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PHYS1: Space 1. The Earth has a gravitational field that exerts a force on objects both on it and around it DEFINE WEIGHT AS THE FORCE ON AN OBJECT DUE TO A GRAVITATIONAL FIELD Gravitational field: a field within which any mass will experience a gravitational force Weight: the force on an object in a gravitational field. It is a vector quantity and the measurement unit is the Newton (N). Pg 1,2 Mass of Earth: 6 x 1024 kg Radius of Earth: 6370 km G (constant): 6.67 x 10-11 Nm2kg-2 Gravitational forces are always attractive forces EXPLAIN THAT A CHANGE IN GRAVITATIONAL POTENTIAL ENERGY IS RELATED TO WORK DONE Pg 4 Gravitational potential energy is the energy of a mass due to its position within a gravitational field When lifting an object against a gravitational field, work is done on the object, that is, energy is transferred to the object. The object’s gravitational potential energy Ep (the energy it has due to its position within the gravitational field) increases as a result. When an object moves toward the source of the gravitational field, such as when dropping a stone, energy due to position in a field is transformed into kinetic energy (the stone speeds up). Work Done = Fs = mgh = GPE DEFINE GRAVITATIONAL POTENTIAL ENERGY AS THE WORK DONE TO MOVE AN OBJECT FROM A VERY LARGE DISTANCE AWAY TO A POINT IN A GRAVITATIONAL FIELD The position of lowest Ep in the gravitational field surrounding a planet is at the surface of the planet. An object only has zero Ep when it is no longer within the gravitational field i.e. distance must be infinite. Therefore, GPE of an object in a gravitational field is equal to the work done in moving the object from an infinite distance away to that point Ep G m1m2 r Pg 4 PERFORM AN INVESTIGATION AND GATHER INFORMATION TO DETERMINE A VALUE FOR ACCELERATION DUE TO GRAVITY USING PENDULUM MOTION OR COMPUTER-ASSISTED TECHNOLOGY AND IDENTIFY REASON FOR POSSIBLE VARIATIONS FROM THE VALUE 9.8 MS-2 Pg 3 Earth’s crust shows variations in thickness and structure Earth is flattened at the poles Spin of Earth creates a centrifuge effect that reduces effective value of g (more so at the equator) Variation with altitude GATHER SECONDARY INFORMATION TO PREDICT THE VALUE OF ACCELERATION DUE TO GRAVITY ON OTHER PLANETS Pg 3 𝑔=𝐺 𝑀𝑝𝑙𝑎𝑛𝑒𝑡 (𝑅𝑝𝑙𝑎𝑛𝑒𝑡 )2 ANALYSE INFORMATION USING THE EXPRESSION: F mg TO DETERMINE THE WEIGHT FORCE FOR A BODY ON EARTH AND FOR THE SAME BODY ON OTHER PLANETS Pg 1, 3 2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth DESCRIBE THE TRAJECTORY OF AN OBJECT UNDERGOING PROJECTILE MOTION WITHIN THE EARTH’S GRAVITATIONAL FIELD IN TERMS OF HORIZONTAL AND VERTICAL COMPONENTS Projectile motion can be analysed by considering its horizontal and vertical components at particular instances during the flight. The horizontal motion of the projectile is a constant velocity (air resistance is assumed negligible). Its vertical motion is changing all the time due to the effect of gravity, which causes the projectile to accelerate at 9.8 m s-2 downwards. o The trajectory of a projectile in the Earth’s gravitational field is parabolic, provided that air resistance is ignored and the acceleration due to gravity is uniform. Pg 5 SOLVE PROBLEMS AND ANALYSE INFORMATION TO CALCULATE THE ACTUAL VELOCITY OF A PROJECTILE FROM ITS HORIZONTAL AND VERTICAL COMPONENTS USING: v2x u2x v u at v2y u2y 2a y y x u x t 1 y u yt a y t 2 2 DESCRIBE GALILEO’S ANALYSIS OF PROJECTILE MOTION All objects accelerate at the same rate when they fall, independent of mass o A stone and a feather would reach the ground at the same time if they were dropped from the same height, provided there was no air resistance Horizontal (constant velocity) and vertical (constant acceleration) components of projectile motion occur simultaneously, independently of each other o This explained why a stone dropped from a tower would not be left behind as the Earth rotated; it shared the same horizontal velocity as the tower initially As a result, all projectiles took a parabolic trajectory Pg 6, 7 PERFORM A FIRST-HAND INVESTIGATION, GATHER INFORMATION AND ANALYSE DATA TO CALCULATE INITIAL AND FINAL VELOCITY, MAXIMUM HEIGHT REACHED, RANGE AND TIME OF FLIGHT OF A PROJECTILE FOR A RANGE OF SITUATIONS BY USING SIMULATIONS, DATA LOGGERS AND COMPUTER ANALYSIS EXPLAIN THE CONCEPT OF ESCAPE VELOCITY IN TERMS OF THE: – GRAVITATIONAL CONSTANT – MASS AND RADIUS OF THE PLANET Escape velocity: the initial velocity required by a projectile to rise vertically and just escape the gravitational field of a planet, so that it doesn’t return to that planet under the influence of their mutual gravitational attraction o It is the velocity which will result in zero