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Topic: Circular orbit

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Standard assumptions in astrodynamics

Specific angular momentum

Hohmann transfer orbit

Orbital equation

Orbit

Geosynchronous orbit

Geostationary orbit

Geosynchronous orbit derivation

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	SPACE.com -- Newfound Planet in Circular Orbit Around Another Star
		But the newest discovery is among the minority found in a relatively circular orbit, adding to the likelihood that Earth-like planets could exist.
		It wasn't clear whether their odd orbits would turn out to be the norm or not, said Chris McCarthy, a researcher at the Carnegie Institution of Washington who participated in the latest find.
		The percentage of planets in these more "normal" circular orbits will likely grow as methods are refined and more planets are found farther from their stars, McCarthy said.
	www.space.com /scienceastronomy/astronomy/new_planet_020917.html (666 words)

	Orbit (astronomy and physics) - MSN Encarta
		The size of the orbit is given by the periapsis distance (SP) and the elongation of the orbit is given by the eccentricity (e).
		The three orbital elements that describe an orbit's orientation are the inclination (i), the longitude of the ascending node (Ω), and the argument of the periapsis (ω).
		The argument of the periapsis measures the angular displacement in the plane of the orbit between the ascending node and the line that passes through the center of the orbit (C) and the periapsis (P).
	encarta.msn.com /encyclopedia_761556131/Orbit_(astronomy_and_physics).html (940 words)

	CSA - Orbital
		The effect of this burn is to change the satellite's orbit from a circular orbit to an elliptical orbit whose apogee (highest point), is at the altitude required for a geosynchronous orbit.
		This circular orbit is called a geosynchronous orbit because the orbital period (24h) of a satellite in this orbit is synchronized with the rotational period (24h) of the Earth.
		A satellite in geosynchronous orbit will not necessarily appear to "hover" over a single geographic location on the Earth's surface unless the orbital plane of the satellite is in the same plane as the Earth's equator.
	www.space.gc.ca /asc/eng/educators/resources/orbital/orbital_planes.asp (508 words)

	Free Orbit (Site not responding. Last check: )
		In accordance with the laws of gravitational movement, a focal point of the orbit (the center in the case of a circle) must always coincide with the center of mass (center of gravitaty) of the orbiting celestial body.
		As a result of the centrifugal force generated during the orbit, the effect of the sun's gravity on the Earth is offset and, therefore, we perceive nothing of its existence.
		Because of this, the counteracting centrifugal force and consequently the orbiting velocity must be correspondingly greater (because the centrifugal force increases with the square of the orbiting velocity).
	www.hq.nasa.gov /pao/History/SP-4026/noord3.html (453 words)

	Orbits
		An elliptical orbit is described by several parameters: the length of its semimajor axis, its eccentricity, its inclination, its period, the location of its nodes, and the location of its apsides.
		The length of the orbit’s semimajor axis is the average distance from the planet to its primary.
		The inclination of an orbit is the angle between the plane of the orbit and a reference plane.
	library.thinkquest.org /29033/begin/orbits.htm (1054 words)

	Aerospaceweb.org \| Ask Us - Orbit Ground Tracks
		Since an orbit must be concentric with the center of the Earth, the orbit of a vehicle launched from such a location becomes inclined with respect to the equator.
		Since the three-dimensional orbit of the HST is inclined at an angle to the equator, its ground track upon a two-dimensional map also crosses north and south of the equator.
		Drawing this three-dimensional circular orbit on a two-dimensional map results in the periodic sinusoidal shape referred to in the question.
	www.aerospaceweb.org /question/spacecraft/q0282.shtml (899 words)

	Near Earth Orbiting Satellites
		That is, the velocity is not constant in an elliptical orbit.
		A circular orbit is a special case where the magnitude of the velocity is constant throughout the orbit.
		Thus to make a circular orbit change we can calculate the velocity increases needed at perigee and apogee and then change from the lower circular orbit to the elliptical orbit and from the elliptical orbit to the higher circular orbit by applying these velocity increases.
	www.math.ubc.ca /~cass/courses/m309-01a/hunter/satelliteOrbits.html (1530 words)

