Orbit (celestial mechanics)

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Topic: Orbit (celestial mechanics)

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	Orbital Mechanics
		The root of orbital mechanics can be traced back to the 17th century when mathematician Isaac Newton (1642-1727) put forward his laws of motion and formulated his law of universal gravitation.
		To mathematically describe an orbit one must define six quantities, called orbital elements.
		In general, three observations of an object in orbit are required to calculate the six orbital elements.
	www.braeunig.us /space/orbmech.htm

	Racist Celestial Mechanics, Lecture 1: Orbital Elements to Heliocentric State Vectors
		Throughout this web page, I consider the celestial mechanics of objects orbiting the sun, which is assumed to be the only important source of gravitational attraction.
		Racist Celestial Mechanics, Lecture 1: Orbital Elements to Heliocentric State Vectors
		Celestial mechanics like to represent T as decimal days (e.g., 4.75 days instead of 4 days 18 hours) in order to avoid the necessity of converting years, months, hours, minutes, and seconds into decimal day form.
	www.jabpage.org /posts/trans1.html

	IngentaConnect Eccentricity as a vector: a concise derivation of the orbit equat...
		Eccentricity as a vector: a concise derivation of the orbit equation in celestial mechanics
		In celestial mechanics, qualitative and quantitative analyses of an orbit are usually based on the conserved angular momentum and total energy of the motion.
		IngentaConnect Eccentricity as a vector: a concise derivation of the orbit equat...
	www.ingentaconnect.com /content/iop/ejp/2004/00000025/00000003/art00004

	Celestial Mechanics
		For this discourse, I will use two very familiar celestial bodies: the Sun and Earth.
		The "primary" law of physics, F = ma, adequately models reality at the celestial scale.
		I will attempt to discover the possible ways for our Earth to have come to orbit the sun as it does.
	www.onr.com /user/driven/celestial_mechanics.htm

	Orbit Reconstruction, Simulation and Analysis Website
		ORSA is an interactive tool for scientific grade Celestial Mechanics computations.
		Developers and contributing users are welcome to update their local copy, test it and report any problem.
		Asteroids, comets, artificial satellites, Solar and extra-Solar planetary systems can be accurately reproduced, simulated, and analyzed.
	orsa.sourceforge.net

	The Technology of Space Travel
		To implement this in accordance with the laws of celestial mechanics, the original orbital movement would have to be accelerated if the vehicle (according to the position of the target body) is to move away from the sun (Figure 98), and to be decelerated if it is to approach it.
		As determined mathematically by Hohmann, the propellant expenditure reaches a minimum when the orbits of the original celestial body and that of the destination body are not intersected by the transfer orbit of the vehicle, but are tangential to it (touch it) (Figure 99).
		Landing can, if the celestial body has an atmosphere similar to that of the Earth, occur in the same fashion as previously discussed for the Earth (Hohmann's landing manoeuver, Figures 44 and 45).
	www.hq.nasa.gov /pao/History/SP-4026/noord56.html (772 words)

	Computing at Columbia Timeline
		I did a celestial mechanics course one year; it was really a mélange of spherical trig, practical and theoretical astronomy (meaning time and position determination, and orbit computing), and brief mentions of planetary and satellite mechanics.
		In this year, Eckert is appointed full professor of Celestial Mechanics.
		The Astronomical Computing Bureau in Pupin, now directed by Jan Schilt (but with Eckert still running the show from Washington), was assigned to tasks for the looming war, such as ballistic firing tables, and trajectory calculations, and later, design calculations for the B-29 sighting station [57,59] — "Mathematics Goes to War" [9].
	www.columbia.edu /acis/history (14540 words)

	Physics
		The next six sections are an introduction to the physical and mathematical foundations of orbit mechanics.
		Some mastery of this information is necessary to appreciate and correctly apply the algorithms of orbital mechanics.
		Mars Academy - Celestial Mechanics applied to planning a mission to Mars
	www.tamuk.edu /math/scott/stars/physics.htm (14540 words)

	"Amateur Astronomy". Celestial Mechanics Definitions List
		For the purpose of locating celestial objects on the celestial sphere the latter is subject to various coordinate systems.
		The celestial meridian defines where celestial objects are reaching their highest point in the sky relative to observer.
		In the northern hemisphere the celestial meridian begins on the northern horizon, passes through the north celestial pole, then overhead the observer (or zenith).
	stars5.netfirms.com /definitions.htm (2244 words)

