HSC Physics Space Notes

HSC Physics Summary

©

Ben 2010-present

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UNIT 1: Space

a. Definitions

b. Earth’s Gravitational Field

c. Factors of a Rocket Journey (Projectile Motion)

d. Gravity in the Solar System

e. Theories of Time & Space (Aether + Special Relativity)

a. Definitions

Weight (N)

The force (Newtons) that acts upon an object due to the

presence of a gravitational field. The magnitude of the weight

force depends on the strength of the field at a point and the

mass of the object:

F

W

= mg

F

W

is weight in Newtons

m is mass in Kilograms

g is acceleration due to gravity in ms

-2

Work (W)

Work is a measure of energy required to displace an object a

specific distance. Work is given by the formula:

W = Fs

W is work in joules

F is force in Newtons

s is displacement in metres

Gravitational

Field

Region in which a mass experiences a force towards the centre of

gravity – usually the centre of a large mass (e.g. planet) The

gravitational force experienced by a mass at a point is given by

Netwon’s Gravitational Force Equation:

F

g

=

where: F

g

is the gravitational force in Newtons (N)

G is the universal gravitational constant (6.67x10

-11

Nm

2

kg

-2

)

d is the distance between the centre of the two masses (m)

m

o

& m

p

are the masses of the object and planet respectively (kg)

The acceleration due to gravity (g) caused by a mass (planet) is given

by:

g = G

where: g is the acceleration due to gravity in ms

-2

G is the universal gravitational constant (6.67x10

-11

Nm

2

kg

-2

)

d is the distance from the centre of the mass (planet) in metres

Acceleration due to gravity at earth’s surface is 9.8ms

-2

downwards

Universal

Gravitational

Constant

A numerical constant existing in many of Newton’s equations. It equal

to:

G = 6.67 x 10

-11

( units: Nm

2

kg

-2

)

Gravitational

Potential

Energy (E

p

)

Potential energy possessed by a mass according to its position within a

gravitational field. The work done on an object to raise it from the

surface of a planet to a higher altitude is equivalent to the object’s E

p

:

E

p

= mass x gravity x height = mgh

Conversely, work is done by gravity to lower an object and reduce its

E

p

.

On an Astronomical scale, E

p

= 0 at an infinite distance away ( )

i.e. At any tangible distance, E

p

< 0, as represented by the equation:

E

p

=

where: E

p

is Gravitational Potential Energy in joules

G is the universal gravitational constant (6.67x10

-11

Nm

2

kg

-2

)

d is the distance between the centre of the two masses (m)

m

1

& m

2

are the masses of the object and planet respectively (kg)

Projectile

Any moving object that moves only under the sustained force of

gravity.

Escape Velocity

The velocity that must be attained by an object in order to escape the

gravitational field of a planet. Escape velocity is determined by the

mass and radius of the planet. Earth’s escape velocity is 11.2 kms

-1

v

2

=

G-Force

A ‘Force’ is a unit of force acting upon an Astronaut. Multiple

G-Forces equate to multiples of the Astronauts regular Weight Force.

(i.e.

2

G-Force

=

2x

Normal

Weight)

The G-force scale is an easily understood and communicated scale.

The scale is applicable to all Astronauts, regardless of their mass. This is

because the force they experience will be relative their personal weight.

g-force =

Launch Window

Frame of time during which a rocket needs to be launched so that it

reaches its destination at the right time. Launch windows are largely

based upon Earth’s rotation and Earth’s orbit around the sun.

Uniform

Circular Motion

Uniform Circular Motion is undergone by objects travelling along a

circular path. The circular path is caused by the object’s velocity, which

attempts to keep it travelling straight, while an external centripetal

force (such as gravity) directed towards the axis at a right angle causes

it to follow a circular path for as long as the centripetal force acts.

Kepler‟s Law of

Periods

=

This equation, derived from Newton’s Law of Universal Gravitation, can be used to find the orbital period, T, of any orbiting mass around any planet.

Orbital Decay

Orbital Decay refers to the orbital descent and eventual fall to earth experienced by satellites in LEO orbits. It is caused by atmospheric drag.

Atmospheric

Drag

Atmospheric friction causes a satellite to lose forward velocity,

and hence causes it to lose altitude (according to

F

c

< F

g

.)

Friction slows the satellite, causing it to lose altitude where there is more friction which further slows the satellite… and so on!

