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Topic: Eccentric anomaly

Related Topics

True anomaly

Mean anomaly

Orbital eccentricity

Orbital position vector

Eccentricity vector

Keplerian harmonic law

Argument of periapsis

Astrodynamics

Keplerian elements

Orbit

Ellipse

Perigee

Eccentricity

Echo satellite

Moon

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	Anomaly - LoveToKnow 1911
		Mean R anomaly is the anomaly which the body would have if it moved from the pericentre around F with a uniform angular motion such that its revolution would be completed in its actual time (see Orbit).
		Eccentric anomaly is defined thus: - Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit.
		In the ancient astronomy the anomaly was taken as the angular distance of the planet from the point of the farthest recession from the earth.
	www.1911encyclopedia.org /Anomaly (402 words)

	Wikinfo \| Anomaly
		The eccentric anomaly is observed from the centre of the ellipse, using a projection of the planet's position onto the circumscribing circle; and
		In spacecraft operations, an anomaly is an event that results in an unexpected and unwanted event that may cause a negative impact to the state of health of the spacecraft.
		The Ararat anomaly, an object on Mount Ararat clamed to be Noah's Ark.
	www.wikinfo.org /wiki.php?title=anomaly (324 words)

	Anomaly - Wikipedia, the free encyclopedia
		Eccentric anomaly, the angle between the direction of periapsis and the current position of an object on its orbit
		Pioneer anomaly, the observed deviation of the trajectories of various unmanned spacecraft
		Coronary artery anomaly, a congenital abnormality in the coronary anatomy of the heart
	en.wikipedia.org /wiki/Anomaly (466 words)

	anomaly
		The true anomaly is the angle between the periapsis of an orbit and the object’s current orbital position, measured from the body being orbited and in the direction of orbital motion.
		The mean anomaly is 0° at periapsis and 180° at apoapsis, just as for the true anomaly, but at other points along the orbit the values of the mean and true anomalies differ.
		The eccentric anomaly is an angle related to both the true anomaly and the mean anomaly that is encountered when solving Kepler’s equation.
	www.daviddarling.info /encyclopedia/A/anomaly.html (209 words)

	Astronomy Answers: Kepler's Equation
		The equation that expresses the relationship (for elliptical and hyperbolic orbits) between the mean anomaly and the eccentric anomaly is called Kepler's Equation, and this equation is nearly but not completely the same for elliptical orbits and for hyperbolic orbits.
		For elliptical orbits and hyperbolic orbits the eccentric anomaly cannot be calculated directly from the mean anomaly (but the other way around does work), so a special method must be used to yet find a solution.
		is the eccentricity of the orbit, and all angles are counted in radians (2π radians equal 360 degrees).
	www.astro.uu.nl /~strous/AA/en/reken/kepler.html (1024 words)

	Eccentric - definition from Biology-Online.org
		Deviating or departing from the center, or from the line of a circle; as, an eccentric or elliptical orbit; pertaining to deviation from the center or from true circular motion.
		eccentric hook or gab, a hook-shaped journal box on the end of an eccentric rod, opposite the strap.
		eccentric rod, the rod that connects as eccentric strap with any part to be acted upon by the eccentric.
	www.biology-online.org /dictionary/Eccentric (469 words)

	Method for the efficient determination of GPS satellite orbital position - Patent 6016117
		The subsequent sample is uniformly spaced with respect to eccentric anomaly in comparison to the first sample and the second sample.
		Calculating the new samples in terms of eccentric anomaly allows the step size between samples to be relatively large, for example, as large as the sample spacing, and thus, greatly decrease the computational load on the GPS receiver.
		The preferred embodiment estimates the corresponding eccentric anomaly E to within 4 seconds by substituting mean anomaly M for E as the argument of the sine function in an approximate version of Kepler's equation:
	www.freepatentsonline.com /6016117.html (6794 words)

	Satellite Observing: Orbital Elements
		An ellipse with an eccentricity of 0 is a circle, and when eccentricty is close to 1, the ellipse is long and skinny.
		This is done with the eccentric anomaly which the angle between the satellite's position and the perigee in the plane of the orbit.
		Kepler's equation relates the eccentric anomaly and the mean anomaly for an eccentric orbit.
	www.znark.com /sat/elements.html (936 words)

	Calculating E or M from a State Vector
		The true anomaly is the angle, subtended at the sun, measured from the perihelion, in the plane of the orbit, in the direction of motion, to where the planet truly is.
		The mean anomaly is also an angle, subtended at the sun, measured from the perihelion, in the planet of the orbit, in the direction of motion...but there's a difference in where the angle is measured to.
		The true, mean, and eccentric anomalies all have the same values at perihelion (zero) and at aphelion (pi radians).
	www.physicsforums.com /showthread.php?p=343357 (2272 words)

