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Topic: Orbital energy conservation equation

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Specific orbital energy

Hohmann transfer orbit

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	Energy - Engineering
		Energy can be in several forms: mechanical potential—due to possible physical interactions with other objects (for example, gravitational potential energy); kinetic—contained in macroscopic motion; chemical—potential stored in chemical bonds between atoms; electrical—potential due to possible charge interactions; thermal—contained in the kinetic energy of individual molecules[[2]]; nuclear energy[[3]]—potential stored between constituents of atomic nucleus [[4]].
		In contrast to kinetic energy, which is the energy of a system due to its motion, or the internal motion of its particles, the potential energy of a system is the energy associated with the spatial configuration of its components and their interaction with each other.
		Internal energy is the kinetic energy associated with the motion of molecules, and the potential energy associated with the rotational, vibrational and electric energy of atoms within molecules.
	engineering.wikia.com /wiki/Energy (2597 words)

	Orbital Mechanics II
		The kinetic energy of a satellite in a circular orbit is half its gravitational energy and is positive instead of negative.
		To satisfy the minimum energy requirements of this problem the satellite should be launched from someplace on the equator where the speed of rotation (and thus the kinetic energy) is a maximum.
		Assuming that energy is conserved (which it is for the most part in the vacuum of space), the total energy of the satellite would remain constant.
	hypertextbook.com /physics/mechanics/orbital-mechanics-2/index.shtml (1031 words)

	Particle Interactions and Conservation Laws
		These conservation laws are in addition to the classical conservation laws such as conservation of energy, charge, etc., which still apply in the realm of particle interactions.
		Strong overall conservation laws are the conservation of baryon number and the conservation of lepton number.
		This rule is a little more complicated than the conservation of baryon number because there is a separate requirement for each of the three sets of leptons, the electron, muon and tau and their associated neutrinos.
	hyperphysics.phy-astr.gsu.edu /hbase/particles/parint.html (1185 words)

	Natural Length Contraction Mechanism Due to Kinetic Energy
		Equations 5 and 6 only mean that when a particle or even a macroscopic body is accelerated to a moving frame, there is a real physical increase of mass due to the addition of the external kinetic energy to that mass.
		In equation 17, we see that when the atom is located in the [v] frame and using the [v] reference units, using classical physics, we get the same mathematical relationship as the one using the stationary units, with the atom in the stationary frame.
		Equation 25 gives the relative change of local units of energy, due to the important change of velocity of the atom in a moving frame of reference.
	www.newtonphysics.on.ca /kinetic/length.html (5891 words)

	Is Energy Conserved in General Relativity?
		In Newtonian physics, energy conservation and momentum conservation are two separate laws.
		Equation 1 may remind you of Gauss's theorem, which deals with flux across a boundary.
		We will not delve into definitions of energy in general relativity such as the Hamiltonian (amusingly, the energy of a closed universe always works out to zero according to this definition), various kinds of energy one hopes to obtain by "deparametrizing" Einstein's equations, or "quasilocal energy".
	www.math.ucr.edu /home/baez/physics/Relativity/GR/energy_gr.html (2204 words)

	Circular orbit - Wikipedia, the free encyclopedia
		The orbital period is the same as that for an elliptic orbit with the semi-major axis (
		Thus the escape velocity from any distance is â2 times the speed in a circular orbit at that distance: the kinetic energy is twice as much, hence the total energy is zero.
		a geostationary orbit, requires a larger delta-v than an escape orbit, although the latter implies getting arbitrarily far away and having more energy than needed for the orbital speed of the circular orbit.
	en.wikipedia.org /wiki/Circular_orbit (268 words)

	Kepler's Second Law--Lesson Plan #21
		This is made evident in two ways: by calculating the ratio of greatest and smallest orbital velocities (in the lesson plan, not given in "Stargazers"), and by invoking the concept of energy.
		That energy comes in two forms--energy of speed, or kinetic energy, and energy of position, or potential energy, higher at the hilltops and higher at apogee.
		The energy of an object with velocity V, at the surface of the Earth, is
	www-istp.gsfc.nasa.gov /stargaze/Lkepl2nd.htm (1937 words)

	Articles - Specific orbital energy (Site not responding. Last check: 2007-10-15)
		According to the orbital energy conservation equation (also referred to as vis-viva equation) it is the same at all points of the trajectory :
		This corresponds to the fact that for such orbits the total energy is one half of the potential energy, because the kinetic energy is minus one half of the potential energy.
		The energy is â’29.6 MJ/kg [2]: the potential energy is â’59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg.
	www.poncier.com /articles/Specific_orbital_energy (854 words)