mechanical energy at an infinite distance away o Depends on mass of the planet and distance from centre of the planet (radius), as G is a constant o For Earth: 11.2 km/s It is worth noting that this is a hypothetical concept only. It would not be possible to successfully perform such a launch for two reasons. o Trying to travel through the Earth’s dense lower atmosphere at this speed would produce an enormous amount of heat, sufficient to vaporise the projectile. o Any living thing or delicate equipment would be crushed by the enormous g forces created by the process of suddenly being accelerated to 40 000 km h-1 Pg 8 OUTLINE NEWTON’S CONCEPT OF ESCAPE VELOCITY A person climbed a very tall mountain and launched a projectile horizontally from the peak. The projectile follows a parabolic path before striking the ground. If a projectile were launched fast enough (orbital velocity), it should be able to travel around the Earth because, as it falls, the surface of the Earth curves away from it at the same rate. The curve of the projectile’s motion would match that of the Earth’s surface. This projectile would then be in a circular orbit at a fixed height above the earth’s surface. If a projectile is launched still faster, its orbit will stretch out into an elliptical shape. Even faster launch velocities result in the projectile following a parabolic or hyperbolic path away from the Earth, escaping it entirely. DISCUSS THE EFFECT OF THE EARTH‘S ORBITAL MOTION AND ITS ROTATIONAL MOTION ON THE LAUNCH OF A ROCKET Pg 10, 11 Rockets launched to the East to receive a 1700 km/h boost from Earth’s rotational motion towards target velocity of about 30 000 km/h o This velocity boost is maximised if a rocket is launched from the equator, as radius and hence tangential velocity are greatest here o First, the rocket is launched vertically to penetrate dense lower portion of the atmosphere by shortest possible route, then its trajectory is tilted to an easterly direction. Rockets heading away from Earth are launched when direction of Earth in its orbit around the Sun corresponds with desired direction, to receive a 107 000 km/h boost from Earth’s orbital motion o If a rocket is launched in the direction of earth’s orbital motion, this gives it a greater velocity and hence larger orbit around the sun than the Earth, allowing it to intercept a further planet. o If a rocket is launched in the opposite direction to earth’s motion through space, this gives it a lesser velocity and hence smaller orbit around the sun than the Earth, allowing it to intercept a planet closer to the sun (Mercury or Venus) These velocity boosts help rockets save fuel in achieving their required velocities ANALYSE THE CHANGING ACCELERATION OF A ROCKET DURING LAUNCH IN TERMS OF THE: – LAW OF CONSERVATION OF MOMENTUM – FORCES EXPERIENCED BY ASTRONAUTS Rocket is subject to the following forces: Weight force directed downward Thrust directed upward Reaction force of the ground on the rocket directed upward (equal to difference between weight and thrust while rocket is on the ground) Air resistance directed downward against the motion of the rocket once it has left the ground Law of Conservation of Momentum: The launch begins with the rocket producing thrust by burning fuel and expelling the resulting hot gases out one end. These hot gases have a momentum in one direction, and since the total momentum of the rocket-fuel system is zero, the rocket itself has an equal momentum in the opposite direction. Thus, the rocket moves off in the opposite direction to the expelled gases, in accordance with the Law of Conservation of Momentum. By Newton’s 3rd Law of Motion… While the left side of the equation remains quite constant during a burn, the terms on the right side are changing. The mass of the rocket is decreasing significantly as the fuel is burned (typically, 90% of a rocket’s mass is fuel). This means that the velocity of the rocket must increase significantly. o Rate of acceleration will increase as its flight progresses, and its velocity will increase logarithmically When in orbit, acceleration is (–g), and g-force is zero. Forces experienced by Astronauts: Two forces act upon the rocket during launch: the upward thrust (T) as well as the downward weight (W or mg). As described above, if the mass of the rocket decreases during flight and the thrust remains constant, the acceleration of the rocket (and astronauts) increases. The force experienced by the astronaut is given by: Apparent weight = (mass of astronaut) (gravitational acceleration + external acceleration) Since the rocket’s acceleration is increasing, the apparent weight force experienced by the astronaut increases. Pg 12, 13, 14, 15 Textbook pg 32 Longitudinal