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Topic: Orbital equation

Related Topics

Circular orbit

Parabolic orbit

Standard assumptions in astrodynamics

Specific angular momentum

Hyperbolic trajectory

Capture orbit

Orbit

Geostationary orbit

Geosynchronous orbit

Orbital period

Rocket equation

Escape Speed

Conic section

Spaceflight

Eccentricity

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	Planetary orbit - Biocrawler (Site not responding. Last check: 2007-11-04)
		The equations of motion of the moon, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation.
		To analyse the motion of a body moving under the influence of a force which is always directed towards a fixed point, it is convenient to use polar coordinates with the origin coinciding with the centre of force.
		In the case of an inverse square force law the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (upto a shift of origin of the dependent variable).
	www.biocrawler.com /encyclopedia/Orbit (2552 words)

	Specific orbital energy - Wikipedia, the free encyclopedia
		According to the orbital energy conservation equation (also referred to as vis-viva equation) it is the same at all points of the trajectory:
		In the case of circular orbits, this rate is one half of the gravity at the orbit.
		The International Space Station has an orbital period of 91.74 minutes, hence the semi-major axis is 6738 km [1].
	en.wikipedia.org /wiki/Specific_orbital_energy (776 words)

	Two-Body Problem -- from Eric Weisstein's World of Physics
		Equation (16) is a second-order ordinary differential equation,
		This determined one of the constants for the second-order differential equation (28).
		This equation is known as the vis-viva equation.
	scienceworld.wolfram.com /physics/Two-BodyProblem.html (550 words)

	Orbital Mechanics
		Inclination is the angular distance between a satellite's orbital plane and the equator of its primary (or the ecliptic plane in the case of heliocentric, or sun centered, orbits).
		Note that equations (1.52) and (1.53) are the same as equation (1.6), and equations (1.54) and (1.55) are variations of equations (1.16) and (1.17) respectively.
		Orbital transfer becomes more complicated when the object is to rendezvous with or intercept another object in space: both the interceptor and the target must arrive at the rendezvous point at the same time.
	www.braeunig.us /space/orbmech.htm (6414 words)

	Effective Nuclear Charge (Site not responding. Last check: 2007-11-04)
		Unlike a hydrogen-like atom, for which analytical solutions of the Schrodinger equation are available, the Schrodinger equation cannot be solved analytically for multi-electron atoms owing to the electron-electron repulsion terms.
		On the left is the hydrogen s orbital for a given shell, and the s orbital from the same shell for a fluorine atom is shown on the right.
		(The orbitals for the fluorine atom were obtain from numerical solutions of the Schrodinger equation.) The slider can be used to move the atoms together or apart; the VRML controls can be employed to zoom in or out.
	www.chm.davidson.edu /ChemistryApplets/AtomicOrbitals/Zeff.html (678 words)

	The Net Equation: Your Online Source for Chemistry Solutions
		Orbitals in a subshell but differ in their orientation--one might point "up," another to the "left," etc. Possible orbital values range from the negative value of l through zero to the positive value of l.
		For example, in a hypothetical 3D space, one orbital in the "p" subshell may have its nodes facing along the left-right axis, the second along the front-back axis, and the third from top to bottom.
		The rest of the orbitals are more normal, with four balloon-shaped regions of high electron density extending along various planes.
	library.thinkquest.org /C004970/atoms/orbital.htm (1458 words)

	A Correction to the Equation a=v²/r by Miles Mathis
		The equation is used today in many esoteric theories, including the derivation of the Schwarzchild radius, the predicted intensity of a gravity wave, and on and on.
		The reason the equation is used so often in contemporary physics is that it is also assumed to describe the relationship, in its simplest form, between an orbiting body and the force of gravity felt by that body.
		The tangential velocity is the tangent and the orbital velocity is the arc.
	geocities.com /mileswmathis/avr.html (7591 words)

