisserand's Criteria is a requirement that conservation of energy and momentum hold during the flyby of a Planet.
	www.go.ednet.ns.ca /~larry/orbits/gravasst/gravasst.html (933 words)

	Re: Planet X/12th Planet Long Elliptical Orbit (Site not responding. Last check: 2007-10-27)
		If the math of orbits was worked out centuries ago, based on what they knew and had observed, then this same math must be applied.
		If all you have seen are objects looping far out in their orbits around a single foci, then this is all there is? It's a fact that most suns are binaries, and some so close at to give the appearance of barely keeping each other at arms length.
		Clearly, some of the new highly elliptical orbits recently discovered by your fellows show that orbiting bodies, much larger than dirty snowballs, are influenced by SOMETHING out there pulling on them.
	www.zetatalk.com /usenet/use00562.htm (280 words)

	Orbital Mechanics
		A space vehicle's orbit may be determined from the position and the velocity of the vehicle at the beginning of its free flight.
		) is a nondimensional parameter of the orbit.
		When transferring from a smaller orbit to a larger orbit, the change in velocity is applied in the direction of motion; when transferring from a larger orbit to a smaller, the change of velocity is opposite to the direction of motion.
	www.braeunig.us /space/orbmech.htm (6414 words)

	Orbit Reply
		The situation where the Sun, for instance, would be exactly in the center of a perfectly circular planetary orbit couldn't happen in our Solar System since there are other planets that would gravitationally affect the orbit and cause it to be immediately non-circular by pulling the object to one side or the other.
		While the familiar objects are in elliptical orbits, there are a lot of objects that fall into the Sun on a spiral path.
		The elliptical orbit idea was so simple while neatly explaining and predicting planetary motion extremely well that it was seen as a fundamental revolution in scientific thinking.
	www.astro-tom.com /technical_data/why_elliptical.htm (824 words)

	HIGHLY ELLIPTICAL ORBITS
		The Radio Regulations define GSO as “the orbit of a geosynchronous satellite whose circular and direct orbit lies in the plane of the Earth’s equator”.
		However, for the efficient use of orbit spectrum, a relatively small number (less than 10) should be taken to estimate the aggregate interference to terrestrial systems with a given pfd mask.
		The period of the orbit is a multiple of that of the geostationary-satellite orbit.
	www.itu.int /itunews/issue/2003/05/heo.html (1614 words)

	Elliptical Orbits Revisited
		1.The orbits are not circles: The orbits of the planets are ellipses with the Sun at one focus.
		We can relate the periods of the planets' orbits to the sizes of their orbits: The square of the sidereal period, in years, equals the cube of the semi-major axis, in AU.
		So in what follows we assume that the orbits of the planets are, for all practical purposes, perfect circles even though we know this is not exactly true.
	www.polaris.iastate.edu /EveningStar/Unit6/unit6_sub1.htm (379 words)

	Elliptical orbits in space as function of time - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-27)
		The orbit is elliptical, so a simple x=cos(t) won't work...
		Simulating orbit by using small incremental steps is not an option, I need a function where I can input time, and get the current position.
		However for closed and stable orbits its possible to analytically determine the orbiting objects position and velocity at any time given its position and velocity at any other time.
	www.gamedev.net /community/forums/ViewReply.asp?id=1767511 (728 words)

	History and Philosophy of Western Astronomy
		Planet orbits have small eccentricities (nearly circular orbits) which is why astronomers before Kepler thought the orbits were exactly circular.
		Most comet orbits have large eccentricities (some are so eccentric that the aphelion is around 100,000 AU while the perihelion is less than 1 AU!).
		As the eccentricity increases, the Sun's position is closer to one side of the elliptical orbit, but the semi-major axis remains the same.
	www.astronomynotes.com /history/s7.htm (1569 words)

	Hunting Planets Beyond
		The star-hugging orbit of the 51 Pegasi planet and the eccentric orbit of the 70 Virginis planet shook our myopic, heliocentric expectation that planetary systems would be nearly identical to ours.
		Comets were gravitationally flung into their present-day elliptical orbits when they ventured too close to planets, in much the same way spacecraft receive gravitational assists from planets.
		The predominance of elliptical orbits implies that planetary systems with circular orbits may be the exception rather than the norm.
	astron.berkeley.edu /~paul/astro2000/Astronomy_Mag_mar2000.html (2419 words)

	[No title]
		The discovery that gravity must cause elliptical orbits for any two-body system was one of Newton's greatest discoveries.
		Thus the planet orbits the Sun in an ellipse where the Sun is a focus of the ellipse.
		The ECLIPTIC ANGLE is the angle inclination of the plane of the orbit from ecliptic plane (i.e., the plane of the Earth's orbit).
	www.physics.unlv.edu /~jeffery/astro/ellipse/ellipse.html (1059 words)

	Satellite Orbits
		Orbits are categorized by altitude, inclination and eccentricity.
		A low Earth equatorial orbit would cover a belt around the equator, whereas a polar orbit would cover a belt around the pole orthogonal to the equator, thus covering the full Earth due to the Earth's west east motion beneath.
		Eccentricity of an orbit determines the shape of the orbit.
	www.satellitetvref.com /Orbit.html (177 words)

	Untitled Document (Site not responding. Last check: 2007-10-27)
		While focusing on planetary orbits, he became interested in trying to create a model that would explain how the planets moved, yet also verify Tycho Brahe's observational data.
		Kepler began his investigation with the orbit of Mars, which is the most eccentric and which exhibits the most retrograde motion.
		An elliptical orbit deviated from the geometrical perfection of the circle, and because Kepler at heart believed that God was a divine geometer, ellipses seemed a little messy for the heavens.
	www.d.umn.edu /~aroos/kepler3.html (495 words)

	Johannes Kepler: The Laws of Planetary Motion
		In retrospect, the reason that the orbit of Mars was particularly difficult was that Copernicus had correctly placed the Sun at the center of the Solar System, but had erred in assuming the orbits of the planets to be circles.
		Thus, by the "radius" of a planet's orbit one usually means the length of the semimajor axis.
		As an example of using Kepler's 3rd Law, let's calculate the "radius" of the orbit of Mars (that is, the length of the semimajor axis of the orbit) from the orbital period.
	csep10.phys.utk.edu /astr161/lect/history/kepler.html (1409 words)

	Anomalous Precessions
		The large tolerances for Venus and Earth are mainly due to the fact that their orbits are so nearly circular, making it difficult to precisely determine the axes of their elliptical orbits.
		To determine the relativistic prediction for the advance of an elliptical orbit, let's work in the single plane q = p/2, so of course dq/dt and all higher derivatives also vanish, and we have sin(q) = 1.
		Calculation gives for the planet Mercury a rotation of the orbit of 43" per century, corresponding exactly to the astronomical observation (Leverrier); for the astronomers have discovered in the motion of the perihelion of this planet, after allowing for disturbances by the other planets, an inexplicable remainder of this magnitude.
	www.mathpages.com /rr/s6-02/6-02.htm (1112 words)

	Kepler's Laws
		The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
		The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
		The elliptical shape of the orbit is a result of the inverse square force of gravity.
	hyperphysics.phy-astr.gsu.edu /hbase/kepler.html#c1 (293 words)

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