	ANOMALY (from Gr. lwvw) - Online Information article about ANOMALY (from Gr. lwvw)
		Mean R anomaly is the anomaly which the body would have if it moved from the pericentre around F with a See also:
		Eccentric anomaly is defined thus: Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit.
		Owing to the precession of the equinoxes it is longer than a tropical or sidereal year.
	encyclopedia.jrank.org /ANC_APO/ANOMALY_from_Gr_lwvw_.html (637 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		An auxiliary angle, called the eccentric anomaly, E, is used to relate true anomaly to an inscribed circle around the satellite’s elliptical orbit.
		Equation EMBED Equation.3 = 42819.41 km The eccentricity of this orbit is 0.00663; the eccentricity of a circle is 0.
		Since the difference between the elliptical orbit and a circle is 0.00663, it is reasonable to assume that the velocity of the satellite on this orbit is approximately that of the circular orbit with a radius of 42819.41 km.
	www-personal.engin.umich.edu /~tlrichar/TR2Final3.doc (3958 words)

	OEDILF - Word Lookup
		The word anomaly refers to a time-varying angle along an orbit in the direction of the body's motion, so it can be thought of as a growing argument.
		The true anomaly of a body in an elliptical orbit is the angle from periapsis to the body, measured at the focus of the ellipse.
		Related angles, the eccentric anomaly and mean anomaly are useful in orbital mechanics.
	www.oedilf.com /db/Lim.php?Word=anomaly (190 words)

	Glossary
		The eccentric anomaly is an auxiliary angle used in relating true anomaly (which is observed) and mean anomaly (which is calculated).
		The eccentricity e of the orbital ellipse is one of the "orbital elements" characterizing it.
		True anomaly The polar angle of an object in a Kepler orbit, measured from in the orbital plane from the position at closest approach.
	www-spof.gsfc.nasa.gov /stargaze/Sgloss.htm (14613 words)

	Orbits in 2D
		Below find the geometric construction that relates the true anomaly and the eccentric anomaly, the formula relating these two, and the formula relating time and the eccentric anomaly.
		The red parts of the diagram have to do with the geometric construction for the eccentric anomaly which is measured from the center (C) of the ellipse.
		For eccentricities similar to those of the planets it would be hard to distinguish the elliptical orbit from a circle (although for some planets--like Mars--the position of the Sun would look noticeably "off-center"...because the Sun is at a focus rather than the center).
	www.physics.csbsju.edu /orbit/orbit.2d.html (1468 words)

	Matlab function examples
		In these functions, oe is a 6x1 matrix containing the semimajor axis, eccentricity, inclination, argument of periapsis, right ascension of the ascending node, and true anomaly (at epoch).
		The difference is that the 6th orbital element in the oee2rv version is eccentric anomaly at epoch instead of true anomaly.
		Note that the 6th orbital element is eccentric anomaly at epoch.
	www.aoe.vt.edu /~cdhall/courses/matlab (312 words)

	Pluto New Horizons
		This equation obviously cannot be solved explicitly for the eccentric anomaly, so the Newton Raphson iteration technique must be used.
		In order to find the position of these planets at the times of interest, the eccentric anomalies must be converted to true anomalies.
		The eccentricity calculated for this orbit is 7.830.
	ccar.colorado.edu /~nerem/zipfiles/hunkins (4237 words)

	Kepler's equation and the Equation of Centre
		Below is a Visual Basic for Applications routine for returning the eccentric anomaly (e) given the mean anomaly (m), the eccentricity (ecc) and the precision parameter (eps).
		Above this value of eccentricity, and for certain values of mean anomaly, there will be problems with convergence, especially with the 10 decimal digit accuracy on the TI-80.
		I found the value of the true anomaly produced by each method for each degree of mean anomaly for values of mean anomaly from 0 degrees up to 180 degrees.
	www2.arnes.si /~gljsentvid10/kepler.html (2984 words)

	planet orbits
		The mean anomaly gives the planet's angular position for a circular orbit with radius equal to the semi major axis.
		It is the angle (at the Sun) between perihelion of the orbit and the current location of the planet.
		By using the true anomaly, the heliocentric radius, and some of the orbital elements, the formulas below compute the heliocentric coordinates in the plane of the ecliptic.
	home.att.net /~srschmitt/script_planet_orbits.html (1743 words)

	Dr. Dobb's \| Orbit Propagation \| April 15, 2003
		The eccentric anomaly E is defined (for elliptical orbits) by circumscribing a circle around the ellipse, then dropping a perpendicular from a point p on the circle so it passes through the current position of the object on the ellipse (see Figure 4).
		The angle between the major axis and a line drawn from the center of the circle to p is called the eccentric anomaly.
		The inputs are the mean anomaly M, the starting estimate E0 for the solution to Kepler's equation, the orbit eccentricity e, and two parameters, mi and t, which determine when the iteration will terminate.
	www.ddj.com /dept/cpp/184402360?pgno=10 (2767 words)