Ionosphere

Thermosphere. Upper layers of Earth’s atmosphere (80km – 640km)

Exosphere

Outermost sphere of Earth’s Atmosphere extending 9600km.

Re-Entry

Return of a spacecraft into Earth’s atmosphere and subsequent descent

to Earth

Point of

Weightless

-ness

An object between the moon and earth will experience a point of

weightlessness where the gravitational attraction due to gravity from

both the Earth and moon will be equal and opposite.

Slingshot Effect

a.k.a. Gravity Assist Effect. Method used by astronauts to

“slingshot” a spacecraft around a planet, exploiting its gravitational field to

accelerate the craft.

Geostationary

Orbit

a.k.a Geosynchronous orbit. An orbit in which a satellite travels with the

earth’s atmosphere, remaining at the same point in the sky relative to

earth’s surface. (e.g. Foxtel, Communications, GPS.)

Low Earth Orbit

(LEO)

Satelites in LEO are usually between 250-1000km above sea level, and

never higher than 1500km. They have shorter periods (1-5 hours) and

their position in respect to earth is constantly changing.

(e.g. satellite imaging, weather forecasting, spying.)

Serendipity

The art of making scientific discoveries accidentally. Many major

breakthroughs in science have been ‘stumbled upon’ in this manner.

(e.g. Michelson & Morely)

Electromagnetic

Radiation

(EMR)

Self-propagating waves of varying wavelengths that travel at the speed

of light (c). They do not need a medium through which to travel and

include all the radiation on the electromagnetic spectrum. (e.g. x-rays)

Measurement

A comparison between a quantity to a selected standard and expressing

the measured quality as a factor of that standard. (e.g. 2 x std. metre)

All measured quantities are relative quantities.

in the fraction

of a second. (i.e. defined in terms of time)

Simultaneity

Events will occur at different times in different frames of reference

based upon the observer’s velocity. Both perspectives are correct.

Observers in relative motion will disagree on the simultaneity of

events separated in space.

Limiting

Velocity

No object can travel faster than the speed of light (c = 3x10

8

ms

-1

)

Scalar or Vector Quantity

SI Units

Distance / Displacement / Radius

metres (m)

Time / Period (T)

seconds

Speed / Velocity

metres-per-second (ms

-1

)

Impulse / Momentum

Newton-seconds (Ft)

Work Done / Gravitational Potential Energy

Joules

Momentum

Kilogram-metres-per-second (Kgms-1)

b. Earth’s Gravitational Field

DOT POINTS 1.1.1 – 1.1.3



Mass (the amount of matter of which an object consists) does not change with location



Weight (the force acting upon a mass due to gravity) changes according to gravity



Gravitational Fields are regions in which a mass experiences a force towards the centre

of gravity – usually the centre of a large mass (e.g. planet) the gravitational force of

such a field at a point is given by Newton’s Gravitational Force Equation:

F

g

=

This equation is derived from the below equation, from which g (a) is replaced by (F = ma)



The acceleration due to gravity (g) at a point caused by a large mass is given by:

g = G

PRACTICAL: Perform an investigation to determine a value for acceleration due to gravity using pendulum

motion and identify reasons for possible deviations from the correct value of 9.8ms-2

AIM: Determine acceleration due to gravity using a pendulum and compare experimental

results to published results. The relationships between the period (T) of a simple pendulum

is related to its length (l) and acceleration due to gravity (g) is shown by:

T = 2

EQUIPMENT: Retort stand, bosshead and clamp, roll of string, masses, stopwatch

METHOD:

1. Set up a retort stand and clamp on the edge of a desk and tie a length of string to it

2. Tie a 200g mass 1 metre down the string (cut off excess string)

3. Release the masses from 20

o

deviation from vertical

4. Using a stopwatch, time how long it takes for the pendulum to complete 10 full periods

5. Record this time in a results table with the corresponding length of string

6. Perform a total of three times for each length of string

7. Shorten the length of string by 10cm after each set of three trials and repeat steps 4-7

until results are obtained for a string length of 50cm.

