General Relativity - Revision history

WikiSysop: /* Gravity Near Black Holes */

2012-04-02T17:56:55Z

Gravity Near Black Holes

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	Visualizing gravity's effect on space		Visualizing gravity's effect on space
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	There is an effect on time too, and clocks near a large mass run slowly compared to those farther away. Even near Earth, a clock will slow down if you move it from the attic to the basement (not by much, but it can be measured!).		There is an effect on time too, and clocks near a large mass run slowly compared to those farther away. Even near Earth, a clock will slow down if you move it from the attic to the basement (not by much, but it can be measured!).

WikiSysop: /* Gravitational Lensing */

2012-04-02T17:54:50Z

Gravitational Lensing

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	[[File:emplanet_col.gif~~\|300px~~\|center]]		[[File:emplanet_col.gif\|center]]

	If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a [http://bustard.phys.nd.edu/MPS/ global network of telescopes] searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.		If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a [http://bustard.phys.nd.edu/MPS/ global network of telescopes] searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.

WikiSysop: /* Gravitational Lensing */

2012-04-02T17:54:16Z

Gravitational Lensing

← Older revision		Revision as of 17:54, 2 April 2012
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	[[File:emplanet_col.gif\|~~600px~~\|center]]		[[File:emplanet_col.gif\|300px\|center]]

	If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a [http://bustard.phys.nd.edu/MPS/ global network of telescopes] searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.		If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a [http://bustard.phys.nd.edu/MPS/ global network of telescopes] searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.

WikiSysop: /* Gravity Near Black Holes */

2012-04-02T17:53:48Z

Gravity Near Black Holes

← Older revision		Revision as of 17:53, 2 April 2012
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	To escape completely from the pull of gravity of planet, star, or black hole you would have to start with enough energy of motion to climb out of the "well". This determines the escape velocity, the minimum speed it would take to get away. For instance, to send a satellite beyond Earth we have to give it a speed of about 11 km/s. To escape the solar system from Earth's orbit takes 42 km/s, but to escape from the surface of the Sun takes 617 km/s. The escape velocity from R is		To escape completely from the pull of gravity of planet, star, or black hole you would have to start with enough energy of motion to climb out of the "well". This determines the '''escape velocity''', the minimum speed it would take to get away. For instance, to send a satellite beyond Earth we have to give it a speed of about 11 km/s. To escape the solar system from Earth's orbit takes 42 km/s, but to escape from the surface of the Sun takes 617 km/s. The escape velocity from R is

	[[File:escape_velocity.png\|200px\|center]]		[[File:escape_velocity.png\|200px\|center]]

	G is the constant of gravitation, which sets the strength of gravity in the universe. If R is very small, or if M is very big, it is possible for the escape velocity to be bigger than the speed of light. Matter cannot travel that fast. This means there must be objects so massive and so small that light cannot escape from them. That's a black hole.		G is the constant of gravitation, which sets the strength of gravity in the universe. If R is very small, or if M is very big, it is possible for the escape velocity to be bigger than the speed of light. Matter cannot travel that fast. This means there must be objects so massive and so small that light cannot escape from them. That's a '''black hole'''.

	To make a black hole the mass must all be inside a distance to make the escape velocity the speed of light. This distance is known as the Schwarzschild radius, after the astrophysicist who recognized the possibility even before Einstein completed General Relativity. The distance is		To make a black hole the mass must all be inside a distance to make the escape velocity the speed of light. This distance is known as the Schwarzschild radius, after the astrophysicist who recognized the possibility even before Einstein completed General Relativity. The distance is
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	Those of us outside watching you fall in would never see you reach the boundary. The closer you are to it, the more redshifted light from you will appear. It will seem to us that your clocks are slowing down, that time is stopping for you, as you reach the point of no return.		Those of us outside watching you fall in would never see you reach the boundary. The closer you are to it, the more redshifted light from you will appear. It will seem to us that your clocks are slowing down, that time is stopping for you, as you reach the point of no return.

