General Theory of Relativity Essay Example for Free

General Theory of Relativity Essay The universe consists of many fascinating objects. Unfortunately, some of which cannot be known with just the naked eye. This is because it cannot be seen from Earth, and other technological advancements are needed to fully determine its nature. This is also the reason why several people have acquired false notions of what those objects are. One of those objects is the black hole. Science fiction films and and television shows have given the public a different view of black holes (Lochner 2006), poles apart from what they really are. This research paper seeks to discuss the definition and characteristics of black holes. Before the characteristics of a black hole can be discussed, it is first necessary to define what it is. An introduction is in order. So what is black hole? According to Lochner (2006), it is the â€Å"evolutionary end point of massive stars (p. 2). † There are stars which has sizes much bigger than that of the Sun. In fact, some of them are â€Å"at least 10 to 15 times as massive as the Sun (Lochner, 2006, p. 2). † When a star of this size sustains a supernova explosion, it leaves behind some stellar residue. Since in space there are no other forces to fight gravity, the residue will crumble unto itself. Lochner (2006) narrates, â€Å"The star eventually collapses to the point of zero volume and infinite density, creating what is known as a singularity (p. 2). † Eventually, density will increase; the light rays which is diffused by the star will then be encircling the star. â€Å"Any emitted photons are trapped into an orbit by the intense gravitational field; they will never leave it (Lochner, 2006, p. 2). † The moment the star reaches the point of no density, all the light is trapped. Hence, it is called the black hole. The phrase black hole was coined by John Archibald Wheeler (Bunn, 1995). Prior to that, the objects were called frozen stars (Bunn, 1995). Even in the time of Isaac Newton, the existence of objects as such has been thought of. Now it is more accurately explained using Einsteins General Theory of Relativity. This is â€Å"a geometric theory of gravitation, which incorporates and extends the theory of special relativity to accelerated frames of reference and introducing the principle that gravitational and inertial forces are equivalent (Lochner, 2006, p. 1). † This theory then explains the possibility for such occurrences like bent light caused by massive objects and the very nature of black holes. Such theory enables the event wherein â€Å"space and time become so warped that time practically stops in the vicinity of a black hole (Lochner, 2006, p. 1). † Black holes are identified to have an estimated mass of 4-15 Suns. Since black holes are formed after the death of a star, or supernova explosions, these explosions in turn have after-effects. These effects give way to X-ray binaries which is referred to as black hole candidates (Lochner, 2006, p. 1). Moreover, there exists galaxy-mass black holes. These massive black holes are usually placed in Active Galactic Nuclei, or AGN. AGN is a â€Å"class of galaxies which spew massive amounts of energy from their centers, far more than ordinary galaxies (Lochner, 2006, p. 1). † The black holes in question are said to have a mass of 10-100 billion Suns (Lochner, 2006, p. 1), a testament to how enormous they really are. The mass of one of these enormous black holes was recently determined by radio astronomy (Lochner, 2006, p. 1). The black hole has been portrayed by pop culture as one which sucks objects in; Lochner (2006) refers to the black holes inaccurate depiction as â€Å"a cosmic vacuum cleaner (p. 2). † He notes, â€Å"If our Sun was suddenly replaced with a black hole of the same mass, the earths orbit around the Sun would be unchanged Of course the Earths temperature would change, and there would be no solar wind or solar magnetic storms affecting us (Lochner, 2006, p. 2). † This is because a black hole can â€Å"exert the same force on something far away from it as any other object of the same mass would (Lochner, 2006, p. 1). † If in any instance, an object gets â€Å"sucked† into the hole, that very same object will pass through what is called â€Å"Schwarzschild radius (Lochner, 2006, p. 2). † â€Å"This is the radius r of the event horizon for a Schwarzschild black hole (Lochner, 2006, p. 2). † In the Schwarzschild radius, the escape speed and light speed is equal. Therefore, in the instance that