	Celestial mechanics - Wikipedia, the free encyclopedia
		Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects.
		Using Lagrangian mechanics it is possible to develop a single polar coordinate equation that can be used to describe any orbit, even those that are parabolic and hyperbolic.
		The theory of quantum mechanics has not been merged with the theory of general relativity to produce a so-called "theory of everything".
	en.wikipedia.org /wiki/Celestial_dynamics (1133 words)

	Belbruno, E.: Capture Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers.
		Belbruno, E.: Capture Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers.
		A good choice would be Edward Belbruno, a celestial mechanician who seems to specialize in such lost causes.
		Belbruno found the almost magical low energy chaotic orbit that got the Hiten spacecraft successfully to the moon.
	www.pupress.princeton.edu /titles/7687.html (644 words)

	The Motion of Celestial Bodies
		If instead there are three or more bodies with comparable masses, then their relative orbits cannot be predicted by any laws of Mechanics, since their description becomes too complex.
		If two bodies have comparable masses, then their baricenter does not coincide with any of them, and their orbit around this point become visible.
		Indeed, these laws are not only valid for the planets in the Solar System, but also for any celestial body.
	www.pd.astro.it /E-MOSTRA/NEW/A2004ORB.HTM (862 words)

	Circular orbit - Wikipedia, the free encyclopedia
		In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
		Thus the escape velocity from any distance is √2 times the speed in a circular orbit at that distance: the kinetic energy is twice as much, hence the total energy is zero.
		For other meanings of the term "orbit", see orbit (disambiguation)
	en.wikipedia.org /wiki/Circular_orbit (366 words)

	Orbits
		Lagrange introduced the method of variation of the arbitrary constants in a paper in 1776 stating that the method was of interest in celestial mechanics and, in special cases, had been already been used by Euler, Laplace and himself.
		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.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Orbits.html (4382 words)

	nyas.html
		The geocentric dogma was not overthrown by "exquisitely sensitive observations made within the very edifice of a church," but by the successful agreement of Kepler's three empirical laws for his heliocentric model with astronomical observations, and by Newton's development of celestial mechanics.
		Heilbron also concludes that Cassini's "observation unambiguously agreed with the predictions of Kepler's model." But Heilbron is referring here to the model in which the earth traces an elliptical orbit with the sun at one focus, not to the model in which the earth traces a circular orbit, as Kepler originally envisioned.
		Heilbron tells us that Cassini's resultant calculation of the eccentricity of the earth-sun orbit was in disagreement with Ptolemy's geocentric model by a factor of two, he fails to note that the result was equally in disagreement with Copernicus' helio-centric model, which had precisely the same eccentricity as Ptolemy's model.
	mike.ucsc.edu /~michael/nyas.html (4382 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 (4382 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.
		Though the asteroid thus appears to orbit the Earth, this is a result of the frame of reference we are using.
		Also note that the presence of the Earth at the centre of the kidney is simply a result of their mutual synchronization: the Earth is lined up with the asteroid and Sun when the asteroid is at perihelion (its closest approach to the Sun).
	www.astro.uwo.ca /~wiegert/3753/3753.html (2229 words)

	DEOS Presentation Series
		These works have been used as a starting point to study a way to adapt and set up a method to solve problems of celestial mechanics.
		The problem of a perturbed orbital dynamics can be approached in two main ways: a numerical and an analytical one.
		These constraints can either be imposed on the value of the unknowns or they can be of the functional type; they do not have to correspond to physical constraints on the motion, they can however represent a characteristic of the family of solutions one wants to obtain.
	www.deos.tudelft.nl /~rune/max.html (2229 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 (2229 words)

	Orbit Dynamics Software Design and Modeling
		Our team applies the practical application of celestial mechanics to the motion of man-made objects in space outside the earth's atmosphere and studies how external forces, natural or man-made, affect this motion.
		We are knowledgable in the determination of optimal orbits of earth satellites for civilian or military purposes, and in addition, to the determination of heliocentric orbits of the planets, asteroids and comets of our solar system.
		These near earth objects are asteroids or minor planets and comets that move in fairly high eccentric orbits that cross the earth's orbit and could pose a threat to earth.
	www.omitron.com /astro/orbit.asp (2229 words)

