Physics 9. Space Syllabus Notes Physics Coe Topic 9. Space Summay of Contextual Outline Scientists daw on othe aeas of science to deelop iable spacecaft Launch, e enty and landing ae dangeous Huge foces aea equied to enable a spacecaft to escape the Eath s gaitational field o maintain an obit Rapid adances in technology allows fo the exploation of the Uniese Space eseach has impacted on society though deelopment of elated technologies 1. The Eath has a gaitational field that exets a foce on objects both on it and aound it Students lean to: Define weight as the foce on an object due to a gaitational field Weight is defined as the foce on a mass due to the gaitational field of a lage celestial body, such as the Eath. It is a foce and it is measued in Newtons. We can deie F = mg fom Newton s Second Law of Motion, F = ma. Explain that a change in gaitational potential enegy is elated to wok done Gaitational potential enegy is the enegy that a mass possess due to its position within a gaitational field. Gaitation is a foce of attaction, and if an object in the Eath s gaitational field is moed futhe away fom the cente of the Eath, wok must be done on the object. That is, the object gains gaitational potential enegy because it moes against the field. Conesely, if an object moes close to the cente of the Eath, some of its gaitational Gaitational potential enegy is the enegy of a mass due to its position within a gaitational field. Because gaitation is a foce of attaction, if an object is moed fom a point in the Eath s gaitational field to a point futhe away fom the cente of the Eath, wok must be done on the object; that is, the object moes against the field, and so it gains gaitational potential enegy. Conesely, if an object moes close to the cente of the Eath, some of its gaitational potential enegy is changed into kinetic enegy. In such a case, wok is done by the object instead of on the object. Define gaitational potential enegy as the wok done to moe an object fom a ey lage distance away to a point in a gaitational field: m1m E p = G Gaitational potential enegy is the enegy of a mass due to its position within a gaitational field. Due to the inese squae elationship in the Law of Uniesal Gaitation, the foce of attaction between a planet and an object will become zeo only at an infinite distance away fom the planet. We theefoe define infinity (o some point a ey lage distance away) as the leel of potential enegy. Because wok is done on an object (that is, enegy is gien to the object) when it is moed to infinity, all objects within a gaitational field hae a negatie gaitational potential enegy. Students: Pefom an inestigation and gathe infomation to detemine a alue fo acceleation due to gaity using pendulum motion o compute assisted technology and identify eason fo possible aiations fom the alue 9.8 ms 1. Pendulum motion: 1
Physics 9. Space Syllabus Notes When a pendulum swings with a small angle, the mass on the end undegoes a motion l called simple hamonic motion. The peiod of the pendulum is gien by T = π. g Measue the length of the pendulum fom the knot at it top to the base of the mass caie 30 maximum deiation fom etical Use stopwatch to time 10 complete back and foth swings Stat and stop stopwatch at exteme instead of somewhee in the middle Adjust length of sting Gaph of esults: Plot T on the etical axis and length l on the hoizontal axis; gadient can be used to find the alue of g Vaiations in the alue of g: The Eath s cust o lithosphee shows aiations in thickness and stuctue due to tectonic plate boundaies and dense mineal deposits. The Eath is not a pefect sphee, but is flattened at the poles. This means that the alue of g will be geate at the poles, since they ae close to the cente of the Eath. The spin of the Eath ceates a centifuge effect that educes the effectie alue of g. the effect is geatest at the Equato and thee is no effect at the poles. Vaiation with altitude: the futhe away fom the cente of the Eath, the lowe the me alue of g, as gien by: g = G (E + altitude) Gathe seconday infomation to pedict the alue of acceleation due to gaity on othe planets The fomula used hee is g = G mplanet planet Analyse infomation using the expession F = mg to detemine the weight foce fo a body on Eath and fo the same body on othe planets. Many factos hae to be taken into account to achiee a successful ocket launch, maintain a stable obit and etun to Eath Students lean to: Descibe the tajectoy of an object undegoing pojectile motion within the Eath s gaitational field in tems of hoizontal and etical components A pojectile is any object that is pojected into the ai and then left to complete its flight unde the influence of only one foce, the foce of gaity. The tajectoy is the path that is takes, and in the absence of ai esistance, the path of the flight of a pojectile will tace out the shape of a paabola. In analysing this motion, we obsee that the motion of a pojectile can be egaded as two sepaate and independent motions supeimposed upon each othe. The fist is a etical motion, which is subject to acceleation due to gaity, and the second is a hoizontal motion, which expeiences no acceleation. Because the two motions ae pependicula, and theefoe independent, we can teat them sepaately and analyse them sepaately. Descibe Galileo s analysis of pojectile motion Galileo postulated that all masses, whethe lage o small, fall at the same ate. Pojectiles ae pojected into the ai and then left to complete thei flight in feefall. Thoughout the flight, the pojectile is subject only to the acceleation due to gaity, g. This ate of acceleation applies to all objects, lage o small. All objects ae acceleated towads the Eath