light passes through, the light would not be able to escape. Say for example, a black hole with the same mass as the Sun, takes its place. Then the radius will still be different. The Suns radius is estimated at 700,000 km, while the Schwarzschild radius is only 3km (Lochner, 2006, p. 2). This would entail that the Earth must be of closer proximity to get sucked in a black hole in the center of our solar system. From where we are it is impossible to see the black holes. How do we then determine their existence? Since black holes are merely massive star remains, it would mean that they are of a small size. Also, because all the light gets trapped into itself, it would be impossible to see. Nonetheless, there are instances wherein a black hole can make itself perceivable. According to Lochner (2006), â€Å"if a black hole passes through a cloud of interstellar matter, or is close to another normal star, the black hole can accrete matter into itself. As the matter falls or is pulled towards the black hole, it gains kinetic energy, heats up and is squeezed by tidal forces. The heating ionizes the atoms and when the atoms reach a few million degrees Kelvin, they emit X-rays. The X-rays are sent off into space before the matter crosses the Schwarzschild radius and crashes into the singularity. Thus we can see this X-ray emission (p. 1). † Thus, black holes are dependent on other stars to make its presence known. The very same X-rays are also determinants of â€Å"black hole candidates (Lochner, 2006, p. 2). † It was said that a â€Å"companion star is a perfect source of infalling material for a black hole (Lochner, 2006, p. 2). † Because the X-ray sources are binary, a binary system is also enforced. This system makes the computation of the black hole candidates mass possible. The moment the mass is calculated, it can be deduced whether the said candidate is a black hole or a neuron star. What is a neuron star? It is â€Å"the imploded core of a massive star produced by a supernova explosion (Lochner, 2006, p. 2). † Now these neuron stars are characterized by masses which are estimated to be 1. 5 times more than the sun. Moreover, if there exists random variation of emitted X-rays, this is also a signifier of a black holes presence. Lochner (2006) states, â€Å"The infalling matter that emits X-rays does not fall into the black hole at a steady rate, but rather more sporadically, which causes an observable variation in X-ray intensity(p. 2). † In addition, â€Å"if the X-ray source is in a binary system, the X-rays will be periodically cut off as the source is eclipsed by the companion star (Lochner, 2006, p. 2). † All these characteristics are considered in identifying possible black hole candidates. For further identification, there are X-ray satellites which examines the skies for X-ray sources that may point out black hole candidates. For the longest time, there has been an identified black hole candidate in the name of Cygnus X-1 (Lochner, 2006, p. 2). â€Å"It is a highly variable and irregular source with X-ray emission that flickers in hundredths of a second (Lochner, 2006, p. 2). † When one exhibits such an irregularity, it becomes a black hole candidate. How? It is because it is impossible for an object â€Å"to flicker faster than the time required for light to travel across the object (Lochner, 2006, p. 2). † Lochner (2006) highlights this fact: â€Å"In a hundredth of a second, light travels 3000 kilometers. This is one fourth of Earths diameter (p. 2)! † From this, it can be concluded that the region from which the x-rays surrounding Cygnus X-1 are derived, is relatively small. Now Cygnus X-1 has a companion star with the name HDE 226868. This companion star is â€Å"a B0 supergiant with a surface temperature of about 31,000 K (Lochner, 2006, p. 2). † Now observations found that the spectral lines of HDE 226868, which is the â€Å"light given off at a specific frequency by an atom or molecule (Lochner, 2006, p. 2),† had been changing within 5. 