EXPERIMENTAL ERRORS:

 The trial for each different length of string could be repeated several more times

to allow for greater accuracy

 Observing the time taken for 20 Periods to pass instead of 10 will reduce the error

involved with the reaction time of the person with the stopwatch

 A light gate could be used to gather more precise measurements of the period of

the swing

FACTORS AFFECTING THE VALUE OF g ON EARTH:

 Due to Earth’s spin, there is a slight bulge at the equator and flattening at the

poles. Because the force of a gravitation field (F

g

) acting upon an object is directly

proportional to

, an object’s elevation affects the force it experiences.

 The density and chemical composition of the Earth’s crust between an object and

the origin of force influences the magnitude of the force the object experiences

this is because there is more mass per volume, which equates to greater force.

How is a change in gravitational potential energy related to work done?

 The Gravitational Potential energy possessed by an object is determined by its mass

and its distance from the centre of a gravitational field.

 The work done (Force x Displacement) on an object to move it away from the centre of

gravity is equivalent to the E

p

possessed by that object:

Work Done = Gravitational Potential Energy

W = E

p

This method of deriving Ep applies exclusively in terrestrial situations within Earth’s atmosphere

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.

On an Astronomical scale, a separate trail of logic applies when finding E

p

– Newton’s Law of Universal Gravitation is the basis for this logic:

 The gravitational attraction forces existing between two objects decreases with d

2

 Therefore, F

g

and E

p

only reach 0 when the object is an infinite distance away

 BUT! The E

p

possessed by an object increases equivalent to the work done to move the

object away from the centre of gravity and towards infinity

 Hence, an object gains E

p

as it gets closer towards infinity (where E

p

= 0)

 Therefore, the value of an object’s E

p

at any tangible location has to be less than that

which it possesses at infinity (i.e. at any tangible distance, E

p

< 0)

 Therefore, E

p

has a negative value, as represented by the equation:

E

p

=

U

y

U

x

U

c. Factors of a Rocket Journey (Projectile Motion)

Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components.

TWO types of Projectile Motion:

 Oblique Motion:

o Launched at an angle of elevation

o Initial velocity (u or v

0

) can be illustrated using a vector

diagram [right]

o Horizontal Velocity remains constant (U

x

= V

x

)

o At the apex,

V

y

= 0

and ½ t

o

_initial

=

final

 Horizontal Motion:

o Launched horizontally (usually from a height)

o No vertical velocity at launch (U

y

= 0)

o Height is vertical displacement (S

y

)

o Horizontal Velocity remains constant (U

x

= V

x

)

Describe Galileo’s analysis of projectile motion

1. Projectiles follow a perfect parabolic path

2. Trajectory be split into two components: vertical and horizontal

3. Horizontal velocity remains constant

( U

x

= V

x

)

It isn’t influenced by a sustained force

4. Vertical velocity is uniformly accelerated downwards at 9.8ms

-2

due to gravity

5. Projectiles are subject only to their own inertia and the sustained force of gravity

http://static.newworldencyclopedia.org/thumb/7/73/Newton_Cannon.svg/220px

Solve Projectile Motion Problems using horizontal and vertical components in combination with Newton’s

equations of motion

Newton’s Equations of Motion:

 v = u + at

 v

2

= u

2

+ 2as

 s = ut + ½ at

2

Horizontal

Vertical

U

x

= ucos

U

y

= usin

V

x

= u

x

(a = 0)

V

y

= u

y

+ 9.8t

V

x2

= u

x2

V

2

= u

y2

+ 2a

y

s

y

S

x

= U

x

t (a = 0)

S

y

= u

y

t + ½at

2

Explain escape velocity in terms of the gravitational constant and the mass & radius of the planet

To escape Earth’s gravitational pull, a projectile fired from the surface of Earth needs to be

given kinetic energy equal to its gravitational potential energy:

E

K

=

½m

1

v

2

E

p

=

E

K

> E

p

½ m

1

v

2

>

v

2

>

Escape velocity increases with the planet’s mass and decreases with distance from the centre of gravity. Escape velocity is independent of the projectile’s mass.

Outline Newton’s concept of escape velocity

Newton theorised his principle based on a hypothetical scenario in which a projectile is

fired from an impossibly high vantage point as such as speed (8000ms

-1

) that it never lands

due to the balancing factors of the Earth’s curvature and gravity.

(i.e. the object enters

orbit when fired fast enough.) He thus reasoned that if an object were to be fired faster

than this theoretical value (8kms

-1

), it could escape earth’s gravitational field.