acceleration (3-5g) in the direction of the person’s head can cause black-outs, resulting in chronic cerebral congestion, haemorrhage, and brain damage Longitudinal acceleration (3-5g) in the direction of the person’s feet causes red outs; blood rushes to the head and retina Transverse acceleration can be much better tolerated than longitudinal, but may cause hypoxia and unconsciousness o Humans can tolerate up to 12g transverse acceleration without undue discomfort o ‘Eyeballs in’ upwards g-force is more tolerable than an ‘eyeballs out’ downward force IDENTIFY WHY THE TERM ‘G FORCES’ IS USED TO EXPLAIN THE FORCES ACTING ON AN ASTRONAUT DURING LAUNCH The term ‘g force’ is used to express apparent weight as a proportion of true weight. o Apparent weight is what a person experiences or feels when an external force acts on them to cause a change in their motion o True weight is the force applied due to gravity on an object that is not accelerating These forces are also called inertial forces because they arise from the body’s inertia or resistance to having its motion changed. Pg 13, 14 ANALYSE THE FORCES INVOLVED IN UNIFORM CIRCULAR MOTION FOR A RANGE OF OBJECTS, INCLUDING SATELLITES ORBITING THE EARTH Centripetal force: the force that acts to maintain circular motion and is directed towards the centre of the circle Uniform circular motion: circular motion with a uniform orbital speed Objects do not perform uniform circular motion unless they are subject to a centripetal force. This is a force that is always perpendicular to the velocity of the object. Centripetal force causes the moving object to continually change direction so that it follows a circular path. The centripetal force is always directed toward the centre of the circular motion. Circular motion Source of centripetal force Ball on a string whirled in a circle Tension in the string Car driving around a corner Friction between the tyres and the road Satellite orbiting the Earth Gravitational attraction between the Earth and the satellite SOLVE PROBLEMS AND ANALYSE INFORMATION TO CALCULATE THE CENTRIPETAL FORCE ACTING ON A SATELLITE UNDERGOING UNIFORM CIRCULAR MOTION ABOUT THE EARTH USING: F mv2 r SOLVE PROBLEMS AND ANALYSE INFORMATION USING: r3 GM T 2 4 2 Period (T): the time taken to complete one orbit COMPARE QUALITATIVELY LOW EARTH AND GEO-STATIONARY ORBITS Low Earth Orbit: Higher than 250 km to avoid atmospheric drag Lower than 1000 km (below Van Allen radiation belts) o These belts are regions of high radiation which pose risk to space travellers as well as electronic equipment o Note*: In calculations, these values are altitudes, not radii (e.g. 1000 km altitude corresponds to an orbital radius of: 6370 + 1000 = 7370 km) Orbital velocity: 27 900 km h-1 Period: 90 minutes Covers many locations with a small field of view E.g. space shuttle and Hubble telescope o Reached without too much energy consumed, since this orbit is at a lower altitude A polar orbit flying over the North and South Poles will be able to survey the entire globe as it spins beneath it every 24 hours (remote-sensing survey satellites/spy satellites) Geostationary Orbit: Orbital period equal to Earth’s rotation, i.e. one sidereal day (23 hours 56 minutes) To achieve this, altitude = 35 800 km o Upper edge of the outer van Allen belt Orbital velocity: 11 000 km h-1 Tracks a stationary point on Earth, with a large field of view From the Earth, such a satellite appears to be stationary in the sky above a point on the Equator o Useful for communications/mass media satellites because a receiving dish need only point to a fixed spot in the sky to remain in contact with the satellite, and because of the wide field of view o Useful for weather satellites, as they can monitor weather patterns over one part of the world continuously For a geosynchronous orbit (24 hour period) to be a geostationary orbit (satellite remains at fixed point above the earth), the satellite’s orbit must lie on the plane of the equator. Further, the direction of the satellite’s orbit (clockwise or anticlockwise) around the Earth’s centre must be the same as the motion of the fixed point of the equator around the Earth’s centre. DEFINE THE TERM ORBITAL VELOCITY AND THE QUANTITATIVE AND QUALITATIVE RELATIONSHIP BETWEEN ORBITAL VELOCITY, THE GRAVITATIONAL CONSTANT, MASS OF THE CENTRAL BODY, MASS OF THE SATELLITE AND THE RADIUS OF THE ORBIT USING KEPLER’S LAW OF PERIODS Orbital velocity is the velocity required by a satellite to maintain a particular orbit around a celestial object. It is the instantaneous speed (magnitude) in the direction indicated by an arrow (directional) drawn as a tangent to the point of interest on the orbital path. Pg 16 Orbital velocity depends