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	Schwarzschild radius - Wikipedia, the free encyclopedia
		The Schwarzschild radius of an object is proportional to the mass.
		The Schwarzschild radius of a sphere with a uniform density equal to the critical density is equal to the radius of the visible universe.
		The Schwarzschild radius is proportional to the mass, with a proportionality constant involving the gravitational constant and the speed of light.
	en.wikipedia.org /wiki/Schwarzschild_radius (698 words)

	Black Hole
		Gravitational collapse begins when a star has depleted its steady sources of nuclear energy and can no longer produce the expansive force, a result of normal gas pressure, that supports the star against the compressive force of its own gravitation.
		The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating fl hole, but this was not well understood at that time.
		For example, the radius of a Schwarzschild fl hole is two gravitational radii and the radius of a maximally rotating Kerr fl hole is one gravitational radius.
	www.juliantrubin.com /encyclopedia/astronomy/blackhole.html (5575 words)

	Schwarzschild radius - Biocrawler (Site not responding. Last check: 2007-10-23)
		The Schwarzschild radius or gravitational radius is a characteristic radius associated with every mass.
		The Schwarzschild radius is proportional to the mass.
		The Schwarzschild radius is proportional to the mass, with a proportional constant involving the gravitational constant and the speed of light.
	www.biocrawler.com /encyclopedia/Schwarzschild_radius (666 words)

	The Astrophysics Spectator: The Point Gravitational Lens of a Star
		This lens is a point gravitational lens, because it behaves as though all of the mass of the gravitating object were concentrated at the very center of the lens.
		The structure of a point gravitational lens depends only on the mass of the central object, and the only role the radius of the central source plays is to set the minimum distance a lens must be from us to produce an image of a more distant object.
		For a main-sequence star, the radius of the star is very roughly proportional to the mass, so the minimum distance one must be from a main sequence star to see its lens is about the same for all stars.
	www.astrophysicsspectator.com /topics/generalrelativity/GravitationalLensPoint.html (1291 words)

	Black Hole Conditionis (Site not responding. Last check: 2007-10-23)
		This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass.
		Since it is reduced in frequency, this is called the gravitational red shift or the Einstein red shift.
		Actually, Schwarzchilds's calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression
	hyperphysics.phy-astr.gsu.edu /hbase/relativ/blahol.html (166 words)

	Electromagnetic Gravitational Interaction
		The gravitational field created by all masses of our metagalaxy is the aether in which cosmic objects moves and electromagnetic oscillations are propagated.
		Appearance of all mentioned effects is caused by the simultaneous presence of electric, magnetic and gravitational fields in the area of the converter.
		Magnetogravitational converter transforms gravitational energy of space-time into energy of electric field which in its turn is transformed into mechanical energy of the rotating magnetic system and electric energy of the load.
	www.uic.nnov.ru /~kovy2/conf_in.htm (1513 words)

	[No title]
		D. It meant mass Mbh- and radius Rbh- form a new fl hole, which is less than a fl hole of mass Mbh and radius Rbh, by a factor of the square root of the Golden Ratio for both Mbh- and Rbh-.
		A HIGH mass gravitational event and a LOW mass event are thus arbitrarily created from the same Mbh term, which is the mass of a fl hole confined in the Sun's radius.
		Radius R is the radius of the Sun.
	www.textfiles.com /occult/relative.3 (4548 words)

	2 Light curves in gravitational lensing (Site not responding. Last check: 2007-10-23)
		The amplitude, the shape and the duration of flares of the lensed object are defined by the relationships between the parameters of the binary system, the major semiaxis a, the masses and radii of the components and the orbital plane orientation.
		The luminosity magnification of a uniformly radiating disk in gravitational lensing was analysed in detail in the papers by Refsdal (1964), Liebes (1964), Byalko (1969), Ingel (1972, 1974), Maeder (1973) and Agol (2002).
		Since in gravitational lensing, the surface brightness remains constant, the light curve is determined as variation of the ratio of the image areas and the source itself, depending on the position of the binary system components with respect to the observer, which varies during the period of rotation.
	www.edpsciences.org /articles/aa/abs/2002/41/aa2132/node2.html (1755 words)

	Black hole - Wikipedia, the free encyclopedia
		Under the description provided by general relativity, as an object moves closer to a fl hole, the energy required for it to escape continues to increase until it becomes infinite at the event horizon, the surface beyond which escape is impossible.
		According to general relativity, a gravitating object will collapse into a fl hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius.
		An object with mean density greater or equal to the critical density and with a radius equal to that of the observable universe is a fl hole.
	en.wikipedia.org /wiki/Black_hole (5400 words)