Earth’s escape velocity is 11.2kms

-1

Identify why the term ‘g-forces’ is used to explain the forces on an astronaut

 G-forces are multiples of the normal weight force experienced on Earth

 The G-force scale is used to easily communicate the force acting upon an astronaut,

expressing it in terms of what they normally experience.

 The G-force scale is applicable to every individual based on their personal, unique mass.

This is because experienced forces are relative to their mass.

g-force =

Perform a first-hand investigation to calculate initial and final velocities, range and time of flight of a projectile. i.e. Mega Marble LauncherTM

Projectile Motion Class Assignment\Projectile Motion Assignment – Mega Marble Ludicrous Launcher with graph.docx

AIM:

To determine and graph the relationship between the launch angle and range of an oblique projectile using the Mega Marble Launcher™ - and hence find the optimum launch angle that corresponds to the maximum range possible.

SAFETY:

 Ensure all personelle wear safety goggles at all times throughout the experiment  Conduct experiment in isolated area secluded from students and other hazards

 Only fire projectile when the firing range is clear and all personnel are behind the line of fire

METHOD:

1. Set up the Mega Marble Launcher™ in a remote location, pointed in a direction with at least 50m of space and free from obstruction.

2. Arm the launcher, first setting the launch angle to 20o and placing a marble into the shaft. (Ensure all

marbles launched in the experiment are of the same size and shape)

3. When the firing range is clear, launch the marble.

4. Measure the range with a measuring tape and retrieve the marble. Record this value for the range in a table like the one below with the corresponding launch angle:

Launch Angle Range (m)

20o xx

5. Repeat the trial with the same launch angle a total of 5 times to ensure reliable results are collected. 6. Repeat steps 2-5 with a launch angle of 30o, 45o, then again for 60o, completing each trial a total of 5

times to ensure reliable results are collected.

7. Graph the results, with launch angle (o) on the horizontal axis and average range (m) on the vertical.

RESULTS & ANALYSIS:

Results show range increasing with the launch angle to a maximum value achieved at 45o_{, (as was hypothesised) then decreasing for 60}o_{. The closer to 45}o

the angle, the greater the range achieved. The relationship between the range and the launch angle is non-linear. The range of a projectile is not directly

proportional to its launch angle; the relationship between these variables is more

complex. An online source shows the relationship to be:

R = V

2

x

LIMITATIONS, ERRORS & IMPROVEMENTS:

- The muzzle velocity is only sufficient to achieve small ranges – experimental results are more “bunched up” and hence variations in range are harder to detect. - There are only 4 launch angle settings (20o, 30o, 45o, 60o), making it difficult

- The contour and texture of the test range (grass) caused the marble to roll or bounce upon landing.

- The crosswind proved to be a major factor that influenced the results + Perform more trials for each launch angle to obtain reliable results

+ Apply a greater consistent launching force to the marbles so that longer, more diverse (and hence comparable) ranges are reached.

+ Use a firing range that is flat and sheltered to minimise wind resistance and/or projectile bouncing and rolling.

Analyse the changing acceleration of a rocket during launch in terms of Conservation of Momentum and the forces experienced by astronauts

Rocket launch, Momentum and Forces

 At launch, the downward momentum of exhaust gases provides equal upward impulse (F x t) to propel the rocket (Newtons 3rd _{law) :}

Because change in momentum of an object is equal to the impulse of an applied force, so the impulse of the exhaust gases down will equal the impulse applied to the rocket upwards:

 Pilots experience vision problems at 4g, and lose consciousness at 8g. 3g was once considered safe.

 Astronauts can survive up to 20g if:

 They lying down (stops blood draining from head)

 Facing opposite to the direction of force (stops eyes from popping out)  The forces acting upon a rocket during its launch and flight include:

 Weight Force (down)  Thrust (up; Thrust > Fw)

 Reaction force (up while stationary; =0 when in flight)

Momentum of Rocket

Discuss the effect of Earth’s orbital and rotational motion on rocket launches

Effect of Earth’s motion on Rocket Launch

 The earth spins counter-clockwise (when viewed from above the north pole)

 Rockets are launched eastward from the equator, where the rotational speed of the

earth is greatest, and adds an extra 1700kmh

-1

to their trajectory.

 The orbital speed of the Earth around the Sun can also be harnessed to attain greater

velocity in respect to the solar system (used for Intra-Solar-System travel.)