	Kepler's Equation of Elliptical Motion
		The position of a body in elliptical motion is usually found by way of an intermediate property: the eccentric anomaly, E (refer to the diagram below).
		Given an ellipse with semi-minor axis b and semi-major axis a, a circle of radius a is superposed upon the ellipse.
		M is the mean anomaly, 2πt/T (t is the time since periapse, and T is the period of the motion).
	www.akiti.ca /KeplerEquation.html (882 words)

	Kepler Applet
		Use the third scrollbar (blue) to increase uniformly the true anomaly angle phi.
		The mean anomaly M is the angular distance from perihelion which a (fictitious) planet would have if it moved on the circle of radius a with a constant angular velocity and with the same orbital period T as the real planet moving on the ellipse.
		As the planet P is moving around the ellipse, the end of the velocity vector OP' will move around the gray circle (center M), and FP is always pependicular to to MP'.
	www.jgiesen.de /kepler/index.html (168 words)

	Relativity and the Separation Formula
		The "eccentricity" (e) defines the shape of the curve: e=0 is a circle; 0ellipse; e=1 is a parabola; and 1
		With the mean anomaly in hand, it is not the true anomaly that is calculated first, at least for elliptical and hyperbolic orbits, but the "eccentric anomaly" (E), which is the point on a superscribed circle that corresponds to the point where the planet is on its curve.
		Calculating the eccentric anomaly from the mean anomaly is difficult because the equation M = E - e*sin E (for ellipses) cannot just be solved for E.
	www.friesian.com /separat.htm (4782 words)

	Kepler's Second Law
		The true anomaly f varies periodically around the orbit, quickly near perigee and slowly near apogee.
		The simplest way of expressing f is to use two auxiliary angles, which like f increase by 360 degrees each orbit, the "eccentric anomaly" E (the letter here has nothing to do with energy) and the "mean anomaly" M; an equation then exists connecting f and E, and another that connects E and M.
		The mean anomaly is what is counted as the third orbital element.
	www-istp.gsfc.nasa.gov /stargaze/Skepl2nd.htm (1242 words)

	Help: Orbit generator
		The orbit inclination is the angle between the orbital plane and the equatorial plane, measured at the ascending node in the direction of orbital motion.
		The argument of perigee is the angle measured in the orbital plane from the ascending node to the perigee.
		The true anomaly is the angle from the perigee direction to the satellite direction.
	www.spenvis.oma.be /spenvis/help/models/sapre.html (1726 words)

	Kepler and the First Law of Planetary Motion
		eccentric circle: Planet, P, moves uniformily around a circle with center, C, which is eccentric to the sun, S.
		is the distance for eccentric anomaly i, and i is measured (Figure B).
		So, the distance would have to correspond to the line connecting the sun to a point on the eccentric anomaly, Q.
	math.berkeley.edu /~robin/Kepler (1925 words)

	Kepler's Second Law--Lesson Plan #21
		(Optional) Learn (very qualitatively--how orbital motion is calculated: the polar angle f, ("true anomaly") varies unevenly around the orbit, but another angle, the "mean anomaly" M, varies steadily, and formulas exist to derive from M yet another angle, the "eccentric anomaly" E, from which f can be obtained by another transformation.
		One calculates the mean anomaly M, an angle which is also zero at perigee, but which grows at a constant rate--unlike f.
		Transformations exist from M to an intermediate angle E ("Eccentric anomaly") and from E to f.
	www-spof.gsfc.nasa.gov /stargaze/Lkepl2nd.htm (1937 words)

	5 Relativistic Effects on Satellite Clocks
		Denote the satellite's orbit semimajor axis by a and eccentricity by e.
		The angle f, called the true anomaly, is measured from perigee along the orbit to the satellite's instantaneous position.
		The correction is needed because of a combination of effects on the satellite clock due to gravitational frequency shift and second-order Doppler shift, which vary due to orbit eccentricity.
	relativity.livingreviews.org /Articles/lrr-2003-1/node5.html (1343 words)

	orbit.h Source File (Site not responding. Last check: 2007-10-13)
		Computes the true anomaly from the mean anomaly.
		Generate the eccentric anomaly from the mean anomaly and the eccentricity.
		Computes the true anomaly from the eccentric or hyperbolic anomaly.
	www.psatellite.com /products/html/sctlib_api/orbit_8h-source.html (713 words)

	[No title]
		It is different from An Eccentric Anomaly is defined in an the Longitude of Perihelion, which intermediate step with the solar focus is measured from the First Point of (the eccentric) and a circle with a Aries by the relation: radius equal to the semi-major axis of LONG.PERIH.=W+U the orbit.
		Its relation to the Mean Anomaly is defined by Kepler's Equation: L The Mean Longitude at Epoch is the M=E1-ESIN(E1) (3) reality reference for calculation of Where E1 is the Eccentric* Anomaly.
		The Mean and Eccentric For these programs, the Astronomical Unit anomalies are first and second is used for length and radians is the approximations to the True anomaly.
	pdp-11.trailing-edge.com /rsts11/rsts-11-063/NORTON.DOC (1845 words)

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