	Hydrogen Schrodinger Equation
		Upon separation of the Schrodinger equation for the hydrogen atom, the azimuthal equation is:
		While the azimuthal dependence of the wavefunction only requires the quantum number to be an integer, the coupling to the colatitude equation further constrains that integer to be less than or equal to the orbital quantum number.
		The different orientations of orbital angular momentum represented by the magnetic quantum number can be visualized in terms of a vector model.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/hydazi.html (460 words)

	Introduction to Molecular Orbital Theory
		In physics, periodic phenomena are associated with a "wave equation", and in atomic theory the relevant equation is called the "Schrödinger Equation".
		The upper molecular orbital has a node in the electronic wave function and the electron density is low between the two positively charged nuclei.
		This highest occupied orbital has a lobe pointing away from the three hydrogens, and corresponds to a lone pair orbital localized upon the nitrogen, whereas the three lowest energy MO's lead to the description of the three N-H bonds of the Lewis structure.
	www.ch.ic.ac.uk /vchemlib/course/mo_theory/main.html (2412 words)

	[No title]
		where v is the orbital velocity, C is the circumference and t is the period of the orbit.
		In this simplified equation the numerator has the form of a velocity squared, but it is not a velocity by any meaning of the word.
		Since the wrong equation has been used throughout history and is still being used, this must once again compromise our calculated values for orbital "velocity".
	www.wbabin.net /mathis/mathis13.htm (2583 words)

	Basis Set Study
		This equation is just one basis function, which when combined with the answers of other basis functions, gives a value which gives the mathematics to solve for Psi.
		The "3" stands for the number of equations required for the s orbitals, and the "21" indicates the two similar equations for calculating the p orbitals and the other equation for calculationg p orbitals.
		We were not able to find a linear equation relating the number of basis functions to the amount of CPU time because the equation is quadratic i.e., the data follows a parabola pattern because one of the values in the equation is squared.
	www.shodor.org /succeed/projects/compchem/cchem97/basis (1046 words)

	G.G. Hall about Lennard-Jones, Sir John Edward - concerning : Early Ideas in the History of Quantum Chemistry.
		Thus his first approximation to the molecular orbital is a linear combination of H-like atomic orbitals suitably normalized using the overlap integral.
		As a final contribution, the paper also argued that the notation for the MO should begin with the principal quantum nurnber of the atomic orbital of the separated atom instead of using that of the united atom, as was the custom at that time.
		In these two papers he gave a rigorous derivation of the orbital equations from the Scbrödinger equation using a method he had introduced (14) for the atomic SCF equations.
	www.quantum-chemistry-history.com /LeJo_Dat/LJ-Hall1.htm (1553 words)

	Orbit equation - Wikipedia, the free encyclopedia
		If the conic section intersects the central body, then the actual trajectory can only be the part above the surface, but for that part the orbit equation and many related formulas still apply, as long as it is a freefall (situation of weightlessness).
		The reversal is when the center of the Earth changes from apoapsis to periapsis (the other focus starts near the surface and passes the center of the Earth).
		Extending this to orbits which are horizontal at another height, and orbits of which the extrapolation is horizontal below the surface of the Earth, we get a categorization of all orbits, except the radial trajectories, for which, by the way, the orbit equation can not be used.
	en.wikipedia.org /wiki/Orbital_equation (833 words)

	4.1 Dynamics of a massive binary in a fixed stellar background
		Each ejected star carries away energy and angular momentum, causing the semi-major axis, eccentricity, orientation, and center-of-mass velocity of the binary to change and the local density of stars to drop.
		The binary’s mass ratio was 1:1, and the orientation of the binary’s orbital plane with respect to the
		Orbital shrinkage would occur quite rapidly in the environment of a galactic nucleus if the properties of the stellar background remained fixed.
	relativity.livingreviews.org /Articles/lrr-2005-8/articlesu3.html (950 words)