6 days. It was also said that the mass of HDE 226868 is estimated to be 30 times greater than the Suns mass. This would mean that Cygnus X-1may possess at least a mass of 7 solar masses. Why 7 solar masses? This is what is required to create the tremendous gravitational pull that would result in the fluctuation in the spectral lines of HDE 226868. Astronomers thought that since 7 masses does not characterize a neuron star or a white dwarf, which is a star that has exhausted most or all of its nuclear fuel and has collapsed to a very small size, it must then be a black hole. However, this issue about Cygnus X-1being a black hole has also been surrounded by much skepticism. There is some speculation that the HDE 226868 may be too small for its spectral category, which in turn implies that Cygnus X-1is smaller than was previously declared. Moreover, uncertainty also shrouds the the mass calculations. It is because â€Å"uncertainties in the distance to the binary system would also influence mass calculations (Lochner, 2006, p. 2). † If the computations are inaccurate, the Cygnus X-1may end up only having 3 solar masses. If Cygnus X-1 has only 3 solar masses, it could be classified as merely being a neuron star, and not a black hole. The good news is that there are more binaries which reveal the possibility of a black hole, that which is much stronger than in Cygnus X-1 (Lochner, 2006, p. 2). In the year 1975, an X-ray transient known as A0620-00 was discovered. In the mid-80s, it was found that the mass of this object was more than 3. 5 solar masses. This fact alone eradicates the possibility of a neuron star, since neuron stars usually possess solar masses of 1. 5. In fact, the discovery of A0620-00 may have put into question the feasibility of other theories. Nonetheless, the best finding regarding black holes is V404 Cygni. This star was found to have an estimated 10 solar masses. Several journals have also written about the existence of black holes. In the 1995 edition of Annual Reviews of Astronomy and Astrophysics,there was a review conducted by Kormendy and Richstone, which implied the eight galaxies were thought to have â€Å"massive dark objects in their centers (Bunn, 1995, p. 1). † These cores were found to have masses which range from 1 million to several billion times that of the sun. Their massiveness was determined by noting how â€Å"the speed with which stars and gas orbit around the center of the galaxy: the faster the orbital speeds, the stronger the gravitational force required to hold the stars and gas in their orbits (Bunn, 1995, p. 1). † In fact, this is how astronomy usually measures masses. There are two reasons why these massive galactic centers were deemed as black holes. To begin with, the centers are â€Å"too dense and dark (Bunn, 1995, p. 1)† to even be considered as a group of stars, or just merely stars. â€Å"Second, the only promising theory to explain the enigmatic objects known as quasars and active galaxies postulates that such galaxies have supermassive black holes at their cores (Bunn, 1995, p. 1). † Even though these reasons point out that the galactic centers are really black holes, there is no sufficient evidence to prove it. Nonetheless, there is a continuous discovery for proofs that systems do include black holes. According to Bunn (1995), â€Å"a nearby active galaxy was found to have a water maser system (a very powerful source of microwave radiation) near its nucleus. Using the technique of very-long-baseline interferometry, a group of researchers was able to map the velocity distribution of the gas with very fine resolution (p. 1). † They also determined that the velocity was â€Å"less than half a light-year of the center of the galaxy (Bunn, 1995, p. 1). † It is from this fact that they deemed the object as a black hole, simply because only a black hole can have that much mass concentrated in such a small volume (Bunn, 1995, p. 1). All these results are included in January 12, 1995 issue of Nature, vol. 373. , as was reported by Miyoshi et al (Bunn, 1995, p. 1). Is there a possibility that the Sun can be a black hole? No. According to Bunn (1995), â€Å"only stars that weigh considerably more than the Sun end their lives as black holes (p. 1). † For about five billion years, the Sun will remain in its present state. After that, the Sun will undergo a phase wherein it will be a red giant star. The Sun will then end its life as a white dwarf star. If there are black holes, are there white ones? According to Bunn (1995), â€Å"the equations of general relativity have an interesting mathematical property: they are symmetric in time. That means that you can take any solution to the equations and imagine that time flows backwards rather than forwards, and youll get another valid solution to the equations. If you apply this rule to the solution that describes black holes, you get an object known as a white hole (p. 1). † If a black hole then pulls objects in, a white hole would then push things out. The former sucks in, the latter spits out. However, there