 Less fuel needs to be spent to attain escape velocity and more storage mass (payload)

can be carried if rotational speeds are harnessed.

 ‘Launch Windows’ are frames of time during which a rocket must be launched to arrive

at its destination at the right time – taking full advantage of orbital speeds.

Analyse the forces involved in uniform circular motion for a range of objects, including orbiting satellites

Uniform Circular Motion is undergone by objects travelling along a circular path.

The circular path is caused by the object’s velocity, which attempts to keep it travelling

straight, while an artificial centripetal force directed towards the axis at a right angle

causes it to follow a circular path for as long as the centripetal force acts.

Centripetal Force / Acceleration:



F

c

Acts towards the centre of the Circular Locus



Direction (and velocity) change continuously due F

NET



Velocity & Centripetal force keep object in motion



Speed Remains constant

In the context of a rocket orbiting earth, the force of gravity is considered the

centripetal force as the rocket produces a right-angle velocity around earth.

To stay in orbit, a satellite needs to maintain a speed in proportion with the earth’s gravity, its own mass (m) and its distance from Earth’s centre (r.) This is because the centripetal force (Fc = gravity, in this case) will remain constant, so the satellite must

adjust its velocity to balance it and thus undergo uniform circular motion.

In Orbit: F

c

= F

g

where… F

g

=

Gravitational Force acting upon the object as given by

F

g

=

R = radius of orbit centre-to-centre (in metres)

v = Orbital speed of object [ms

-1

]

m = mass of object in orbit (in kilograms)

F

c

=

a

c

=

F

g

=

=

Compare qualitatively, Low Earth Orbit (LEO) and Geostationary Orbits

Feature

Low Earth Orbit Satellites

Geostationary Satellites

ALTITUDE

(<1500km) 250 – 1 000 km

35 800 km

PERIOD

90mins – 5hrs

~

24hrs (1 Earth-day)

ORBIT

Usually Polar Orbit

Equatorial Orbit

POSITION

Constantly moving about Earth

Fixed position above Equator

USES

Satellite Imaging, Weather

Forecasting, Spying

Communications, GPS, Foxtel,

“bounce” signals

REASON

Closer  High Resolution Images

Constant Line-of-sight to Receivers

SPEED

Fast  High gravitational pull

Slow  Low gravitational pull

Outline the contribution of Tsiolkovsky to space exploration

Tsiolkovsky (1898-1935):

1.

Calculated escape velocity

2.

Suggested propulsion by reaction

3.

Designed (didn’t build) multistage rockets

4.

Examined potential medical implications for Astronauts

5.

First to suggest using oxygen + hydrogen as fuels

Define Orbital Velocity and its relationship with G, the mass of the planet and satellite, and the radius of the orbit, qualitatively and quantitatively

Orbital Velocity

Orbital velocity is simply the speed at which the satellite is travelling. It can be calculated by dividing the distance it travels in its orbit by its orbital period:

When an object is in orbit:

F

c

= F

g

Rearranging the equation

=

:

v

2

₌

_{v =}

The orbital velocity of an object is dependent only upon the mass of the planet and the orbital radius

v =

T r



Solve problems using Kepler’s Law of Periods

Kepler’s Law

Substituting

v =

into the above equation for Orbital Velocity (where

):

₌

=

This equation, known as Kepler’s Law of Periods, can be used to find the orbital period, T, of any orbiting mass around any planet.

When solving questions, first find the ratio = k then equate the ratio (k) to the radius and period of

the planet (Kepler’s law), substituting the pronumeral for the unknown quantity and solve.

Account for orbital decay of satellites in LEO



Orbital Decay refers to the orbital descent and eventual fall to earth

experienced by satellites in LEO orbits. It is caused by atmospheric drag.



Atmospheric friction causes a satellite to lose forward velocity, and hence

causes it to lose altitude (according to

F

c

= F

g

.)



As the satellite loses altitude, encounters more atmospheric friction as it descends further into earth’s ionosphere, where particles are more densely packed. This extra friction causes it to slow further and hence descend further, and so on.