	Infoplease Search: orbit
		(Encyclopedia) Trajectories and Orbits The key contribution of physics is celestial mechanics, the laws that...
		(Encyclopedia) The Orbits of Comets Although the occurrence of many comets had been recorded, it was not until...
		(Encyclopedia) Planetary Orbits From earliest times, astronomers assumed that the orbits in which the planets...
	www.infoplease.com /search?fr=iptn&query=Orbit&in=all (208 words)

	[20040901] THEORY OF ORBITS PERTURBATIVE AND GEOMETRICAL METHODS VOL.2
		Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics.
		Contents: Classical Perturbation Theory in Celestial Mechanics - Equations of Planetary Motion.- Canonical Perturbation Theory and KAM Theory.- Lie Transform Perturbation Theory.- The Theory of Adiabatic Invariants and Its Applications in Celestial Mechanics and Stellar Dynamics.- Periodic Orbits and Resonances.- Chaos.- Numerical Explorations.
		Keywords: Celestial Mechanics, Stellar Dynamics, Orbit Theory, Perturbation, KAM Theory, Lie Transform, Adiabatic Invariants, Chaos, N-body Systems
	three.ticmundi.com /3-540-60355-7.html (208 words)

	Chapter 5 -- Orbital Mechanics
		When Sputnik was placed into orbit in 1957 it reawakened an entire physical and mathematical science which had gone as far as it could go without space travel, Celestial Mechanics.
		Orbital mechanics is the study of the motion of human made objects as they travel around a principal body, in the majority of flights the Earth.
		The orbit's size, major axis, and the orbit's shape, eccentricity, are determined by two factors at orbital insertion: the spacecraft speed and its flight path angle.
	www.space.edu /projects/book/chapter5.html (208 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.
		Though the asteroid thus appears to orbit the Earth, this is a result of the frame of reference we are using.
		The apparent overlap of the asteroid with the Earth does not result in any danger of collision because the asteroid's orbit is highly inclined to that of our planet.
	www.astro.uwo.ca /~wiegert/3753/3753.html (2229 words)

	SIGHTINGS
		The comet Tempel-Tuttle and the Leonid shower were first identified in 1866 by Italian astronomer Giovanni Schiaparelli and experts in celestial mechanics Urbain Le Verrier and Theodor von Oppolzer.
		When the comet comes close to the sun, it leaves particles in its orbit which fall to Earth when its orbit crosses the Earth's orbit.
		Schiaparelli published his calculation for the orbit of the Leonid stream while Le Verrier and Oppolzer spotted a striking resemblance of the Leonid orbit to that of the newly- discovered comet Tempel-Tuttle.
	www.rense.com /ufo/2097.htm (2229 words)

	Trajectories
		In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1.
		In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity (how much the trajectory deviates from a perfect circle) greater than 1.
		Under standard assumptions a body traveling along an escape orbit will coast to infinity, with velocity relative to the central body tending to zero, and therefore will never return.
	users.desk003.com /carol/cporbits/cptrajectoryorbit.htm (2229 words)

	Andrea Milani - preprints
		Symmetries and rank deficiency in the orbit determination around another planet, by C. Bonanno and A. Milani, Celestial Mechanics and Dynamical Astronomy, v.
		From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs, by Andrea Milani and Zoran Knezevic, February 2005, CMDA, in press PDF, PostScript gzipped
		Probing the Nekhoroshev Stability of Asteroids, by Guzzo, Massimiliano; Knezevic, Zoran; Milani, Andrea, Celestial Mechanics and Dynamical Astronomy, v.
	copernico.dm.unipi.it /%7Emilani/preprints/preprint.html (2229 words)

	Escape Velocities, Alaska Science Forum
		The term escape velocity as used in celestial mechanics is usually applied to a surface launch velocity, disregarding aerodynamic friction.
		At velocities higher than that needed to obtain a circular orbit, the path becomes elliptical until escape velocity is approached, at which time the orbit becomes parabolic.
		A circular orbit is achieved at 0.71 times the escape velocity, which is why we often hear of the value of about 17,500 mph (earth's escape velocity X 0.7) for orbiting satellites and space ships.
	www.gi.alaska.edu /ScienceForum/ASF6/661.html (461 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.
		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.
		Remember, there are two types of motion going on: 1) every year, the asteroid traces out a kidney bean, 2) over time, this kidney bean drifts along the Earth's orbit, tracing out a spiral which, when complete (after 385 yrs) fills in an overlapping horseshoe".
	www.astro.uwo.ca /~wiegert/3753/3753.html (2229 words)

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Topic: Orbit (celestial mechanics)

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In the News (Thu 17 Dec 09)