Physics 9. Space Syllabus Notes at the same ate. Galileo ealised that the natual shape of pojectile motion was that of the paabola. Galileo conducted expeiments to ty to poe this. Howee, ai esistance intefeed with his esults. He eentually oecame this by olling balls down highly polished inclines, which educes the effectie acceleation; this lowe ate of acceleation was less affected by ai esistance and was easie to measue. Explain the concept of escape elocity in tems of the a) gaitational constant b) mass and adius of the planet By consideing the kinetic and gaitational potential enegy of a pojectile, it can be shown mathematically that the escape elocity of a planet depends only upon the uniesal gaitational constant G, the mass and adius of the planet. To escape the gaitational field of the planet, the pojectile must hae positie enegy, which means that the magnitude of the pojectile s kinetic enegy must be geate than the magnitude of its gaitational potential 1 m m enegy. Mathematically, mo > G o e, whee m 0 and and Eath espectiely. This educes to Escape elocity = only the mass and adius of the planet. m e ae the masses of the object Gm e e, which is detemined by Outline Newton s concept of escape elocity If we thow an object up, it will ise to a cetain height befoe falling back to Eath. If thown faste, it will ise highe. The easoning behind escape elocity is that if the object is thown fast enough, it should ise up and continue to ise, slowing down but nee etuning to Eath. It will come to est only when it has completely escaped the Eath s gaitational field (at infinity). Identify why the tem g foces is used to explain the foces acting on an astonaut duing launch The tem g foce is used to expess a peson s appaent weight as a multiple of his/he nomal tue weight, the weight when standing on the suface of the Eath. The sensation of weight a peson feels is the appaent weight, which is equal to the sum of the foces esisting the tue weight, including the nomal eaction foce fom the floo, and the tust of a ocket engine. Thus, duing launch, the floo meets the astonaut s downwad weight foce with an upwad eaction foce, and in addition, the floo exets an upwad acceleating foce. The astonaut s appaent weight is geate than his/he nomal weight, and this is expessed as a multiple of g. Discuss the effect of the Eath s obital motion and its otational motion on the launch of a ocket By addition of ectos, a moing platfom offes a boost to the elocity of a pojectile launched fom it, if launched in the diection of motion of the platfom. Because the Eath is eoling aound the Sun, and is otates aound its axis once pe day, the Eath is itself a moing platfom with two diffeent motions to be exploited in a ocket launch to gain a boost in elocity. To achiee the elocity needed fo a stable obit, the ocket can be launched in the diection of the Eath s otation, that is, towads the east. In this way, the otational elocity of the launch site elatie to the Sun will add to the obital elocity of the ocket elatie to the Eath, to poduce a highe obital elocity elatie to the Sun. In the same way, enginees planning a ocket mission heading futhe into space can exploit the Eath s eolution aound the Sun by planning the launch fo a time of yea when the diection of the Eath s obital elocity coesponds to the desied heading. The ocket poceeds in its obit until the diection of its obital elocity coesponds to that of the Eath. 3
Physics 9. Space Syllabus Notes In this way, the Eath s obital elocity elatie to the Sun adds to the ocket s obital elocity elatie to the Eath, to poduce a highe elocity achieed by the ocket elatie to the Sun. Analyse the changing acceleation of a ocket duing launch in tems of the a) Law of Conseation of Momentum a) foces expeienced by astonauts The Law of Conseation of Momentum states that duing any inteaction in a closed system the total momentum of the system emains unchanged, which means that duing a lunch, the magnitude of the momentum of the gases shooting out the back must be equal to the momentum of the ocket itself. Total change in momentum = 0 p = gases p ocket ( m ) gases = ( m) ocket Hence, the mass of the gases duing any gien second is less than the mass of the ocket, which means that the elocity gained by the ocket is less than that of the gases. Howee, as the mass of the ocket deceases as fuel is bunt, change in elocity will incease. Rockets that use liquid fuel engines can be thottled, which gies the ocket the ability to ay the launch thust between 50% and 100%. Pio to lift off, a ocket has zeo acceleation, because of the balance that exists between the weight foce and the eaction foce plus the thust. The astonaut thus expeiences a one g load. This initial condition will not change until the building thust exceeds the weight of the ocket, and which point the ocket will lift off. Since thust now exceeds weight, thee is net foce acting upwads on the ocket, and so it acceleates upwads. The g foce expeienced by the astonauts will hae a alue slightly geate