is no proof that white holes exist, and there are no studies to point out if their existence is a possibility. There has also been speculations about the existence of what is called worm holes. What is a worm hole? It is â€Å"a theoretical opening in space-time that one could use to travel to far away places very quickly (Lochner, 2006, p. 2). † It is characterized by â€Å"two copies of the black hole geometry connected by a throat the throat, or passageway, is called an Einstein-Rosen bridge (Lochner, 2006, p. 2). † As is indicated in the definition, it is merely theoretical. There is no scientific basis nor experimental evidence for such existence. However, it is indeed amazing to think that such existence is possible. Do black holes disappear or evaporate? Even astronomers are not sure as to how black holes end their existence. Bunn (1995) notes that â€Å"Back in the 1970s, Stephen Hawking came up with theoretical arguments showing that black holes are not really entirely black: due to quantum-mechanical effects, they emit radiation. The energy that produces the radiation comes from the mass of the black hole. Consequently, the black hole gradually shrinks. It turns out that the rate of radiation increases as the mass decreases, so the black hole continues to radiate more and more intensely and to shrink more and more rapidly until it presumably vanishes entirely (p. 1)† This is a mere theory. There have been no proof or scientific conclusions as to how black holes really diminish. Black holes are just one of the many things included in the vast universe we are a part of. Thanks to science and the technological advancements at present, we can have greater awareness and knowledge of what is within our universe but beyond our reach. References Bunn, T. (1995). Black Hole FAQ List. Retrieved December 13, 2007, from http://cosmology. berkeley. edu/Education/BHfaq. html. Lochner, J. (2007). Black Holes. Retrieved December 13, 2007, from http://imagine. gsfc. nasa. gov/docs/science/know_l2/black_holes. html.

Strange Fits of Passion Essay -- Literary Analysis, Shakespeare

The lunatic, the lover, and the poet, are of imagination all compact. ~William Shakespeare, Mid-Summer Night's Dream, 1595, this quote by Shakespeare is a definitive illustration of Wordsworth’s persona in his poem Strange Fits of Passion I have known. In the poem the speaker embarks on a moonlight horse ride to his lover lucy’s cottage; it is during his ride there that the speaker engages in â€Å"lunatic† thoughts imagining lucy being dead when he arrives to see her. The poem is uniquely characterized by the adverse effects of love on a person, as well as how nature has an effect on human emotion; the latter being a staple theme in many of Wordsworth’s literary pieces. In the first stanza the speaker begins to vocalize the thought he had experienced while travelling to his lover’s cottage. Strange fits of passion have I known: And I will dare to tell, But in the Lover’s ear alone, What once to me befell. The speaker describes his sudden outburst of emotion as â€Å"strange† as he is keenly aware that his thoughts of lucy being dead are peculiar. It is common that when in love a person may pay heed to their imagination moreso than reality ; The line â€Å"But in the Lover’s ear aloneâ€Å"(Line three) is the speaker saying that he will share his â€Å"strange† thoughts but only to those who, like him, are in the throes of passion for they would understand the affects love can have on a person Wordsworth is known for his references to nature in many of his poems , the second stanza in this poem doesn’t stray from that commonality. When she I loved looked every day Fresh as a rose in June, I to her cottage bent my way, ... ...n his chest. The final stanza at last reveals the speaker’s thoughts that have been accumulating throughout the poem. What fond and wayward thoughts will slide Into a Lover’s head! â€Å"O mercy!† to myself I cried, â€Å"If Lucy should be dead!† Appalled at this final revelation it is apparent that the speaker has experienced similar thoughts and that sometimes despite great efforts your imagination can steer your thoughts to the contrary of rational thinking â€Å"What fond and wayward thoughts will slide ( Line 25) Into a Lover’s head! â€Å"(Line 26). Strange fits of passion is another poem by Wordsworth that uses nature as a medium when conveying human emotion but provides a unique portrayal of the absurdities of emotional experience that can evolve from passionate love.