on mass of the planet and radius of the orbit ACCOUNT FOR THE ORBITAL DECAY OF SATELLITES IN LOW EARTH ORBIT Pg 17 Increase in incoming solar radiation (fluctuations in solar wind) can heat up outer atmosphere causing it to expand, thereby increasing its density and height. This will subject satellites to drag that would not otherwise have been anticipated Friction with outer fringes of the atmosphere results in a loss of energy, which means that current orbit is no longer viable, and satellite drops to an altitude that corresponds with this new, lower energy o It will be moving faster due to its lower altitude, with kinetic energy derived from the lost potential energy The atmosphere is denser in this lower orbit, so the process occurs more rapidly, leading to greater friction and loss of energy DISCUSS ISSUES ASSOCIATED WITH SAFE RE-ENTRY INTO THE EARTH’S ATMOSPHERE AND LANDING ON THE EARTH’S SURFACE Pg 18: Heat o The considerable kinetic and potential energy possessed by an orbiting spacecraft must be lost during reentry. As the atmosphere decelerates the spacecraft, the energy is converted into a great deal of heat. o Spacecraft with a blunt nose produce a shockwave of air in front of them, which absorbs much of the frictional heat (this is why space shuttles re-enter the atmosphere “belly first” o Ablation layer vaporises, or ablates, under extreme heat, dissipating the heat of re-entry o Exterior of space shuttle is covered with porous silica tiles, which don’t ablate, but dissipate heat very well 90% air (good insulator), and conserves mass o Heat can be minimised by taking longer to re-enter or flying in ‘braking ellipses’, thereby lengthening the time over which energy is converted to heat Decelerating g forces o Extending the re-entry and slowing the rate of descent minimises g forces Re-entry angle is controlled to avoid high g forces o Astronauts are reclined in contoured couches, facing the direction of acceleration (upwards during reentry), because transverse g loads and ‘eyeballs in’ force are easier to cope with longitudinal g loads and ‘eyeballs out’ forces Ionisation blackout o Heat building up around spacecraft during re-entry ionises atoms around it, forming a layer which radio signals cannot penetrate, and preventing communication Space shuttle suffers longer 16 minute blackout because of slow rate of descent Reaching the surface o o Even after surviving the issues listed above, the spacecraft must touch down softly onto the surface of the Earth. Early Russian capsules had parachutes to slow the capsule until astronauts could eject and parachute to Earth Early American craft slowed with parachutes and soft landed in the ocean Space Shuttle is unpowered, and so has only one chance at landing on a landing strip Shuttle must be accurately guided, against drag and lift forces causing spacecraft to deviate from trajectory Space shuttle is designed with ‘lift’ like an aeroplane so it can be controlled during descent and landing IDENTIFY THAT THERE IS AN OPTIMUM ANGLE FOR SAFE RE-ENTRY FOR A MANNED SPACECRAFT INTO THE EARTH’S ATMOSPHERE AND THE CONSEQUENCES OF FAILING TO ACHIEVE THIS ANGLE For any given spacecraft wishing to re-enter safely, an optimum angle of re-entry exists. For Apollo capsules this angle was between 5.2° and 7.2°, although this would differ for other spacecraft. If the angle is too shallow then the spacecraft will rebound, due to compression of the atmosphere beneath it. If the angle is too steep then the spacecraft will decelerate too quickly, creating too much heat and burning up the spacecraft. o Lower limit of angle is determined by deceleration load that astronauts are able to withstand o 10g load at 7 degree angle o Spacecraft will burn up at 9 degree angle IDENTIFY DATA SOURCES, GATHER, ANALYSE AND PRESENT INFORMATION ON THE CONTRIBUTION OF ONE OF THE FOLLOWING TO THE DEVELOPMENT OF SPACE EXPLORATION: TSIOLKOVSKY, OBERTH, GODDARD, ESNAULTPELTERIE, O’NEILL OR VON BRAUN Pg 24, 25 Robert H. Goddard Known as the father of modern rocketry Launched rockets from desert launch sites Used gyroscopically controlled steering devices for navigation Developed the first liquid-fuelled rocket o Calculated energy-to-weight ratios for various fuels o Used rockets fuelled by gasoline and liquid nitrous oxide o Identified liquid hydrogen and liquid oxygen as ideal propellant combination Used the de Laval steam turbine nozzle, which efficiently converted energy of hot gases into forward motion o Experimented using ballistic pendulum, on various nozzle designs Experimenting on airtight chambers, he found that rockets could fly in vacuum Developed multi-stage rockets that exceeded the speed of sound Fin-stabilised steering Developed a cooling