than one. Howee, as fuel is bunt, the acceleation inceases, and so the astonauts will expeience highe g foces. Multi stage ockets dop the spent stage away, and expeience zeo g conditions momentaily, acting as a pojectile. The next stage fies and the ocket deelops the necessay thust to exceed the effectie weight at its altitude, and stats to acceleate again, with the g foces expeienced gadually building to a maximum alue. This pocess is epeated fo each stage of the ocket. In ode to aoid exteme g foces, thee is a sequential shutdown of the multiple ockets of each stage. Compae qualitatiely low Eath and geo stationay obits Low Eath obit A low Eath obit is geneally an obit highe than 50 km, in ode to aoid atmospheic dag, and lowe than 1000 km, which is the altitude at which the Van Allen adiation belts stat to appea At 50 km, an obiting spacecaft takes just 90 minutes to complete an obit Space shuttle utilises a low Eath obit between 50 km and 400 km Geostationay obit The altitude is about 35 800 km (adius of obit aound 4 000 km, then subtacting the adius of the Eath), detemined by using Keple s Law of Peiods Peiod of the obit matches that of the Eath; if oe the equato, it will emain stationay oe a fixed point Paticulaly useful fo communications satellites because eceiing dishes only need to point to a fixed spot in the sky; also at uppe limits of Van Allen adiation belts and nea the edge of the magnetosphee, making them useful fo scientific puposes 4
Physics 9. Space Syllabus Notes Define the tem obital elocity and the quantitatie and qualitatie elationship between obital elocity, the gaitational constant, mass of the satellite and the adius of the obit using Keple s Law of Peiods Obital elocity is the ate of change of the diection of a point moing with cicula motion as measued fom a point at est; the magnitude of obital elocity fo a point moing with cicula motion is constant. 3 Gm Keple s thid law (the Law of Peiods) = E = a fixed alue T 4π π When the peiod is known, the obital elocity can be found by = T The mass of the satellite plays no pat in detemining the obital elocity at a paticula distance away fom the cente of the obit. T 3 is a constant alue fo all bodies obiting the same object. Account fo the obital decay of satellites in low Eath obit All satellites in low Eath obit ae subject to some degee of atmospheic dag (fiction) that will eentually decay thei obit and limit thei lifetimes. Oe a peiod of time, the satellite will slow down. As it slows down, its kinetic enegy deceases. Because a lowe obit coesponds to a lowe enegy, the satellite must lost altitude if it slows down. This esult can also be deied using Keple s Thid Law; if the obital elocity, and hence the peiod, 3 deceases, adius must decease since must emain a constant. As it descends, it T encountes highe density ai and highe dag, speeding up the pocess. The amount of atmospheic dag expeienced by a satellite depends on the size of the satellite and the density of the ai along the obit. The ai density is affected by aiables such as time of day, season, latitude and longitude. An incease in sola wind heats up the oute atmosphee, inceasing its density at a paticula height. Discuss issues associated with safe e enty into the Eath s atmosphee and landing on the Eath s suface As the spacecaft e entes, it expeiences fiction with the molecules of the atmosphee and causes it to deceleate. The spacecaft s elocity and obit means that it has consideable kinetic enegy and gaitational potential enegy, which is lost duing e enty. This enegy is coneted into heat, and the heat can cause the spacecaft to each exteme tempeatues, which can apoise the spacecaft. The best shape fo e enty is a blunt one, because it will poduce a shock wae in font of itself, and that will cay the enegy away. Fo example, the space shuttle keeps its nose up while e enteing, and it pesents its flat undebelly to the atmosphee to ceate the shock wae. Howee, the blunt design would still need to cope with high tempeatue. The technique of ablation inoles coeing the nosecone with a ceamic mateial, which is apoised o ablated duing e enty. The apoisation of the suface dissipates the heat and caies it away. The space shuttle uses insulating tiles that ae 90% ai, giing them excellent themal insulation popeties. Thee is also a need to conside the suial of any liing occupants. Geate angles of eenty mean geate ates of deceleation, which would lead to geate g foces expeienced by the astonauts. The maximum safe load on an astonaut is about 8 g, but thee ae ways to incease a human s toleance of g foces. The astonaut should lie down, because tansesal applications of g foces ae easie to handle as blood as not foced away fom the bain. 5