	Physics 11 Lecture Notes - General Relativity & Black Holes (Site not responding. Last check: 2007-10-23)
		Gravitational lenses have rather different properties than "normal" lenses producing multiple images such as the Einstein Cross, a case of a distant quasar imaged by a galaxy between us and the quasar, discovered by J. Huchra and colleagues, shown to the left.
		Predicted sources of strong gravitational waves in the Galaxy are supernova explosions, collapsing stellar cores as they form neutron stars or fl holes, compact binary star systems, collisions of neutron stars and fl holes, or possibly material falling into the blavk hole which may reside in the Galactic Center.
		Gravitational waves have not yet been detected directly, but we believe that they have been detected indirectly by radio astronomers in the binary pulsar system 1913+16.
	cassfos02.ucsd.edu /physics/ph11/lectures/GR.html (3341 words)

	Orbits in Strongly Curved Spacetime (Site not responding. Last check: 2007-10-23)
		Kepler's laws of planetary motion, grounded in Newton's theory of gravity, state that the orbit of a test particle around a massive object is an ellipse with one focus at the centre of the massive object.
		Notice that the test mass radius moves in lockstep on the two charts, as the radius varies on the orbit plot to their right.
		Third law (1618): The square of the orbital period of a planet is proportional to the cube of the major axis of the orbit.
	www.fourmilab.to /gravitation/orbits (2354 words)

	Glossary
		In the simplest case, this surface is described by a sphere with a gravitational radius.
		force of gravitation of an atom-sized fl hole is compared to the force of gravity of the Earth at the distance of one kilometer.
		Gravitational radius of the Earth is equal to one centimeter.
	homepages.nsys.by /~oton/Glossary.htm (439 words)

	0508 - Kanarev - The Foundations of Physchemistry of Microworld
		The possibility of the photon to overcome the gravitational force is increased in the same degree, but it is not taken into account in the formula (89).
		Actually it means that it is necessary to equate the gravitation radius to the wave length of the photon.
		The photons from the infrared range of the spectrum will be the first to be retarded; as the gravitational radius is reduced, the photons of the light, ultraviolet, roentgen and gamma ranges will be retarded.
	guns.connect.fi /innoplaza/energy/story/Kanarev/book/0508.html (2152 words)

	ch17
		At a distance of a few thousand kilometers from the fl hole, the gravitational forces on the probe would be so great that the side of the probe closest to the fl hole would literally be torn away from the side furthest away from the fl hole.
		Near the gravitational radius the matter will be swirling around at speeds close to the speed of light, and temperatures ranging from tens of millions to perhaps as much as a billion degrees are expected.
		Furthermore, since a blob of matter near the gravitational radius would be orbiting the fl hole about once every millisecond, the X-radiation might be expected to show erratic, short-term variability.
	history.nasa.gov /SP-466/ch17.htm (1686 words)

	Janusz Laski, Planetary systems and the Bohr atom model
		In a particular case when the angular velocity and the orbit radius are a constant, the equation (4) means a circular orbit.
		Balance of gravitational force, on the one hand, and the centrifugal (mass) force, on the other hand, determines orbit stability for one mass object revolving around another mass object.
		Gravitational attraction between a proton and an electron is much smaller than the corresponding Coulomb force, however the centrifugal mass force is much greater then the corresponding centrifugal magnetic force.
	www.januszlaski.com /lecture.1.html (1504 words)

	Physics 7 Homework Answers #6 (Site not responding. Last check: 2007-10-23)
		The sun's gravitational force attracts the planets, causing them to follow elliptical orbits through the solar system." Einstein might reply: ``Your theory is all right as far as it goes, but to understand truly large gravitational fields one will see that matter (regardless of form) curves space and objects follow the curved path of space-time.
		Gravitational Redshift --- light loses energy as it escapes from a gravitational field, hence is shifted toward longer (redder) wavelength.
		Gravitational redshift will cause transmissions from the spaceship to be shifted toward longer and longer wavelengths as the ship approaches the fl hole.
	cassfos02.ucsd.edu /physics/ph7/hw/hw6_ans.html (1532 words)

	Relativity
		The new theory of gravitation, the general theory of relativity, adopts this characteristic of the gravitational field as its foundation.
		Thus, the primary result from general relativity is that gravitation is a purely geometric consequence of the properties of spacetime.
		Schwarzschild radius is the radius below which the gravitational attraction between the particles of a body must cause it to undergo irreversible gravitational collapse.
	zebu.uoregon.edu /~js/21st_century_science/lectures/lec07.html (1833 words)

	Solutions to HW #5 for Chapters 12 - 14 (Site not responding. Last check: 2007-10-23)
		The gravitational influence of mass contained within an orbit of a particular size determines the speed (and therefore period) of that orbit.
		If a higher mass is enclosed within the same radius, the gravitational force on the orbiting (much less massive) object is larger, and the orbital velocity required to keep it in orbit (rather than falling) is larger.
		Gravitational lensing of quasars (producing multiple images of a single quasar) implies the quasar is at a greater distance than the galaxy or material causing the lensing.
	setiathome.ssl.berkeley.edu /~korpela/astro10/notes/solns/soln5.html (3610 words)