Eulogy of Piggy Essay

Hello, my name is Ralph. We gather here today to remember our dearest friend, Piggy. Piggy was a misunderstood, brave boy with a big heart, only wanting what was best for his friends, who’s been taken from us by savagery, stupidity and pride. I hadn’t met Piggy before the crash. All I remember was waking up after it happened, and found a boy lying near a tree. When I walked over to him, we introduced each other. I told him my name was Ralph, and waited for a reply in return. But he hesitated to tell me his name was Piggy, as he thought I would I would tease him, but I told him that I would never tease him about it. Later we found the conch to help us locate the other boys who had survived. When we went around introducing ourselves to the others, they weren’t so lenient on teasing Piggy. Piggy was a strong and good hearted boy, especially when the others teased him, took his glasses or talked over him. Even though Jack and his hunters again and again pushed him to the edge, he would stand strong and not lose his temper, and I greatly respect him for not letting his pride or emotions give in to the bullies. Another thing I valued in Piggy was that he was always supportive in the things I did, even if they went wrong or if Jack had something negative to say about it. Piggy had so many good qualities, that no one ever noticed which will be greatly regretted by many. To be truly truthful, Piggy was the closet thingy I had to a best friend, and it kills me to know that I will never see him again, and I guess if he was here with us today, he would say keep you head up Ralph, and everything will be alright. Piggy will be sorely missed.

Battle of Harpers Ferry During the American Civil War

The Battle of Harpers Ferry was fought September 12-15, 1862, during the American Civil War (1861--1865). Background Following his victory at the Second Battle of Manassas in late August 1862, General Robert E. Lee elected to invade Maryland with the goals of resupplying the Army of Northern Virginia in enemy territory as well as inflicting a blow on Northern morale.   With Major General George B. McClellans Army of the Potomac mounting a leisurely pursuit, Lee split his command with Major Generals James Longstreet, J.E.B. Stuart, and D.H. Hill entering and remaining in Maryland while Major General Thomas Stonewall Jackson received orders to swing west then south to  secure Harpers Ferry.   The site of   John Browns 1859 raid, Harpers Ferry was situated at the confluence of the Potomac and Shenandoah Rivers and contained a Federal arsenal.   On low ground, the town was dominated by Bolivar Heights to the west, Maryland Heights to northeast, and Loudoun Heights to the southeast. Jackson Advances Crossing the Potomac north of Harpers Ferry with 11,500 men, Jackson intended to attack the town from the west.   To support his operations, Lee dispatched 8,000 men under Major General Lafayette McLaws and 3,400 men under Brigadier General John G. Walker to secure Maryland and Loudoun Heights respectively.   On September 11, Jacksons command approached Martinsburg while McLaws reached Brownsville approximately six miles northeast of Harpers Ferry.   To the southeast, Walkers men were delayed due to a failed attempt to destroy the aqueduct carrying the Chesapeake Ohio Canal over the Monocacy River.   Poor guides further slowed his advance. The Union Garrison As Lee moved north, he expected the Union garrisons at Winchester, Martinsburg, and Harpers Ferry to be withdrawn to prevent being cut off and captured.   While the first two fell back, Major General Henry W. Halleck, the Union general in chief, directed Colonel Dixon S. Miles to hold Harpers Ferry despite requests from McClellan for the troops there to join the Army of the Potomac.   Possessing around 14,000 largely inexperienced  men, Miles had been assigned to Harpers Ferry in disgrace after a court of inquiry found that he had been drunk during the First Battle of Bull Run the previous year.   A 38-year veteran of the US Army who had been brevetted for his role in the Siege of Fort Texas  during the Mexican-American War, Miles failed to understand the terrain around Harpers Ferry and concentrated his forces in the town and on Bolivar Heights.   Though perhaps the most important position, Maryland Heights was only garrisoned by around 1,600 men under Colonel Thomas H. Ford. The Confederates Attack On September 12, McLaws pushed forward Brigadier General Joseph Kershaws brigade.   Hampered by difficult terrain, his men moved along Elk Ridge to Maryland Heights  where they encountered Fords troops.   After some skirmishing, Kershaw elected to pause for the night.   