	Hohmann Transfer
		To be in a geosynchronous orbit, the satellite must move to an equatorial orbit (inclination = 0 degrees) with an altitude of 38,000+ km.
		Since the point in an orbit where the engines are fired automatically becomes a point in the new orbit (or the burn point becomes the intersection of the old and new orbits), this firing must occur where the current orbit and the desired orbit intersect.
		Velocity in inclined orbit: 7.726 km/sec at 28.5 degrees to equator.
	liftoff.msfc.nasa.gov /academy/rocket_sci/satellites/hohmann.html (852 words)

	ASP: Up, Up, and Away
		The perigee of the new elliptical orbit is the altitude of the low orbit; the apogee is the altitude of the geosynchronous orbit.
		The altitude and circularity of the orbit are not the only things that must match before two spacecraft can meet.
		In an orbit inclined 51.6 degrees to the equator, the station will be easy for the Russians to reach, since their launch site -- the Baikonur Cosmodrome in Kazakhstan -- is at a high latitude.
	www.astrosociety.org /education/publications/tnl/34/space2.html (1385 words)

	Peter Alway Orbit Page (Site not responding. Last check: )
		As a satellite of Earth, the projectile is subject to the same laws as a moon orbiting a planet or a planet orbiting the sun; all three of Kepler's laws apply.
		A satellite orbiting the Moon 4500 miles from its center travels more slowly than one orbiting the Earth at the same distance from the Earth's center, simply because the Moon is less massive than the Earth.
		Of course, the occupants aboard a spacecraft orbiting the earth are not beyond the Earth's gravityÑit is gravity that holds a spacecraft in the Earth's vicinity.
	members.aol.com /petealway/orbit.html (1663 words)

	Orbits in Strongly Curved Spacetime
		That tiny discrepancy in the orbit of Mercury was actually the first evidence for what lay beyond Newtonian gravitation, the first step down a road that would lead to understanding fl holes, gravitational radiation, and the source of inertia, which remains a fertile ground for theoretical and experimental physics almost a century thereafter.
		Orbits at minima are stable, since a small displacement increases the energy and thus creates a restoring force in the opposite direction.
		Orbits at maxima are unstable; the slightest displacement causes the particle to either be sucked into the fl hole or enter a highly elliptical orbit around it.
	www.fourmilab.ch /gravitation/orbits (2354 words)

	Satellite Radio Glossary
		The circular orbit at approximately 35,800 km above the equator, where the satellites travel at the same speed as the earth's rotation (Geostationary Orbit) and thus appear to be stationary to an observer on earth.
		The circular orbit of a geosynchronous satellite whose orbit lies in the plane of the earth's equator.
		An orbit that approximates the geostationary orbit but whose plane is tilted slightly with respect to the equatorial plane, with the consequence that the satellite appears to move about its nominal position in a daily "figure-of-eight" motion when viewed from the ground.
	www.satelliteradiozone.com /Radio-Glossary (2523 words)

	Lecture 7 Kepler
		This became particularly evident in the case of the planet Mars, whose orbit was very accurately measured by the Danish astronomer Tycho Brahe.
		Example: A space vehicle is in a circular orbit of 2080-km radius (orbit A) around the moon.
		To transfer it to a larger circular orbit of 2200-km radius (orbit B), the vehicle is first placed on an elliptical path AB by increasing its speed by 16 m/s as at passes through A. Knowing that the mass of the moon is 73.5x10
	www.csulb.edu /~rtoossi/engr370i/7.htm (486 words)

	Basics of Space Flight Section I. The Environment of Space
		It is possible to choose the parameters of a spacecraft's orbit to take advantage of some or all of these gravitational influences to induce precession, which causes a useful motion of the orbital plane.
		The result is called a walking orbit or a precessing orbit, since the orbital plane moves slowly with respect to fixed inertial space.
		A walking orbit whose parameters are chosen such that the orbital plane precesses with nearly the same period as the planet's solar orbit period is called a sun synchronous orbit.
	www2.jpl.nasa.gov /basics/bsf5-1.html (1166 words)