method, where extremely cold liquid oxygen cools the combustion chamber on its way from the fuel tank Publications o ‘A Method of Reaching Extreme Altitudes’ described the mathematics of rocket flight, and the possibilities he saw in using rockets to explore the Earth and beyond o ‘Calculation of minimum mass required to raise one pound to an "infinite" altitude’ discussed usage of rockets to escape the Earth’s gravitational field Robert H. Goddard, known as the father of modern rocketry, contributed significantly to the development of space exploration. He developed the first liquid-fuelled rocket. Goddard calculated energy-to-weight ratios for various fuels, and identified liquid hydrogen/liquid oxygen as an ideal propellant combination. This technology was later used to launch rockets into space. Experimenting on airtight chambers, he found that rockets could be propelled in a vacuum, as per Newton’s 3rd Law. Also, Goddard used gyroscopically controlled steering devices for navigation, as well as using the de Laval steam turbine nozzle, which made the conversion of energy from hot gases into forward motion much more efficient. Some of his other advances in rocketry include fin-stabilised steering, and a cooling method where extremely cold liquid oxygen cools the combustion chamber on its way from the fuel tank. 3. The Solar System is held together by gravity DESCRIBE A GRAVITATIONAL FIELD IN THE REGION SURROUNDING A MASSIVE OBJECT IN TERMS OF ITS EFFECTS ON OTHER MASSES IN IT A gravitational field is a field within which any mass will experience a gravitational force of attraction towards the central body. The central body exerts a force of attraction, which becomes the centripetal force that allows objects to orbit around it. The strength of a gravitational field around a massive object is proportional to the value of its mass and decreases in inverse proportion to the square of the distance from the centre of the object. Pg 1, 2 PRESENT INFORMATION AND USE AVAILABLE EVIDENCE TO DISCUSS THE FACTORS AFFECTING THE STRENGTH OF THE GRAVITATIONAL FORCE and DEFINE NEWTON’S LAW OF UNIVERSAL GRAVITATION: F G m1m2 d2 The force of attraction between any two bodies in the universe is proportional to the product of their masses and inversely proportional to the square of their distance apart. Pg 19 SOLVE PROBLEMS AND ANALYSE INFORMATION USING: F G m1m2 d2 DISCUSS THE IMPORTANCE OF NEWTON’S LAW OF UNIVERSAL GRAVITATION IN UNDERSTANDING AND CALCULATING THE MOTION OF SATELLITES The planet exerts a force of attraction, which becomes the centripetal force that allows satellites to orbit around it. Pg 19 IDENTIFY THAT A SLINGSHOT EFFECT CAN BE PROVIDED BY PLANETS FOR SPACE PROBES The slingshot effect, or planetary swing-by, or gravity-assist manoeuvre, is a strategy used with space probes to achieve a change in velocity with little expenditure of fuel. Pg 20, 21 4. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light OUTLINE THE FEATURES OF THE AETHER MODEL FOR THE TRANSMISSION OF LIGHT During the nineteenth century, physicists were certain that light was a waveform. o Light rays could interfere with each other to produce a diffraction pattern, which was a wave property o Maxwell produced a set of equations which showed that electric and magnetic fields could move together as waves through space at the speed of light They assumed that, like all other known waveforms, light waves needed a medium through which to travel to us from the Sun and other stars. No medium could be found, and so one was hypothesised, along with a set of expected properties. It was called the luminiferous aether. o Filled all of space o Had low density o Was perfectly transparent o Permeated all matter and was completely permeable to material objects o Had great elasticity to support and propagate light waves Pg 22 DESCRIBE AND EVALUATE THE MICHELSON-MORLEY ATTEMPT TO MEASURE THE RELATIVE VELOCITY OF THE EARTH THROUGH THE AETHER The purpose of the Michelson-Morley experiment was to measure the relative velocity of the Earth through the aether If the aether existed, Earth moving through space at about 30 km s-1 in its orbit around the Sun, should be moving past the aether, creating an ‘aether wind’ The speed of light was supposed to be constant in the aether, so this aether wind should slow down light heading into it, as seen by us o A light ray travelling parallel to the aether wind would be slower than a ray travelling perpendicular to the aether wind, if both rays travelled equal distances forward and backward o The relative velocity of the Earth through the aether could be calculated from the difference in speeds of these light rays The two light rays would meet at a detector to produce an interference