Physics 9. Space Syllabus Notes Toleance can be inceased by suppoting the body in as many places as possible, such as by using a contoued couch. Identify that thee is an optimum angle fo safe e enty fo a manned spacecaft into the Eath s atmosphee and the consequence of failing to achiee this angle Thee is a window of appoximately degees fo e enty. If the angle of e enty is too shallow, the spacecaft may skip off the atmosphee, and if the angle of e enty is too steep, the spacecaft will bun up due to the heat of e enty. Students: Sole poblems and analyse infomation to calculate the actual elocity of a pojectile fom its hoizontal and etical components using =, = u + at, = u + a y, x = u t, y = u t x y + 1 ayt x u x Pefom a fist hand inestigation, gathe infomation and analyse data to calculate initial and final elocity, maximum height eached, ange and time of flight of a pojectile fo a ange of situations by using simulations, data logges and compute analysis Identify data souces, gathe, analyse and pesent infomation on the contibution of the following to the deelopment of space exploation: Tsiolkosky, Obeth, Goddad, Esnault Pelteie, O Neill o on Baun Consideed the theoetical fathe of ockety, he theoised many aspects of space tael and ocket populsion befoe othes, and played an impotant ole in the deelopment of Russian space pogams Influenced by science fiction, he began to intoduce eal technical poblems into his witings, and his deam was fo humanity to become a space ciilisation He demonstated the eaction pinciple by expeimenting with a cask filled with compessed gas; he discoeed that the moement of the cask could be egulated by altenating the pessue of the gas eleased fom it He outlined how a eaction thust moto could demonstate Newton s Thid Law to allow humans to escape the bounds of Eath His dafted design fo the fist ocket inoled an explosie mixtue of liquid oxygen and liquid hydogen, which poduces condensed and heated gases; these gases ae cooled and aefied with the esulting exhaust poiding the thust He also speculated on a multi stage appoach to spaceflight; as each indiidual stage consumed its fuel, it would be discaded to keep the oeall weight to a minimum; he ecognised that it would equie a temendous amount of fuel fo the ocket to each escape elocity He wote oe 500 scientific papes, and although he did not ceate any ockets himself, his fundamental pinciples emain basic to contempoay astonautics Sole poblems and analyse infomation to calculate centipetal foce acting on a satellite undegoing unifom ciculate motion about the Eath using: Sole poblems and analyse infomation using: 3. The Sola System is held togethe by gaity Students lean to: T 3 GM = 4π m F = y y y 6
Physics 9. Space Syllabus Notes Descibe a gaitational field in the egion suounding a massie object in tems of its effects on othe masses in it A gaitational field is a field in which any mass will expeience a gaitational foce. Since the foce of gaity acts on masses suounding the Eath, o any massie object, a gaitational field exists aound the Eath o the massie object, with the gaitational field taking on a adial patten with the field lines pointing towads the massie object s cente. This is because this is the diection of the foce that would be expeienced by a mass within the field, that is, towads the lage object s cente. Close to Eath o the massie object, the field lines ae close togethe, indicating that the field, and its foce, ae stonge in this egion. On a small scale, such as the inteio of a oom, the field lines, o lines of foce, appea paallel and point down since that is the diection of the foce that would be expeienced by a mass placed within the field. Define Newton s Law of Uniesal Gaitation m1m F = G d Newton s Law of Uniesal Gaitation states that the foce of attaction between two masses is popotional to the poduct of the masses and inesely popotional to the squae of the distance between thei centes. This foce is exeted equally on both masses. Discuss the impotance of Newton s Law of Uniesal Gaitation in undestanding and calculating the motion of satellites If a satellite undegoes unifom cicula motion, thee must be a centipetal foce acting to maintain cicula motion, which is diected towads the cente of the cicle. This is because an object will continue in unifom motion in a staight line unless acted upon by a foce, accoding to Newton s Fist Law of Motion. In the case of a satellite, it is the gaitational attaction between the Eath, o anothe massie object, and the satellite that acts as the centipetal foce. By equating the mathematical expessions fo Newton s Law of Uniesal Gaitation and centipetal foce: mems ms G =, whee m E is the mass of the Eath and m S is the mass of the satellite GmE This educes to =, and fom this, we can see that the obital elocity equied fo a paticula obit depends only on the mass of the Eath (o the othe body being obited), the adius of the obit. Since the mass of the Eath is a constant, this means adius (o altitude since the adius of the Eath is also a constant) is the only aiable that detemines the equied elocity. The geate the adius of the obit, the lowe the obital elocity equied. Identify that a slingshot effect can be poided by planets fo space pobes The slingshot effect, o planetay swing by, is a manoeue used with space pobes to pick up speed and poceed on to anothe taget. Een though thee is no contact, the inteaction behaes as a collision, because the spacecaft is captued by the planet s gaitational field fo a peiod of time; howee, because the bodies do not touch in any way, thee ae no enegy losses and hence the collision is elastic. If we conside the elocity of the spacecaft elatie to a planet, then it is possible to assume that the planet is standing still. When a small object collides with elastically with a ey lage, massie object, the small object will ebound without loss of speed, like a ball bouncing off a wall. Howee, the planet is moing elatie to the Sun, and by ecto addition, the speed of the spacecaft elatie to the Sun is its oiginal speed plus the speed of the planet, if we assume that the inteaction happens one dimensionally. Some of the planet s 7
