Download Space #3

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).
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Pg 1,2
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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
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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
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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
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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
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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
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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:
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GRAVITATIONAL CONSTANT
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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
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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:
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LAW OF CONSERVATION OF MOMENTUM
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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…
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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
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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
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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
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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.
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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
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Pg 17
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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
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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


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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
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

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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