pattern If the aether wind existed, and hence the light ray travelling perpendicular to the aether wind was always faster than the ray travelling parallel, then when the apparatus was rotated 90⁰, the previously faster light ray would now be the slower, and vice versa, causing the interference patterns to shift However, no shift in the interference pattern was detected Even when the experiment was repeated at different locations and at different times of the year, no aether wind was detected Pg 23 GATHER AND PROCESS INFORMATION TO INTERPRET THE RESULTS OF THE MICHELSON-MORLEY EXPERIMENT Showed that the speed of light is constant regardless of the relative motion of an observer This contradicted the aether model, that the speed of light is constant only relative to the aether, and hence that the observed speed of light would depend on the motion of an observer relative to the aether. DISCUSS THE ROLE OF THE MICHELSON-MORLEY EXPERIMENTS IN MAKING DETERMINATIONS ABOUT COMPETING THEORIES Pg 26-27 Belief in aether posed a problem for Principle of Relativity o Since, the speed of light was supposed to be fixed relative to the aether, an optical experiment to measure the speed of light within a reference frame provides a way determine the frame’s velocity relative to the aether, and hence violate the Principle of Relativity Einstein realised that if Principle of Relativity was not to be violated, speed of light must be constant for all observers regardless of their motion o This meant that time and distance are relative, depending on motion of an observer Therefore, null result of the Michelson-Morley experiment showed that speed of light was constant regardless of the velocity of an observer, countering the aether model. The experiment provided an observational proof of Einstein’s theory which rendered the aether idea superfluous. OUTLINE THE NATURE OF INERTIAL FRAMES OF REFERENCE An inertial frame of reference is: Not accelerating Moving at constant velocity or is stationary One in which a free body experiences no acceleration One in which Newton’s first law is valid: an object at rest remains at rest, and an object in motion remains in motion unless acted upon by an external force e.g. an astronaut orbiting the Earth; a spaceship in the vacuum of space far from any celestial body Pg 27-28 DISCUSS THE PRINCIPLE OF RELATIVITY The principle of relativity was first stated by Galileo and embodied in Newton’s first law. 1) The fundamental laws of physics are the same in all inertial frames of reference. 2) Therefore, it is not possible to perform an experiment within an inertial frame of reference to detect the motion of the frame of reference 3) Hence you cannot tell whether an inertial frame of reference is stationary or moving with constant velocity The only way to detect the motion of an inertial frame of reference is by referring to another frame of reference. For example, if you are in a spacecraft far from any planet, star or other object, then you cannot tell if you are moving. Einstein’s special relativity: The laws of physics are the same in all inertial frames of reference. The speed of light is constant and independent of the velocity of the source or observer. PERFORM AN INVESTIGATION TO HELP DISTINGUISH BETWEEN NON-INERTIAL AND INERTIAL FRAMES OF REFERENCE DESCRIBE THE SIGNIFICANCE OF EINSTEIN’S ASSUMPTION OF THE CONSTANCY OF THE SPEED OF LIGHT Einstein’s assumption of the constancy of the speed of light regardless of the motion of an observer explained the null result of the Michelson-Morley experiment Rendered the aether model superfluous Logically resulted in relative space and time IDENTIFY THAT IF C IS CONSTANT THEN SPACE AND TIME BECOME RELATIVE In Newtonian physics, space can be relative, but time is an absolute quantity passing at the same rate everywhere In the theory of relativity, which assumes that c is constant for all observers, time is relative as well as space. V = distance/time: Therefore, if the velocity of light is to be a constant c, then distance and time observed must be relative. Time and space observed for an event must be changed depending on the motion of an observer, so that observers within reference frames which are moving at a constant velocity with respect to each other will observe the same value for the speed of light. o In other words, time passes differently for different observers, depending upon how fast they are moving. Perception of length is also different for an observer in relative motion to the rest frame. As neither space nor time are absolute, any event will have four dimensions to fully define its position within its frame of reference. ANALYSE AND INTERPRET SOME OF EINSTEIN’S THOUGHT EXPERIMENTS INVOLVING MIRRORS AND