Physics 9. Space Syllabus Notes momentum is tansfeed to the spacecaft, which esults in the spacecaft haing a highe elocity. The slingshot effect can also be used to change the diection of a spacecaft s motion. Students: Pesent infomation and use aailable eidence to discuss the factos affecting the stength of the gaitational foce m1m Using F = G, the stength of the gaitational foce is popotional to the d poduct of the two masses, and inesely popotional to the squae of the distance between thei centes The foce acts equally on both masses The alue of g on Eath aies accoding to geogaphical location and altitude Sole poblems and analyse infomation using: F = G m m 1 d 4. Cuent and emeging undestanding about time and space has been dependent upon ealie models of the tansmission of light Students lean to: Outline the featues of the aethe model fo the tansmission of light Nineteenth centuy physicists, haing concluded that light moes as a waefom, obseed that many othe wae motions equied a medium though which to tael. Consequently, the luminifeous aethe was the poposed medium fo light and othe electomagnetic waes, befoe it was ealised that these waefoms do not need a medium in ode to tael. The aethe: Filled all of space, had low density and was pefectly tanspaent Pemeated all matte and yet was completely pemeable to mateial objects Had geat elasticity to suppot and popagate the light waes Descibe and ealuate the Michelson Moley attempt to measue the elatie elocity of the Eath though the aethe If the aethe did exist, the Eath should be moing though the aethe. Fom ou point of iew, we should expeience a flow of aethe past us called the aethe wind. Howee, the aethe was thought to be extemely tenuous, so any aethe wind would be had to detect. Thee wee many expeiments designed and pefomed to detect it, but they all failed. The assumption was that the detection mechanisms wee simply not sensitie enough. Michelson and Moley s expeiment was exceedingly sensitie. They used the effect of intefeence of light waes in ode to measue the elatie elocity of the Eath though the aethe. A light wae fom a souce is split into two pependicula beams by the half sileed mio. One ay would tael into the supposed aethe and the othe acoss it. Mios eflect the two ays back, and the ays ae ecombined at the intefeomete, whee a seies of dak and light bands can be seen. If the aethe wind exists, the ays would tael at diffeent elocities; when the appaatus is otated, the intefeence patten should be seen to shift, and the elatie elocity of the aethe wind can be detemined by using this shift. Howee, the esult of the expeiment was null, that is, no such shift was obseed. The expeiment was epeated many times by Michelson and Moley, at diffeent times of the day and yea. Futhe, the Michelson Moley expeiment has been epeated many times since then by diffeent goups with moe sensitie equipment. No eidence of the aethe has ee 8
Physics 9. Space Syllabus Notes been found, and suggestions to explain the null esults of the expeiment hae not suied close scutiny. Discuss the ole of the Michelson Moley expeiments in making deteminations about competing theoies The esults of the Michelson Moley expeiments wee null, meaning that no aethe was detected. Howee, the scientific community was not quick to abandon the aethe model, and adapted the theoy to keep it alie. One suggestion was that a lage object such as a planet could dag the aethe along with it. Anothe was that objects contact in the diection of the aethe wind. Howee, none of these modifications withstood close scutiny. Galileo posed a simple idea, now called the pinciple of elatiity, which states that all steady motion is elatie and cannot be detected without efeence to an outside point. Within an inetial fame of efeence, you cannot pefom any mechanical expeiment o obseation that would eeal to you whethe you wee moing with unifom elocity o standing still. Howee, belief in the aethe posed a difficult poblem fo the pinciple of elatiity, because the aethe was supposed to be stationay in space, and light was supposed to hae a fixed elocity elatie to the aethe. Thus, an optical expeiment wheeby the speed of light is measued poides a way to iolate the pinciple of elatiity whee no mechanical expeiment could. Einstein ealised that if the pinciple of elatiity wee not to be iolated, light must moe 8 1 at a constant speed fo all obsees, at c = 3 10 ms. In this way, the esult of the Michelson Moley expeiments poided an obseational poof of Einstein s theoy, which would ende the idea of the aethe supefluous. Outline the natue of inetial fames of efeence An inetial fame of efeence is a non acceleated enionment, such as one that has steady motion o no motion at all. In an inetial fame of efeence, Newton s laws of motion ae obeyed, and any expeiment pefomed in an inetial fame of efeence will appea the same in anothe inetial fame of efeence. The pinciple of elatiity states that within an inetial fame of efeence, you cannot pefom any mechanical expeiment o obseation that would eeal to you whethe you wee moing with unifom elocity o standing still. Discuss the pinciple of elatiity The pinciple of elatiity states that all steady