At 6:30 AM the next morning, Kershaw resumed his advance with Brigadier General William Barksdales brigade in support on the left.   Twice assaulting the Union lines, the Confederates were beaten back with heavy losses.   Tactical command on Maryland Heights that morning devolved  to Colonel Eliakim Sherrill as Ford had taken  ill.   As the fighting continued, Sherrill fell when a bullet struck his cheek.   His loss shook his regiment, the  126th New York, which had only been in the army  three weeks.   This, coupled with an attack on their flank by Barksdale, caused the New Yorkers to break and flee to the rear. On the heights, Major Sylvester Hewitt rallied the remaining units and assumed a new position.   Despite this, he received orders from Ford at 3:30 PM to retreat back across the river even though 900 men from the 115th New York remained in reserve.   As McLaws men struggled to take Maryland Heights, Jackson and Walkers men arrived in the area.   In Harpers Ferry, Miles subordinates quickly realized that the garrison was surrounded and implored their commander to mount a counterattack on Maryland Heights.   Believing that holding Bolivar Heights was all that was necessary, Miles refused.   That night, he dispatched Captain Charles Russell and nine men from the 1st Maryland Cavalry to inform McClellan of the situation and that he could only hold out for forty-eight hours.   Receiving this message, the McClellan directed VI Corps to move to relieve the garrison and sent multiple  messages to Miles informing him that aid was coming.   These failed to arrive in time to inf luence events. The Garrison Falls The next day, Jackson commenced emplacing guns on Maryland Heights while Walker did the same on Loudoun.   While Lee and McClellan fought to the east at the ​​​Battle of South Mountain, Walkers guns opened fire on Miles positions around 1:00 PM.   Later that afternoon,  Jackson directed Major General A.P. Hill  to move along the west bank of the Shenandoah to threat Union left on Bolivar Heights.   As night fell, Union officers in Harpers Ferry knew that the end was approaching but remained unable to convince Miles to attack Maryland Heights.   Had they moved forward, they would have found the heights guarded by a single regiment as McLaws had withdrawn the bulk of his command to aid in blunting VI Corps advance at Cramptons Gap.   That night, against Miles wishes, Colonel Benjamin Davis led 1,400 cavalrymen in a breakout attempt.   Crossing the Potomac, they slipped around Maryland Heights and rode north.   In the course of their escape, they c aptured one of Longstreets reserve ordnance trains and escorted it north to Greencastle, PA. As dawn rose on September 15, Jackson had moved around 50 guns into position on the heights opposite Harpers Ferry.   Opening fire, his artillery struck Miles rear and flanks on Bolivar Heights and preparations commenced for an assault at 8:00 AM.   Believing the situation hopeless and unaware that relief was en route, Miles met with his brigade commanders  and made the decision to surrender.   This was met with some hostility from a number of his officers who demanded the opportunity to fight their way out.   After arguing with a captain from the 126th New York, Miles was struck in the leg by a Confederate shell.   Falling, he had so angered his subordinates that it initially proved difficult to find someone to carry him to the hospital.   Following Miles wounding, Union forces moved forward with the surrender. Aftermath The Battle of  Harpers Ferry saw the Confederates sustain 39 killed and  247 wounded  while Union losses totaled 44 killed, 173 wounded, and 12,419 captured.   In addition, 73 guns were lost.      The  capture of the Harpers  Ferry garrison represented the Union  Armys largest surrender of the  war and the US Armys largest until the fall of  Bataan in 1942.   Miles  died  from his wounds on September 16 and never  had to face the consequences for his performance.  Ã‚  Occupying the town, Jacksons men took possession of a large volume of Union  supplies and the arsenal.   Later that afternoon, he received urgent word from Lee to rejoin the main army at Sharpsburg.   Leaving Hills men to parole the Union prisoners, Jacksons troops marched north where they would play a key  role in the Battle of Antietam on September 17. Armies Commanders Union Colonel Dixon S. Milesapprox. 14,000 men Confederate Major General Thomas Stonewall Jacksonapprox. 21,000-26,000 men Selected Sources: Civil War Trust: Battle of Harpers FerryNational Park Service: Battle of Harpers FerryHistoryNet: Battle of Harpers Ferry