	To the Planets
		Students should correctly determine the equation for the elliptical motion of the planet, and use techniques of implicit and explicit differentiation to find the equations for velocity and acceleration.
		Students will use word processing (including an equation editor function), the Internet, a graphing calculator, and other appropriate and available software and hardware to create an integrated written document describing a mission to the chosen planet and giving the appropriate equations for motion, velocity, and acceleration.
		All students should be able to organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely.
	www.glc.k12.ga.us /BuilderV03/lptools/lpshared/lpdisplay.asp?LPID=25181 (1143 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		The first term in the square brackets in equation (\ref{RelEng1}) is the Keplerian energy of the relative orbit $E$, $2E=\mu v^2-2k\mu/r$, and the second term is a relativistic contribution.
		These equations for the planar problem are closely related to corresponding equations for the variation of the orbital elements of the osculating ellipse.
		In general, the path of the osculating ellipse in the six-dimensional manifold of orbital elements encounters singularities at $e=0$ and $e=1$.
	www.ma.utexas.edu /mp_arc/html/papers/96-382 (5497 words)

	quantumredshift (Site not responding. Last check: 2007-11-04)
		This is achieved by imposing a quantum condition on the second of the two equations governing the behaviour of the Bohr atom (the orbital energy equation).
		This is done by obtaining a set of four simultaneous partial differential equations based on (a) Gauss’s theorem applied to electrostatics; (b) Gauss’s theorem applied to magnetic fields; (c) Faraday’s and Lenz’s law of electromagnetic induction; and (d) Ampere’s law for magnetomotive force.
		As the resultant equations from (a) and (b) eventually become e div E = 0 and m div H = 0 for a vacuum, then it is apparent that they are independent of any variations in e and m.
	www.setterfield.org /quantumredshift.htm (9041 words)

	Electron ls Orbital Binding Energy Equation
		The equation is based upon the spin structure of spacetime, the fine structure constant, and the kinetic energy of the electron.
		But the equation is more accurate and instructive than any other electron binding energy equation, applied across a wide spectrum of atoms, known to-date.
		The nonsense is that I have presented a verifiable equation that comes closer to predicting the electron binding energies for ALL atomic isotopes in the history of physics and you haven't provided anything but a personal opinion.
	www.physicsforums.com /showthread.php?p=91229 (1043 words)

	Kepler's Laws and Gravitation II.
		In the equation for the force of gravity, the amount of force generated depends on the masses of the two objects, and the distance between them.
		The orbital parameters are just right that the gravity of the parent star is not able to hold on to the planet.
		Now, one side of this equation has a square root in it-get rid of this by squaring both sides of the equation and then simplifying the result.
	astronomy.nmsu.edu /astro/a110labs/labmanual/node6.html (4580 words)

	Hv review.sm.copy
		The orbitals, however, must somehow be optimized for maximal ab initio accuracy and, therefore, must differ in precise form from the (actually often partially unspecified) orbitals in the semiempirical methods.
		This crossing of orbital energies for orbitals of the same spatial symmetry is permissible because the 10a' and 11a' orbitals are eigenfunctions of different Fock operators, namely, the 10a' orbital is obtained from the ground state SCF wavefunction, while the 11a' orbital is an IVO from a 1¡A'' state computation.
		In a similar vein, the 11a' and 13a' orbitals become nearly degenerate for a CS distance of 3au, while these two orbitals are rather close in energy over the whole range of SH distances, suggesting the need for including the 13a' orbital in the Hv valence space.
	home.uchicago.edu /~freed/Hvreview.html (11512 words)

	MAPLE (Site not responding. Last check: 2007-11-04)
		This assignment consisted of using MAPLE in analyzing the electron orbitals; 1s,2s, and 2p.
		We graphically displayed the mathematical equations assigned to each orbital on three dimensional plots.
		This is the graph of a 1s orbital.
	people.clarkson.edu /~finnerhm/ass.3.html (98 words)