motion is elatie and cannot be detected without efeence to an outside point. The pinciple of elatiity only applies fo nonacceleated steady motion standing still o moing with a unifom elocity. Fo example, when you ae inside a moing ehicle, you cannot tell if you ae moing at a steady elocity o standing still without looking out the window. The pinciple states that within an inetial fame of efeence, you cannot pefom any mechanical expeiment o obseation that would eeal to you whethe you wee moing with unifom elocity. Fo example, if you held up a sting with a small object tied to the end, the object would hang so that the sting was etical. Howee, if the ehicle in which you wee taelling in acceleated, the object would swing backwads so that the sting is no longe etical. When you stop acceleating and each a constant elocity, the sting would swing back into the etical position. When ounding cones, the sting would lean one way o the othe. This plumb bob acts as a simple acceleomete, but it is unable to distinguish between being motionless and steady motion. Descibe the significance of Einstein s assumptions of the constancy of the speed of light The speed of light though a acuum is assumed constant elatie to all obsees so that the pinciple of elatiity cannot be iolated by using optical expeiments. Howee, if 9
Physics 9. Space Syllabus Notes obsees at elatie motion to each othe obsee the speed of light to be constant, then since speed = distance, then the distance and time witnessed by both obsees must be diffeent. time Because of the constancy of the speed of light, an outside obsee will see that an object moing with elatie elocity to the outside obsee will expeience time dilation, length contaction in the diection of motion, and mass dilation. In addition, because space and time become elatie if the speed of light is constant, simultaneous eents in one fame of efeence ae not necessaily obseed to be simultaneous in a diffeent fame of efeence; any eent has thee dimensions of space and one of time. Identify that if c is constant then space and time become elatie By Einstein s theoy, the speed of light in a acuum has the same alue c independent of the motion of the obsee. This can only be tue if an obsee and anothe obsee moing with elatie motion obseed diffeent times as well as diffeent distances in such a way that distance diided by time always equals the same alue c. In Newtonian physics, distance and elocity can be elatie tems, but time is an absolute and fundamental quantity. Einstein adically alteed the assumptions of Newtonian physics so that now the speed of light is absolute, and space and time ae both elatie quantities that depend on the motion of the obsee. Since both space and time ae no longe absolute, the theoy of elatiity has eplaced them with the concept of a space time continuum. Any eent then has fou dimensions (thee space coodinates plus a time coodinate) that fully define its positie within its fame of efeence. Discuss the concept that length standads ae defined in tems of time in contast to the oiginal mete standad The mete as a unit of length was fist defined in 1793 when the Fench goenment deceed it to be a faction of the length of the Eath s quadant passing though Pais. Thee platinum standads and seeal ion copies wee made. When it was discoeed that the quadant suey was incoect, the mete was edefined as the distance between two maks on a ba. In 1875, the Systeme Intenationale (SI) of units defined the mete as the distance between two lines inscibed on a single ba of platinum iidium alloy. Copies, o atefacts, wee made fo dissemination of this standad. Thee is always a need fo the accuacy of a unit of measue to keep pace with impoements in technology and science. The cuent definition of the mete uses the constancy of the speed of light in a acuum and the accuacy of the definition of one second to achiee a definition that is both highly accuate and consistent with the idea of space time. One mete is now defined as the length of the path taelled by light in a acuum duing a paticula time inteal. Such a definition of a mete ensues that the mete emains the same length fo all obsees, iespectie of the fame of efeence (the speed of light and the ibation of the Cs atom is the same fo all obsees). Explain qualitatiely and quantitatiely the consequence of special elatiity in elation to: the elatiity of simultaneity One of the consequences of special elatiity is that we can no longe conside time to be an absolute quantity. The time inteal between two eents, een if the to eents appea to be simultaneous, depends on the obsee s fame of efeence. Two eents ae said to be simultaneous if they occu at the same time. Conside the following thought expeiment. Two people ae equidistant fom two light flashes x and y. Peson A is moing to the ight towads y with a elocity, while peson B is stationay. At the instant A passes B, two light flashes occu, one at x (to the left), and one at y (to the ight). The light waes will each B fom x and y at the same time; B will conside the two eents to be simultaneous. Howee, 10