TRAINS AND DISCUSS THE RELATIONSHIP BETWEEN THOUGHT AND REALITY Thought and reality can be used together to explore new scientific ideas Reality is the physical world, the source of observations of which scientists strive to find explanations for o Reality has limitations including time, cost, materials, conditions difficult to change Thought acts as a drawing board where ideas can be explored without the limitations of reality o However, it is difficult to express with others unlike reality o Ideas cannot be proven by one’s thoughts alone, but need to be confirmed in reality o What you imagine is based upon your common sense, that is, your collective experiences of the way things normally happen. Einstein used thought experiments to investigate situations that could not be tested in reality since experiments at near light-speed velocities are impossible with current technologies. _____________________________________________________________________________________________ Imagine that you are sitting in a train facing forwards. The train is moving at the speed of light. You hold up a mirror in front of you, at arm’s length. Will you be able to see your reflection in the mirror? The experiment could have one of two possible outcomes: No, the reflection will not appear. This is the result predicted by the aether model, since light can only travel at a set speed (3 × 108 m s-1) through the aether. If the train is travelling at that speed then the light cannot catch the mirror to return as a reflection. Unfortunately, this violates the principle of relativity, which states that in an inertial frame of reference you cannot perform any experiment to tell that you are moving. Yes, the reflection will be seen because, according to the principle of relativity, it would not be possible for the person in the train to do anything to detect the constant motion with which he or she is travelling. However, a person watching this from the side of the track should see the light from your face travelling at twice its normal speed! Einstein decided that: The reflection will be seen as normal, because he believed that the principle of relativity should always hold true The person at the side of the track sees the light travelling normally. BUT, this means that time passes differently for you on the train and for the person at the side of the track Confirmation of these conclusions in reality: the flying of atomic clocks to determine the existence of time dilation the dilated lifetimes of mesons penetrating the Earth’s atmosphere the energy yield from converted mass in nuclear reactions the observed increase in the mass of particles accelerated to near-light speed in particle accelerators EXPLAIN QUALITATIVELY AND QUANTITATIVELY THE CONSEQUENCE OF SPECIAL RELATIVITY IN RELATION TO: – THE RELATIVITY OF SIMULTANEITY – THE EQUIVALENCE BETWEEN MASS AND ENERGY – LENGTH CONTRACTION – TIME DILATION – MASS DILATION Note*: a rest frame is the frame of reference within which a measured event occurs or a measured object lies at rest The Relativity of Simultaneity Pg 30-31 Simultaneous events in one frame of reference are not necessarily observed to be simultaneous in a different frame of reference. The Equivalence between Mass and Energy The rest mass of an object is equivalent to a certain quantity of energy. Mass can be converted into energy under extraordinary circumstances and energy can be converted into mass For example, part of the mass is converted into energy in nuclear fission reactions. When a particle and its anti-particle collide, the entire mass is converted into energy. o The energy yield from converted mass in nuclear reactions (e=mc2) In Special Relativity, the Law of Conservation of Energy and the Law of Conservation of Mass have been replaced by the Law of Conservation of Mass-Energy. Length Contraction The length of an object measured within its rest frame is called its proper length (Lo). Observers in different reference frames in relative motion will always measure the length (Lv) to be shorter. The shortening of an object occurs in the direction of its motion as observed from a reference frame in relative motion Time Dilation The time taken for an event to occur within its rest frame is called the proper time (to). Observers in different reference frames in relative motion will always judge the time taken (tv) to be longer. o The flying of atomic clocks to determine the existence of time dilation. One of the synchronised clocks was placed in an airplane which flew at maximum speed. The other stayed on the ground. When the clocks were brought together again, time on the clock in the plane passed more slowly than time for the clock on the ground. o The time dilated lifetimes of