	Chapter 5 -- Orbital Mechanics (Site not responding. Last check: )
		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.
		A circular orbit has no varying of kinetic energy because the velocity is always the local circular speed and there is also no varying of potential energy because the distance of the satellite from the center of the Earth remains the same.
		V must be performed to boost the spacecraft from Earth orbit using the Sun as the new primary body to arrive at the target planet at the spacecraft's aphelion point (Point in orbit farthest from the Sun which corresponds to apogee, the farthest point in orbit from the Earth).
	www.space.edu /projects/book/chapter5.html (5633 words)

	Earth Orbits
		The circular orbit is a special case since orbits are generally ellipses, or hyperbolas in the case of objects which are merely deflected by the planet's gravity but not captured.
		The orbit can be expressed in terms of the acceleration of gravity at the orbit.
		This leads to Kepler's 3rd law (the Law of Orbits) which is useful for the analysis of the orbits of moons and binary stars.
	hyperphysics.phy-astr.gsu.edu /hbase/orbv.html (521 words)

	Tidal circularization of orbits (Henry Spencer) (Site not responding. Last check: )
		The effect of deceleration at periapsis is lower apoapsis -- that is, circularization of the orbit.
		The dominant effect on the Moon's orbit, after all is said and done, is the way it is being raised (and Earth's rotation slowed) by the tides the Moon raises in the Earth.
		In the case of rings, they tend to be circular for a more prosaic reason: collisions between ring particles circularize their orbits very quickly.
	yarchive.net /space/orbits/tidal_circularize.html (564 words)

	Filling space with non-colliding orbits (Site not responding. Last check: )
		All the blue orbits have period 1.000, their major axes are all in the same plane as the circular orbit (the major axes are the green lines).
		By taking a single blue orbit and spinning its major axis around the sun in the plane of the circular orbit, a donut-shaped tube is formed, and the cross section of that tube is the red shape.
		The cross-section of the tube is determined by the angle of the minor axis to the circular orbit's plane, and by the eccentricity of the orbits.
	burtleburtle.net /bob/scifi/itzuorb.html (574 words)

	[No title]
		A geosynchronous orbit is an orbit which has an orbital period close to that of the earths rotation.
		A geostationary orbit is a special case of the geosynchronous orbit where inclination = 0 and the period is equal to the rotation period of the earth (approx 1436 minutes), corresponding to a circular orbit of approx.
		A satellite in this orbit appears essentially stationary in the sky, which is why this orbit is used extensively for telecommunications & weather satellites.
	www.lycos.com /info/geosynchronous-orbit.html (311 words)

	Millennium Theory of Inertia and Gravity 4
		from the center of mass in the cases of both, circular orbits and elliptical orbits, the sum of these distances is equal to the half the distance across a circle, but more than half the distance across an ellipse.
		are used to derive such formulas for circular orbits, the distance to the center of the ellipse is used in the derivation of the formulas for elliptical orbits.
		A-1; that is, the circular orbits in the Copernican model are replaced by ellipses.
	www.mrelativity.net /InertiaGravity/Inertia&Gravity4.htm (2896 words)

	Homann Transfers
		A Hohmann Transfer is half of an elliptical orbit (2) that touches the circular orbit the spacecraft is currently on (1) and the circular orbit the spacecraft will end up on (3).
		Discuss with students the speed of an object in a circular orbit (constant because the radius is constant) and the force of an object (also constant).
		Now that students can find the velocity of an object in a circular and elliptical orbit, and the velocity of an object at the apogee and perigee of an elliptical orbit, they can begin to explain how to move a spacecraft from one circular orbit to another.
	jwilson.coe.uga.edu /EMAT6680Fa05/Bacon/hohmanntransfers.html (932 words)