Physics 9. Space Syllabus Notes A is still moing towads y and will obsee the light flash fom y befoe obseing the light flash fom x; they ae not simultaneous eents to A. Altenatiely, we can analyse the situation with a moing tain. An opeato of a lamp ides in the middle of a tain caiage. The doos at the end of the caiage ae light opeated. At an instant in time when the opeato is alongside an outside obsee, the opeato switches on the lamp, which in tun, opens the doos. Inside the tain, the opeato will see the doos open simultaneously, because the light will tael the same distance at the same speed. Howee, to the outside obsee, the tain has moed while the light is taelling. The font doo is futhe away, and the back doo is close. The light taels fowads and backwads at the same speed c, but the fowad jouney is now longe than the backwad jouney, so the back doo is seen to open befoe the font doo does. If an obsee sees two eents to be simultaneous, then any othe obsee, in elatie motion to the fist, geneally will not judge them to be simultaneous. Simultaneous eents in one fame of efeence ae not necessaily obseed to be simultaneous in a diffeent fame of efeence. Simultaneity is not an absolute concept, but is elatie. the equialence between mass and enegy When we acceleate an object, we must apply a foce to it, that is, we do wok on it: W = Fs Howee, because the speed of an object cannot exceed the speed of light, it cannot acceleate indefinitely. Usually, the wok done on the object, that is, the enegy being gien to the object, takes the fom of inceased kinetic enegy as the object speeds up. Howee, as we appoach the speed of light, the enegy is changed into mass, and as a consequence, the enegy is no longe being used to acceleate the object. The total enegy equals the est enegy plus the kinetic enegy: E = EK + mc When an object is stationay, it has no kinetic enegy, but it will hae enegy due to mass. This is called its est enegy, the enegy equialent of a stationay object s mass measued within the object s est fame. length contaction As a consequence of peceiing time diffeently (a consequence in itself of the postulates of special elatiity), obsees in diffeent fames of efeence also peceie length (in the diection of motion) diffeently. We will constuct anothe thought expeiment. Thee is a light clock on a tain so that the light beams will un the length of the tain, with the lamp and senso located on the back wall and the mio on the font wall. As the tain passes the obsee on the embankment, the light clock emits a light pulse, which taels to the font of wall and then etuns to the back wall whee it is picked up by the senso, which then goes click. To an obsee inside the tain, the length of the light jouney is simply twice that of the length of the tain measued fom its est fame. Howee, to an obsee at the side of the tack, the tain is moing at the same time that the light ays moe. This lengthens the fowad leg of the light pulse s jouney and shotens the etun leg. Taking into account the fact that each obsee peceies time diffeently, we aie at a qualitatie elationship: L = L o 1 c Since the tem 1 c is always less than one, the length of the tain as obseed by the peson on the embankment is less than that obseed by the peson inside the tain. Thus, the length of an object measued within its est fame is called its pope length L, o est length. o 11
Physics 9. Space Syllabus Notes Measuements of this length L made fom any othe inetial efeence fame in elatie motion ae always less. time dilation Time is peceied diffeently by obsees in elatie motion to each othe. A light clock is aanged etically in a speeding tain, with the lamp at the ceiling and the mio on the floo. An obsee is watching fom the embankment outside the tain. To someone inside the tain, the light beams appea to tael staight up and staight up and staight down. Howee, the obsee on the embankment sees the light taelling along a longe jouney, detemined accoding to Pythagoas Theoem. The obsee sees the light tael futhe but with the same speed, and hence time slowed down on the tain. The elationship between the times obseed by obsees at elatie to motion to each othe is t =, whee t o is the time as measued by the tain taelle, 1 c and t is the time as measued by the extenal obsee. We can see that 1 c is always less than one, so t is always geate than t o. Time is passing moe slowly on the tain as obseed by the peson outside the tain. Geneally, let to be the time taken fo an eent to occu within its own est fame. Measuements of this time t made fom any othe inetial efeence fame in elatie motion to the fist, ae always geate. In othe wods, moing clocks appea to un slow. mass dilation When two paticles inteact with each othe, the pinciples of conseation of momentum and conseation of enegy should hold fo all obsees moing at abitay elocities with espect to the two inteacting paticles. By postulating momentum conseation to be tue fo all obsees, Einstein found that the mass of an object is not measued as the same by obsees with diffeent elocities elatie to the object. In othe wods, the mass of an object inceases as its elocity incease elatie to the obsee: mo m = 1 c Discuss the implications of mass incease, time dilation and length contaction fo space tael Acceleation is always the most enegy costly phase of a space mission. The effect of mass accumulation (which deceases the acceleation fo a gien thust) and time dilation (which means that the foce will hae a shote time in which to act in), means that acceleations beyond 0.9 c will be impactical; geate and geate foces and enegy input only account fo maginal