	[No title]
		Once a mass gravitating towards the core passes the point represented by (2.5), or as approximated by (2.6), it starts to be decelerated by the positive acceleration resulting from its velocity through the spatial gradient of the temporal rate generated by the core.
		Of course, if this material is limited, the gravitational radius will become constant while the physical boundary of the Universe will start to shrink under the gravitational influence of the core.
		Hence the minimum contraction radius of the Universe at the point of inflexion is given by (2.20), and expansion in the remainder of Phase II starts from that radius.
	www.relativitydomains.com /Cosmology/Assoc2/FurtherCosmology.htm (1454 words)

	The Anatomy of Black Holes - Page 2
		According to Einstein, infinite gravitational force occurs as the radius of the moon approaches the so-called "gravitational radius" of the body (which can be far from being point-size).
		The size of the gravitational radius is determined by the amount of mass: the smaller the mass, the smaller the gravitational radius.
		Only when the compressed radius of the object approaches its gravitational radius do the values calculated by the two theories begin to differ significantly...and the value given by Einstein’s theory proves to be the correct one.
	imagine.gsfc.nasa.gov /docs/teachers/blackholes/imagine/page2.html (646 words)

	Cepheid Variable Velocity Graph Analysis
		Since Newton's Laws show that only the mass and radius of an object are involved in establishing the surface gravity of any celestial object, this slope value seems to represent an extremely accurate value which can be used to establish either the radius or the mass if the other is known.
		If the radius of RT Aurigae is around the 26 million km that is currently accepted, then the variation of 2.2 million km in star radius represents about an 8% change in radius.
		The gravitational local acceleration should therefore be around 17% weaker at the maximum radius as it is at the minimum radius.
	mb-soft.com /public2/cepheid.html (1827 words)

	The Moon Always Falls Towards the Sun
		This table shows that our Moon is unique among all the satellites of the planets, is so far as it is the only planetary satellite whose orbital radius exceeds the threshold value, which means it is the one satellite on which the Sun's gravitational acceleration exceeds the host planet's gravitational acceleration.
		It stands to reason that most stable moons would be situated in orbits such that the gravity of the host planet is stronger than the Sun's gravity, because otherwise there would be a tendency for the bodies to become separated.
		The radius of Pluto's orbit is about 39 AU, so this is well inside the threshold (by a factor of about 45).
	www.mathpages.com /home/kmath405/kmath405.htm (818 words)

	Einsteins field equations and Black Holes
		He mailed his paper "On the Gravitational Field of a Point Mass according to Einsteinian theory" to Einstein in 1916, and within a half year he died because of illness catched in the war (see [8] p.
		If all the mass is concentrated inside the gravitational radius, we have a spherical symmetric Black Hole, where all the geometric distortion effects can be experienced by falling particles...
		The impact parameter is a function of the tangent of the angle between the trajectory and the direction to the center of the Black Hole.
	members.tripod.com /~albert51/non.html (1473 words)

	Schwarzschild Geometry
		Curiously, the Schwarzschild radius had already been derived (with the correct result, but an incorrect theory) by John Michell in 1783 (this reference is from Erk's Relativity Pages) in the context of Newtonian gravity and the corpuscular theory of light.
		Inside the Schwarzschild radius, proper radial distances and proper times appear to become imaginary (that is, the square root of a negative number).
		Spacetime itself is well-behaved at the Schwarzschild radius, as can be ascertained by computing the components of the Riemann curvature tensor, all of whose components remain finite at the Schwarzschild radius.
	casa.colorado.edu /~ajsh/schwp.html (2298 words)

	Chapter 9: Black Holes
		At the Schwarzschild radius the gravitational time dilation goes to infinity and lengths are contracted to zero.
		A gravitational lens is produced when light passes through the enormous gravitational field of an object, such as a massive galaxy.
		Gravitational redshift has been measured for light falling toward the Earth, and a slight frame-dragging effect occurs even for objects such as the Earth and Sun.
	astsun.astro.virginia.edu /~jh8h/Foundations/chapter9.html (1011 words)

	Wormholes and Galaxies.
		Schwarzschild Radius also called gravitational radius, distance that defines the size at which a spherical astronomical object such as a star becomes a fl hole.
		The formula for the Schwarzschild radius of a body is the Schwarzschild radius of the body, G is a constant known as the universal constant of gravitation, M is the mass of the object, and c is the speed of light.
		To find the equation for the Schwarzschild radius of an object, Schwarzschild needed to know how massive a body has to be to keep light from escaping and how light behaves in such a strong gravitational field.
	myweb.tiscali.co.uk /newuniverse/real_galaxies.html (1658 words)

	Gravity due to Space Flow
		In the paper the gravity is explained by means of a space flow falling into a mass, and on the idea of the gravitational acceleration identical with the acceleration of the spaceflow speed.
		The mass, defined by means of the flow of the space is a physical quantity complying with both inertial and gravitational properties of the mass.
		The two principal experiments confirming the theory of general relativity, the bending of the light rays, and, the shift of the culminating points of the free objects, in gravitational field, are confirmed by the spaceflow theory as well.
	spaceflow.sk /index.html (1431 words)

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