	Re: Is the Earth Moving in Eliptical Orbit ? Are you sure it is not Circular Orbit ? - Astronomy.com Forums
		I did a small test with relative measurement and though the object moved in circular orbit, the time compression and expansion (that is how it is visualized) while measuring caused it appear as if it is moving in elliptical orbit.
		In practice, the object moved in perfect circular orbit relative to center despite the fact that the time got compressed and expanded that can be visualized as if it had moved in elliptical orbit with respect to a linear time scale.
		However, the fact that the Sun would be shifted from the center of the orbit by 1.7% of the length of the semi-major axis should be apparent to someone carefully studying that orbital diagram.
	www.astronomy.com /ASY/CS/forums/324155/ShowPost.aspx (2056 words)

	Elliptical Orbit - Math
		The formula for eccentricity of orbit was derived from the book, "Practical Astronomy With Your Calculator", by Peter Duffett Smith, Cambridge University Press, ISBN 0-521-35699-7.
		The "Avg Angle per Day" column is what the average angle would be if the orbit were circular.
		You can see from the chart that after 10 days, the sun has drifted to the east and would take over 1 minute to reach its highest point in the sky even though according to your watch, it should be straight overhead.
	www.analemma.com /Pages/EllipticalOrbit/EllipticalOrbitMath/EllipOrbitMath.html (659 words)

	Orbits 101 (Site not responding. Last check: )
		Since the kinetic energy of escape velocity is twice that of a circular orbit, and the kinetic energy required for a circular orbit approaches infinity as distance goes to zero, we see that the maximum potential energy that can be lost is infinite.
		When two worlds orbit one another, the orbits of both worlds are ovals (ellipses), and the center of gravity of the two worlds is one of the focii of both ovals.
		Moons orbiting clockwise around planets moving clockwise around their sun are not stable, although it takes several minutes before the orbit falls apart.
	burtleburtle.net /bob/physics/orbit101.html (1170 words)

	Approaching the Black Hole
		The circular orbit at 2 Schwarzschild radii is unstable, a type of circular orbit which exists in General Relativity, but not in Newtonian gravity.
		The unstable orbit at 2 Schwarzschild radii is that orbit which corresponds to zero kinetic energy (zero velocity) at infinity.
		Outside 3 Schwarzschild radii, all circular orbits are stable, meaning that a small blast on the manoeuvering thrusters by a rocket in circular orbit would not perturb the orbit greatly.
	casa.colorado.edu /~ajsh/approach.html (1324 words)

	A New Paradigm for Lunar Orbits - Salem-News.Com
		For a lunar orbit higher than 430 miles, Earth's pull is actually strong enough to whisk a spacecraft out of the game.
		Indeed, to any satellite in Earth orbit, the gravitational pull of the Sun is 160 times stronger than any lunar influence.
		Ely and his colleagues calculate that certain elliptical, high-inclination, high-altitude lunar orbits may remain stable for periods of at least a century.
	www.salem-news.com /articles/november302006/lunar-orbits.php (865 words)

	The ISS orbits the Earth in a ~circular orbit at an altitude of 353 km
		The ISS orbits the Earth in a ~circular orbit at an altitude of 353 km.
		Circular orbital velocity for this orbit would be:
		It’s farthest point from Earth would be equal to the orbit of the ISS.
	orbitsimulator.com /BA/spatula.htm (350 words)

	Can you put the moon into orbit?
		You cannot get the moon into an orbit that is lower than its starting position because the nature of every orbit is that the object must return to the place where it started.
		The only circular orbit you can get the moon into from outer space is an orbit that is in outer space.
		Namely because every orbit is either circular or elliptical it always returns to its starting position.
	isthis4real.com /orbit.xml (648 words)

	Aerospaceweb.org \| Ask Us - Space Shuttle Speed in Orbit
		The word "orbit" is defined as the path a body follows when being acted upon by the force of gravity.
		The reason the speed is constant is because the orbiting object is always accelerating toward the center of the primary body while moving in a straight line.
		Note how simple this equation is. It says that the velocity of an object in a circular orbit is proportional to nothing more than the mass of the primary body and the radius of the circular orbit.
	www.aerospaceweb.org /question/spacecraft/q0164.shtml (1074 words)

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