inceases. Thus, highe speeds, which ae equied if humans ae to each distant locations in a easonable timefame, inceases the enegy equiements, meaning that the cost of the enegy could be pohibitie. The effect of time dilation and length contaction means that it may be possible fo human astonauts to undego exceptionally long space jouneys in a easonable amount of time, as judged by the taelles. The distance to the distant location appeas to shoten, and thus the jouney will appea to take less time. As well, when the astonauts etun to Eath, they will hae aged less time compaed to the amount of time that has actually passed on Eath. This will incease the pacticality of long space jouneys as they may become possible to achiee within a lifetime, but the enomous speeds equied fo this effect to be noticeable, 1
Physics 9. Space Syllabus Notes and hence the enegy and fuel equied, cuently make this an impactical situation. At the speeds attained by cuent day astonauts, elatiistic effects due to time ae negligible. Time dilation aises the situation known as the twin paadox. One twin stays on Eath, while the othe boads a spaceship and flies off at speeds neaing c. This poblem is often consideed a paadox, because the pinciple of elatiity demands that no inetial fame of efeence be pefeed oe anothe. In othe wods, elatiity s effects should be eesibly simply by looking at them fom anothe iewpoint. Both siblings will see each othe flying away fom each othe, and each can claim that the othe should be younge. Howee, the one that boads the spaceship has acceleated and deceleated, and thus the fame of efeence of the spaceship has not emained inetial. Only the Eath twin can apply time dilation in this situation because only this twin has an inetial fame of efeence. Hence, the two fames of efeence ae not equialent and thee is no paadox because the one that stays on Eath will be younge. Students: Gathe and pocess infomation to intepet the esults of the Michelson Moley expeiment Use the example whee two boats ae acing each othe on a ie. One boat is taelling acoss the cuent, while the othe taels with the cuent and then against the cuent. Pefom an inestigation to help distinguish between non inetial and inetial fames of efeence Pendulum expeiment: the pendulum acts as a simple acceleomete. Let a mass suspended on a line swing feely. In a non inetial fame of efeence, the mass will swing in the opposite diection to the acceleation; in an inetial fame of efeence, the mass will hang etically. This assumes that the gaitational field at that point is acting downwads. Rolling balls: see whethe objects within the fame of efeence obey Newton s Law of Motion. Roll two identical balls acoss the oom, the diections being pependicula to each othe. By Newton s Fist Law of Motion (if we ignoe fiction), the balls should moe in staight lines acoss the floo, because no extenal foce is acting on them. Howee, if the balls ae being olled in a noninetial fame of efeence, then they will appea to oll in the diection opposite to the diection of the acceleation. Two balls must be olled in diections pependicula to each othe, because the acceleation may be paallel to one of the motions and be undetected. Analyse and intepet some of Einstein s thought expeiments inoling mios and tains and discuss the elationship between thought and eality See aboe notes fo the light clocks Due to the belief in the aethe model, whee light has a fixed speed elatie to the supposed aethe, you would be able to tell whethe you wee moing o not by simply measuing the speed of light going one way and then the othe. In othe wods, an optical expeiment allows fo elatiity to be iolated whee no mechanical expeiment could. Einstein had an ability to educe a poblem down to its simplest fom and pesent it as a thought expeiment. This was because Einstein had a stong belief in the unity of physics and the pinciple of elatiity must not be iolated. The effects of elatiity elatiity of simultaneity, time, length and mass ae eesible by looking at it fom a diffeent efeence fame; thus, two obsees moing with elatie elocity may judge a situation to be diffeent, but both ae coect in thei own fames of efeence. 13
Physics 9. Space Syllabus Notes Thee is eidence fo the elatiistic effects that follow fom the assumption that the speed of light in acuo is a constant. Analyse infomation to discuss the elationship between theoy and the eidence suppoting it, using Einstein s pedictions based on elatiity that wee made many yeas befoe eidence was aailable to suppot it Thee is an abundance of mesons stiking the gound. These mesons wee ceated in the uppe atmosphee by incoming cosmic ays. At the elocity of 0.996c, the mesons should take aound 16 μs to tael though the atmosphee. Howee, when measued in a laboatoy, they hae an aeage lifetime of aound. μs. This is because. μs epesents thei lifetime as measued in thei est fame, wheeas 16 μs is a dilated lifetime due to thei elatiistic speed. Time dilation can also be eified by compaing atomic clocks that hae been flown oe long jouneys with clocks that emained stationay fo the same peiod. These expeiments ae possible now because of the exteme accuacy of moden atomic clocks. The clocks that wee flown aound wee slow compaed to those that stayed on the gound. Sole poblems and analyse infomation using: E = mc, l = l 1, t c o to =, m = 1 c m o 1 c 14