	At the center of the black hole is the singularity, an infinitely small point of infinite density. It is hidden from us by the event horizon, the boundary defined by the Schwarzschild radius. We know now that suprmassive black holes exist in the nuclei of galaxies. One in the Milky Way is more than a million times the mass of the Sun, and there are larger ones in other active galaxies. There are also stellar mass black holes that result from a supernova and collapse of an evolved star. We think that these stellar mass black holes can merge in dense stellar environments like globular star clusters. Supermassive black holes are linked to the formation of galaxies, and one suggestion currently being explored is that they came first, formed in the primordial universe, and were the seeds about which galaxies grew.		At the center of the black hole is the '''singularity''', an infinitely small point of infinite density. It is hidden from us by the '''event horizon''', the boundary defined by the Schwarzschild radius. We know now that suprmassive black holes exist in the nuclei of galaxies. One in the Milky Way is more than a million times the mass of the Sun, and there are larger ones in other active galaxies. There are also stellar mass black holes that result from a supernova and collapse of an evolved star. We think that these stellar mass black holes can merge in dense stellar environments like globular star clusters. Supermassive black holes are linked to the formation of galaxies, and one suggestion currently being explored is that they came first, formed in the primordial universe, and were the seeds about which galaxies grew.

WikiSysop: /* Gravitational Waves */

2012-04-02T17:51:59Z

Gravitational Waves

← Older revision		Revision as of 17:51, 2 April 2012
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	When a mass moves, it creates ripples in spacetime that spread at the speed of light. The effect is like ripples on a pond, where the "pond" for gravitational waves is the spacetime of the entire universe. We have seen the indirect effect of gravitational waves in the effect of the energy they carry away from rapdily rotating neutron stars. Experiments are underway now to see the waves directly by detecting them with masses here on Earth with the Laser Interferometer Gravitational-Wave Observatory (LIGO).		When a mass moves, it creates ripples in spacetime that spread at the speed of light. The effect is like ripples on a pond, where the "pond" for gravitational waves is the spacetime of the entire universe. We have seen the indirect effect of gravitational waves in the effect of the energy they carry away from rapdily rotating neutron stars. Experiments are underway now to see the waves directly by detecting them with masses here on Earth with the [http://www.ligo.caltech.edu/ Laser Interferometer Gravitational-Wave Observatory] (LIGO).


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	When gravitational waves pass through LIGO's detector, they ripple spacetime, and change the distance between mirrors attached to test masses. The movement of the mirrors is detected by a laser. The system is so sensitive that micro-earthquakes or other nearby events create a constant background noise. LIGO has two detectors, one in Washington state, and another in Louisana, separated by 3200 km (2000 mi). The scientists are looking for events that occur simultaneously at both sites.		When gravitational waves pass through LIGO's detector, they ripple spacetime, and change the distance between mirrors attached to test masses. The movement of the mirrors is detected by a laser. The system is so sensitive that micro-earthquakes or other nearby events create a constant background noise. LIGO has two detectors, one in Washington state, and another in Louisana, separated by 3200 km (2000 mi). The scientists are looking for events that occur simultaneously at both sites.



	== Gravity Near Black Holes ==		== Gravity Near Black Holes ==

WikiSysop: /* Gravitational Lensing */

2012-04-02T17:51:15Z

Gravitational Lensing

← Older revision		Revision as of 17:51, 2 April 2012
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	[[File:emplanet_col.gif\|600px\|center]]		[[File:emplanet_col.gif\|600px\|center]]

	If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a global network of telescopes searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.		If there is a planet around the closer star, the planet's gravity will also create a lens. The sharp spike in this graph tells where the planet is and how big it is by the way in which the light brightens. There is a [http://bustard.phys.nd.edu/MPS/ global network of telescopes] searching for these "microlensing" events to use gravitational lenses to find "extrasolar" planets.