mesons penetrating the Earth’s atmosphere Mass Dilation Another consequence of the theory of Special Relativity is that the mass of a moving object increases as its velocity increases. This effect is noticeable only at relativistic speeds. As an object is accelerated close to the speed of light its mass increases. The more massive it becomes, the more energy has to be used to give it the same acceleration, making further acceleration more and more difficult. The energy that is put into attempted acceleration is instead converted into mass. The total energy of an object is then its kinetic energy plus the energy embodied in its mass o The observed increase in the mass of particles accelerated to near-light speed in particle accelerators (mass dilation) SOLVE PROBLEMS AND ANALYSE INFORMATION USING: E mc 2 lv l0 1 tv c2 t0 1 mv v2 v2 c2 m0 1 v2 c2 ANALYSE INFORMATION TO DISCUSS THE RELATIONSHIP BETWEEN THEORY AND THE EVIDENCE SUPPORTING IT, USING EINSTEIN’S PREDICTIONS BASED ON RELATIVITY THAT WERE MADE MANY YEARS BEFORE EVIDENCE WAS AVAILABLE TO SUPPORT IT When Einstein proposed his special theory of relativity in 1905 and his general theory of relativity in 1915, the technological capability to verify the predictions did not exist Evidence supporting the Special Theory of Relativity: o the flying of atomic clocks to determine the existence of time dilation One of the synchronised clocks was placed in an airplane which flew at maximum speed. The other stayed on the ground. When the clocks were brought together again, time on the clock in the plane passed more slowly than time for the clock on the ground o the time dilated lifetimes of mesons penetrating the Earth’s atmosphere o the energy yield from converted mass in nuclear reactions (energy mass equivalence: e=mc2) o the observed increase in the mass of particles accelerated to near-light speed in particle accelerators (mass dilation) Evidence supporting the General Theory of Relativity: o In 1919, the general theory of relativity was able to be used to explain the perihelion precession of Mercury. o Observations of star light passing close to the eclipsed Sun confirmed general relativity's prediction that massive objects bend light. A slight apparent shift in the position of a star could be accounted for by the General Theory of Relativity DISCUSS THE IMPLICATIONS OF MASS INCREASE, TIME DILATION AND LENGTH CONTRACTION FOR SPACE TRAVEL Provided that relativistic speeds could be reached, the nearest stars should be able to be reached in several years. For example, travelling to Alpha Centauri (~4 light years away) at half the speed of light should take a little over eight years. From the Earth’s point of view the clocks on the spacecraft are moving slowly, so that less time passes on the spacecraft compared to the Earth. o Mathematically, time as measured on earth is tv = 8 years. The time within the rest frame (t0) will be less than tv = 8 years From the point of view of the spacecraft occupants, the length of the journey (4 light years) has contracted to a significantly shorter distance, which at a speed of 0.1c, they will cover in less time. Accelerating to relativistic speeds would incur considerable energy costs, due to the conversion of energy into mass. o Mass increase means that if a particle was to be accelerated to the speed of light it would have infinite mass, so to accelerate it to this point would require infinite energy. Therefore an object cannot be accelerated to the speed of light. DISCUSS THE CONCEPT THAT LENGTH STANDARDS ARE DEFINED IN TERMS OF TIME IN CONTRAST TO THE ORIGINAL METRE STANDARD In 1793, the metre was defined for the first time by the French government to be one ten-millionth of the length of Earth’s quadrant passing through Paris. After this was surveyed incorrectly, 3 platinum standards were made, with several iron copies In 1875, the Systeme International (SI) of units defined the metre to be distance between two lines inscribed on a bar of platinum-iridium alloy o Inaccuracies increase with copies made o Temperature change can cause metal to expand/contract o Length changes with speed (length contraction) Currently, one metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458th of a second o Supported by the idea of space-time that even though length will change if speed changes, the speed of light is always constant in a vacuum Therefore, the measurement of a metre is unaffected by time dilation or length contraction o Takes advantage of technological capabilities to measure time and speed of light with great accuracy The definition of one second is very precise (9 129 631 770 oscillations of the 133Cs atom) o Can be found in any lab anywhere in the world with the right equipment