	Limitation of the Law of Energy Conservation
		Since in a neutral atom the velocity fields in the vortices of the orbital electrons and the central nucleus cancel each other, the electromagnetic field of the electrons (arising due to their structural vortices) confined within the atom is not the agency to produce light (electromagnetic wave) from an atom under oscillation.
		As concluded earlier, the changes in the gravity potential of the oscillating neutral atom produce light, and therefore, the phenomenon of light is an effect of Galilean relativity in the sense that during oscillation, to and fro displacement of atom relative to space produces light.
		However, when the spatial reality of fields and absence of energy at electron's centre are recognized, the law of conservation of energy becomes applicable only to the universe as a whole, though for the phenomena involving material interactions due to conservation of momentum, the energy conservation law will be valid also in isolated systems.
	depalma.pair.com /Tewari/Chap8.html (3480 words)

	Articles - Elliptic orbit (Site not responding. Last check: 2007-10-15)
		Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter one
		The orbital period is equal to that for a circular orbit with the orbit radius equal to the semi-major axis (
		Specific energy for elliptic orbits is independent of eccentricity and is determined only by semi-major axis of the ellipse.
	www.lcdproctor.com /articles/Elliptical_orbit (225 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)

	Natural Length Contraction Due to Gravity
		We must realize that the equations of mechanics, as given in equations 11 and 12 are valid only, when we use the number of units, as measured by an observer using the units existing in the frame where the phenomenon takes place.
		Equation 51 shows that when a mass acquires velocity (kinetic energy) inside a frame at the same time that it loses gravitational potential, equation 51 is applied.
		However, in the case of kinetic energy, there is a momentum transfer to the electron since the energy must be in motion to transmit energy to a moving mass.
	www.newtonphysics.on.ca /Gravity/gravity.html (7910 words)

	Hydrino Study Group
		predict that the excited state rotational energy levels are nondegenerate as a function of the l quantum number even in the absence of an applied magnetic field, and the predicted energy is over six orders of magnitude of the observed non-degenerate energy in the presence of a magnetic field.
		Therefore, the non-degeneracy is nonsensical and violates conservation of angular momentum of the photon.
		Dirac's equation, which was postulated to explain spin, relies on the unfounded notions of negative energy states of the vacuum, virtual particles, and gamma factors.
	www.hydrino.org /introduction.php (894 words)

	Gravity
		Energy comes in three basic forms: kinetic energy, which is energy of motion; potential energy, which represents energy stored for later conversion into kinetic energy; and radiative energy, which is energy carried by light.
		Thermal energy, or the energy of heat, is actually a form of kinetic energy since all the individual particles in a warm substance are moving.
		The energy levels are different and unique for each different type of atom and ion, which means these energy levels essentially represent a "fingerprint" from which we can identify the type of atom or ion.
	www.astro.washington.edu /larson/Astro150b/Lectures/Gravity/gravity.html (1764 words)

	Rotational energy Summary
		The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.
		The rotational energy of a rolling cylinder varies from one half of the translational energy (if it is massive) to the same as the translational energy (if it is hollow).
		Due to conservation of angular momentum this process transfers angular momentum to the Moon's orbital motion, increasing its distance from Earth and its orbital period (see tidal locking for a more detailed explanation of this process).
	www.bookrags.com /Rotational_energy (732 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).
		Conservation of energy states that the sum of the kinetic energy and the potential energy of a particle remains constant.
		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)

	bcxcvx
		The law of conservation of energy holds good for all bodies, particle or waves; thus the derivation must be in general and applicable to all cases.
		Here energy evolved is negative implies that energy is created at the cost of mass; and reaction is exothermic in nature, also energy is scalar quantity, hence only magnitude is associated with it and not direction.
		In electric bulb electrical energy changes to light energy, in radio electrical energy is converted into sound energy, in cell chemical energy is changed to electrical energy, in photocell light energy changes to electrical energy there are many such examples of inter conversion of one form of energy to other.
	wbabin.net /ajay/sharma2.htm (12968 words)

	[No title]
		Molecular Orbital Theory [A]ssumes that molecules are multi-nucleated atoms: the molecular orbitals, MOs, are assumed to encompass the two nuclei.
		The principle of the molecular orbital theory is that the electronic structures of molecules are determined primarily by the nuclei of the atoms which constitute them and the arrangement of those nuclei in space.
		It emerged from his work that the conservation of the number of nodes in each orbital as R changed was very significant.
	www.lycos.com /info/molecular-orbital--molecular-orbital-theory.html (665 words)

	Conservation of Angular Momentum and Energy
		Hidden in Newton's laws are the conservation of energy, and the conservation of angular momentum.
		Now the gravitational potential energy is the energy that a body has which can subsequently be used to accelerate the body to a larger magnitude of velocity.
		Thus, conservation of angular momentum demands that a decrease in the separation r be accompanied by an increase in the velocity v, and vice versa.
	www.pas.rochester.edu /~blackman/ast104/angmom.html (843 words)