	== Gravitational Waves ==		== Gravitational Waves ==

WikiSysop: /* Sun's Gravity Bends Starlight During the 1919 Total Solar Eclipse */

2012-04-02T17:50:20Z

Sun's Gravity Bends Starlight During the 1919 Total Solar Eclipse

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	The 1919 total solar eclipse offered an opportunity to measure the apparent positions of stars whose light passed near the Sun. Einstein predicted that just as acceleration causes light to appear to follow a curved path, gravity would also bend beams of light from stars as the light passed close to the Sun. This is how he sketched what would happen in letter he wrote to American solar astronomer George Ellery Hale in 1913, urging a measurement of the effect. The small angle, 0.84 seconds of arc, is the change arising from Newton's theory of gravity. Einstein's theory of General Relativity was published 3 years later, in 1916, predicting twice the "classical" value.		The [http://www.wired.com/thisdayintech/2009/05/dayintech_0529/ 1919 total solar eclipse] offered an opportunity to measure the apparent positions of stars whose light passed near the Sun. Einstein predicted that just as acceleration causes light to appear to follow a curved path, gravity would also bend beams of light from stars as the light passed close to the Sun. This is how he sketched what would happen in letter he wrote to American solar astronomer George Ellery Hale in 1913, urging a measurement of the effect. The small angle, 0.84 seconds of arc, is the change arising from Newton's theory of gravity. Einstein's theory of General Relativity was published 3 years later, in 1916, predicting twice the "classical" value.


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	General Relativity explains gravity in an entirely new way. In Einstein's view, gravity is a distortion of space and time caused by mass. We'll see that time runs slower when there is mass present. The bending of the path of starlight near the Sun occurs because the Sun curves the spacetime through which the starlight passes.		General Relativity explains gravity in an entirely new way. In Einstein's view, gravity is a distortion of space and time caused by mass. We'll see that time runs slower when there is mass present. The bending of the path of starlight near the Sun occurs because the Sun curves the spacetime through which the starlight passes.

	In 1976 to 1977, when Mars was on the far side of the Sun seen from Earth, radio signals between the Viking spacecraft on Mars surface and stations on Earth passed very close to the Sun. The signals were delayed by the effect of the Sun's gravity on spacetime, and the measurements matched the prediction of General Relativity to within 0.1%.		In 1976 to 1977, when Mars was on the far side of the Sun seen from Earth, radio signals between the Viking spacecraft on Mars surface and stations on Earth passed very close to the Sun. The signals were delayed by the effect of the Sun's gravity on spacetime, and the measurements matched the prediction of [http://en.wikipedia.org/wiki/Introduction_to_general_relativity General Relativity] to within 0.1%.



	== Mercury's Orbit is Influenced by the Relativity of Sun's Gravity ==		== Mercury's Orbit is Influenced by the Relativity of Sun's Gravity ==

WikiSysop: /* Light, Gravity, and Elevators */

2012-04-02T17:49:15Z

Light, Gravity, and Elevators

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	Near Earth's surface, gravity accelerates mass at 9.8 meters/second each second (9.8 m/s2). Drop a ball, and for each second of fall the ball speeds up by 9.8 meters/second. According to the '''principle of equivalence''', if an elevator far out in space accelerates at 9.8 m/s2, the person inside will feel the same as he would if he were standing on Earth. The acceleration cannot be distinguished from gravity.		Near Earth's surface, gravity accelerates mass at 9.8 meters/second each second (9.8 m/s<sup>2</sup>). Drop a ball, and for each second of fall the ball speeds up by 9.8 meters/second. According to the '''principle of equivalence''', if an elevator far out in space accelerates at 9.8 m/s2, the person inside will feel the same as he would if he were standing on Earth. The acceleration cannot be distinguished from gravity.