	Final Gallery (Site not responding. Last check: 2007-11-04)
		Earthâs velocity at a, determined by the equation Orbital Speed =2Pir/Period (from lesson ten): 2pi150,000,000 km/365.25 days = 2579055.44 km/day = 29.85 km/sec = 66,772.5 mph Difference is 4809.5 mph 2.
		Because Pathfinder is closer to the sun at a, the sunâs gravitational pull is stronger, causing Pathfinder to move faster at point a than at point b.
		Also, the fact that Pathfinderâs orbital speed is not constant because it is in an elliptical orbit explains why its velocity is different than that of the planet whose orbit it is entering or exiting.
	aerospacescholars.jsc.nasa.gov /has/Students/finalGall.cfm?id=162 (342 words)

	PHYS 20083 - Spring 2001 Complete Study Guide
		Given the relationship between frequency, speed and wavelength (the wave equation) and the relationship between photon energy and wavelength, be able to identify regions of long and short wavelength, regions of high and low frequency, and regions of high and low photon energy on a spectrum (a graph of intensity vs wavelength).
		Given the equation of orbital velocity and the period equation, explain how we use the period and the spectral line shifts to estimate the mass of the central star in an edge-on binary system.
		Given the two orbit equations, be able to answer simple proportionality questions such as: "Star A and Star B have the same orbital distances to their companion stars, but star A's companion shows large Doppler shifts compared to star B's companion.
	personal.tcu.edu /~dingram/phys20083/sp01_sg0.html (6603 words)

	Comparing STO's and GTO's Lab (Site not responding. Last check: 2007-11-04)
		Although the STO equation is a wonderful approximation for the molecular orbitals, the problem lies in the calculations.
		With carbon, you see the addition value, so the first is the orbital exponent, the second is the s-part of the sp-hybrid, and the third part is the p-part of the sp-hybrid.
		The "squiggle" is a Greek character standing for an orbital coefficient, similar to alpha in gaussian curves.
	chemviz.ncsa.uiuc.edu /content/lab-s-STOGTO.html (2066 words)

	Humancafe's Bulletin Boards
		The values we then ascribe to this equation become a function of how we wish to measure it, provided it is adjusted for mass and remains consistent with the rest of the equation.
		This unified equation says that electric force times lightspeed is Energy, and that (g), which ranges from near zero to its maximum of one, is inversely proportional to (Bm), in relation to the E density of any given star system.
		This equation is not yet complete, however, for there may be an energy density factor to be considered, which if so should make for another value of E to be identified.
	www.humancafe.com /cgi-bin/discus/show.cgi?70/108.html (16097 words)

	ABET course syllabus - EAS 4505
		Orbital Mechanics: PR: EGN 3321 and MAP 2302
		Two-body problem, orbital equations, orbital transfer, earth satellite operation.
		Understand the definition and the formulas to calculate orbital elements.
	classes.cecs.ucf.edu /eas4505/lin/Syllabus.htm (80 words)

	MCTD Orbital Equation For Channel #tex2html_wrap_inline370# (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-04)
		MCTD Orbital Equation For Channel #tex2html_wrap_inline370# (via CobWeb/3.1 planetlab2.cs.virginia.edu)
		Next: Inhomogeneity Side of Linear Algebraic Equations for Mixing Coefficients of Excited Bound Configurations
		The other terms in the orbital equations are;
	www.osc.edu.cob-web.org:8888 /PET/CCM/skeleton/training/courses/foundations/rqm456/node3.html (45 words)

	AA4362_homepage.html
		The Orbital Velocity Vector and Kepler's Third Law
		Orbital Period as a Function of Orbit Size
		Projection of the Orbital Position onto the Earth's Surface
	web.nps.navy.mil /~ssweb/AA4362/AA4362.html (284 words)

	Orbital equation
		Im having a little trouble finding the orbital period of Earth using:
		The following code was used to generate this LaTeX image:
		I believe the problem is asking for the orbital period in seconds.We all know that the orbital period of Earth is 1 year,but we want to find that using physics and not our senses.
	www.physicsforums.com /showthread.php?p=429553 (784 words)

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