	Overview of Computational Chemistry
		Bohr's orbital theory had the problem that if we wanted to describe the movement of an electron from Orbit 1 to Orbit 2, the rules more or less stated that the electron made an instantaneous leap from one level to the next.
		Schroëdinger's equation eliminated this illogical quantum jump, replacing it with a transitional process in which the wave pattern gradually fades out, while the new wave pattern fades in, during which time light is being emitted.
		Schroëdinger's equation is one of the starting points for most of the quantum chemical calculations that are done now, mostly using supercomputer technology.
	www.shodor.org /chemviz/overview/schroeq.html (1352 words)

	Lecture 7 - Orbital Mechanics III: Energy (10/1/98) (Site not responding. Last check: 2007-10-15)
		There are 3 conserved quantities in an isolated mutually gravitating two-body system: linear momentum, angular momentum, and total energy.
		The energy equation is derived by considering the work done while moving a particle on a path near a gravitating mass (the path integral of F · d r).
		This is the all-important energy equation for a body in orbit at radius r with velocity v around a dominant gravitating mass M. The limiting case r -> infinity is particularly interesting.
	www.aoc.nrao.edu /~smyers/courses/astro11/L7.html (357 words)

	Beyond the Farthest Star, by Robert L. Carroll (Site not responding. Last check: 2007-10-15)
		We have found that energy is scattered from a photon when it is deflected from a straight line path by the action of a gravitational field.
		Since the energy density is reduced as the inverse fourth power of the radius vector, and the mass density is reduced as the inverse third power, in interstellar space there exists nothing of sufficient magnitude to prevent the attainment of any velocity within the limits of the fuel used.
		The left member describes the energy of a linear oscillator with the implication of a solid nucleus in which the masses are bound in virtual orbits.
	www.pride-net.com /physics/FarthestStar/fstar3.htm (2096 words)

	conservation of energy & angular momentum in a comet orbit
		conservation of energy and angular momentum in a comet orbit
		The goal of this page is to guide the reader through a spreadsheet exercise that shows that the total energy (kinetic and gravitational) and the orbital angular momentum of a comet orbiting the sun are the same at each position in the comet's orbit.
		The total energy will be negative if the comet is bound to the sun, i.e., if it has an elliptical orbit and not a hyperbolic one; the total energy will be positive if the comet is unbound and has a hyperbolic orbit about the sun.
	www.phy.duke.edu /~kolena/comet.html (1835 words)

	Orbital Velocities (Site not responding. Last check: 2007-10-15)
		When the conservation of energy is applied to an orbiting body we have
		It is the total mechanical energy which determine the shape a bodies orbit - in particular the orbit's semimajor axis a.
		The equations describing hyperbolic orbits are basically the same except for a few signs associated with a.
	www.ac.wwu.edu /~vawter/PhysicsNet/Topics/Gravity/OrbitalVelocities.html (190 words)

	E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws
		They led to a deeper understanding of laws such as the principles of conservation of energy, angular momentum, etc., and also were instrumental in the great discoveries of gauge field symmetries of the 20th century.
		Physically in such theories one has a localized, conserved energy density; and one can prove that in any arbitrary volume the net outflow of energy across the boundary is equal to the time rate of decrease of energy within the volume.
		The energy balance locally cannot be discussed independently of the coordinates one uses to calculate it, and consequently different results are obtained in various different coordinate frames — some being artifacts of the calculation itself.
	www.physics.ucla.edu /~cwp/articles/noether.asg/noether.html (5320 words)

	Classical Orbits and Quantum Mechanics
		If an electron falls to a lower energy level, a photon escapes; by the conservation of energy, we know that the energy of this photon is equal to the energy the electron lost--that is, the difference between the higher energy level and the lower one.
		But we also know that the photon's energy is equal to Planck's constant times its frequency; thus, if we know what the energy levels are, we can figure out what the frequency should be.
		When the energy levels get close together, there isn't much "space" between them, so the photon's frequency is squeezed closer and closer to the orbital frequency.
	www.colorado.edu /physics/2000/quantumzone/frequency2.html (738 words)

	Humancafe's Bulletin Boards
		What this equation does is unify the various relationships between mass, electromagnetic energy, and gravity into an equation of Energy, showing how these components interact to become the matter of the observable universe.
		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 /discus/messages/70/108.html (16157 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Oct 22: Focault pendulum, components of tension force, small angle approximation, equations of motion in x'- and y'-components, ansatz for time-dependent coordinate rotation, decoupling of the differential equations, elliptic motion with superimposed rotation, precession period; CHPT.
		Nov 3: energy equation for the orbit and rederivation of the orbit equation, relation between total energy and orbit type; comet motion, astronomical units, eccentricity and orbital period, centrifugal and effective radial potential, 1-D radial equation of motion, turning points, minimal energy, bound and open orbit solutions;
		Nov 5: Rutherford scattering: repulsive Coulomb potential, orbit equation, impact parameter and scattering angle and their relation, differential cross section, derivation of Rutherford scattering formula, remark on deviations from the Rutherford behavior; CHPT.
	xray1.physics.sunysb.edu /~kirz/p303f03/phy303progress_f03.html (692 words)

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