	Imagine first a beam of light when there is no motion such as the image on the left. Inside the elevator, the beam goes straight across and strikes the opposite wall. It follows a straight path parallel to the floor.		Imagine first a beam of light when there is no motion such as the image on the left. Inside the elevator, the beam goes straight across and strikes the opposite wall. It follows a straight path parallel to the floor.

WikiSysop: /* Light, Gravity, and Elevators */

2012-04-02T17:48:39Z

Light, Gravity, and Elevators

← Older revision		Revision as of 17:48, 2 April 2012
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	Near Earth's surface, gravity accelerates mass at 9.8 meters/second each second (9.8 m/s2). Drop a ball, and for each second of fall the ball speeds up by 9.8 meters/second. According to the principle of equivalence, if an elevator far out in space accelerates at 9.8 m/s2, the person inside will feel the same as he would if he were standing on Earth. The acceleration cannot be distinguished from gravity.		Near Earth's surface, gravity accelerates mass at 9.8 meters/second each second (9.8 m/s2). Drop a ball, and for each second of fall the ball speeds up by 9.8 meters/second. According to the '''principle of equivalence''', if an elevator far out in space accelerates at 9.8 m/s2, the person inside will feel the same as he would if he were standing on Earth. The acceleration cannot be distinguished from gravity.

	Imagine first a beam of light when there is no motion such as the image on the left. Inside the elevator, the beam goes straight across and strikes the opposite wall. It follows a straight path parallel to the floor.		Imagine first a beam of light when there is no motion such as the image on the left. Inside the elevator, the beam goes straight across and strikes the opposite wall. It follows a straight path parallel to the floor.

WikiSysop: /* Light, Gravity, and Elevators */

2012-04-02T17:48:03Z

Light, Gravity, and Elevators

← Older revision		Revision as of 17:48, 2 April 2012
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	Einstein's Special Theory did not explain gravity, but it created a framework for understanding space and time. The General Theory of Relativity provides a description of gravity quite different from Newton's. It rests on a simple idea:		Einstein's Special Theory did not explain gravity, but it created a framework for understanding space and time. The [http://www.youtube.com/watch?v=0rocNtnD-yI&feature=related General Theory of Relativity] provides a description of gravity quite different from Newton's. It rests on a simple idea:

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	As a consequence, in a freely falling elevator or spacecraft you do not feel gravity and seem "weightless", although gravity from the Earth is still present. Astronauts working on the Hubble Telescope do not experience gravity because they are falling freely as they orbit Earth. On the final Hubble repair mission astronauts will feel weightless as they prepare the telescope for 5 more years of use. Gravity will be pulling on them, keeping them in orbit around Earth, and their acceleration will cancel gravity from their point of view.		As a consequence, in a freely falling elevator or spacecraft you do not feel gravity and seem "weightless", although gravity from the Earth is still present. [http://www.youtube.com/watch?v=0bjhDN5b5J4 Astronauts working on the Hubble Telescope] do not experience gravity because they are falling freely as they orbit Earth. On the [http://www.youtube.com/watch?v=CYLMXCqkuBg final Hubble repair mission] astronauts will feel weightless as they prepare the telescope for 5 more years of use. Gravity will be pulling on them, keeping them in orbit around Earth, and their acceleration will cancel gravity from their point of view.

	In an elevator such as shown here, the beam of a flashlight will behave differently depending on the motion of the elevator, at rest, at constant velocity, or accelerating.		In an elevator such as shown here, the beam of a flashlight will behave differently depending on the motion of the elevator, at rest, at constant velocity, or accelerating.
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	Since acceleration and gravity have equivalent effects, it must be that gravity also curves the path of light.		Since acceleration and gravity have equivalent effects, it must be that gravity also curves the path of light.




	== Sun's Gravity Bends Starlight During the 1919 Total Solar Eclipse ==		== Sun's Gravity Bends Starlight During the 1919 Total Solar Eclipse ==