Discuss issues associated with safe re-entry into the atmosphere and landing on the surface

Safe Re-entry



At 92km, spacecrafts experience intense heat  atmospheric friction



Space Shuttle = 7.5kms-1 _{/ Apollo 11.1kms}-1 _{ Atmosphere slows}



Heat ionises surrounding air, blocking out radio communications



Little noise as it glides without motors and heat shield in front



Shuttle = 16 mins / Apollo 3-4 mins



Maximum heating experienced at 80km altitude



Apollo Craft  Heat shield temperature = 3 000o_C

Safety Devices used to ensure safe re-entry:



Blunt Nose + Wings + Belly  distribute heat



Sacrificial Skins  initially metal alloys  later fibreglass & heat-resistant ceramics: absorb heat and vaporise



Coated spongifoam fibreglass (90% air) is lightweight and its coat prevents

it from absorbing moisture.

F = mg

F

g

=

Identify optimum angle for re-entry into Earth’s atmosphere and consequences of failing to achieve this



The optimum re-entry angle for survival: 6.2o to the horizontal (plus or minus 1o)



Angle too shallow: Spacecraft bounces off atmosphere and be lost in space



Angle too large: g-forces will exceed fatal magnitudes and capsule melts



The purpose of the re-entry angle is to minimise the g-forces experienced by the astronauts while still preventing the craft from “bouncing off” the atmosphere.

d. Gravity in the Solar System

DOT POINTS 3.1 – 3.3

Gravitational Fields

 Gravitational fields are regions in which a mass experiences a force

 All bodies exert Gravitational fields proportional to their mass

Newton’s Law of Universal Gravitation

Every object in the universe attracts every other object with a

gravitational force that is depended upon:



the masses of both objects



the distance between both objects’ centres of gravity

Newton’s Law of Universal Gravitation is

represented by the Equation:

Because we know the value of g on earth (9.8ms

-2

), the gravitational force acting

on any object on earth’s surface is given by its weight force:

The following formula can be used to

determine the value of g on any planet:

where

G = 6.67 x 10

-11

(universal gravitational constant)

r = distance between the objects’ centres of gravity

m

o/p

= mass of the object/planet respectively

Discuss factors that affect the strength of gravitational force



Altitude – higher elevation equates to a further distance from the centre of

gravity and hence a smaller gravitational force will exist at higher altitudes



Position on Earth – The earth isn’t a perfect sphere: the equator has a

higher elevation than the poles, hence gravitational force is less at the

equator, as gravitational attraction (force) becomes less with distance

2

.



Density of Earth’s Crust – Different parts of the earth’s crust have greater

density (more mass per volume) than others (e.g. land / ocean) Regions with

greater density will exhibit a slightly greater gravitational force.

Discuss the importance of Newton’s Law of Universal Gravitation in calculating the motion of satellites

Gravity and Satellite Motion



Newton’s gravitational Equation lets us calculate orbital velocities of satellites



From it, we derive the formula for gravitational potential energy ( Ep = )



Formula is used to explain and calculate launch windows & the slingshot effect



Gravity is the reason rocket launches are expensive and require so much energy

Identify that a slingshot effect can be provided by planets for space probes



a.k.a = Gravity Assist Effect



Refers to the method used by astronauts to “slingshot” a spacecraft around a planet, exploiting its gravitational field to accelerate the craft.



Maximum velocity is harnessed when the craft passes around the planet in the

direction of rotation. The velocity gained will be twice the rotational speed

of the planet.



Passing a craft around a planet opposing its direction of rotation will slow the craft



Relative to the planet, the craft does not appear to gain/lose speed, but relative to the sun, the object speeds up/slows down.



The slingshot effect is technically “a non-elastic collision that occurs between the craft and planet.” The rotational kinetic energy of the planet is transferred to the craft as translational (straight line) kinetic energy. The planet has lost kinetic energy, but its mass is so large in comparison, this amount is negligible.

e. Theories of Time & Space (Aether + Special Relativity)

Outline the features of the aether model for the transmission of light.

The Aether Theory:

 In the scientific search for the properties of light during the 19

th

_{century, scientists}

proposed the existence of an invisible medium, which they called aether, through which

light was thought to travel in the same manner as other waves (sound, water, seismic.)

 The properties of this alleged light-medium, aether, were:

o Had no mass, Filled all space, had low density and was perfectly transparent

o Frictionless, distributed evenly throughout universe, incompressible, rigid

o Had great elasticity to support and propagate light waves

 After many years of attempting to prove the existence of aether, two conclusions were

finally drawn about the proposed medium:

o Aether does not exist

o Electromagnetic waves (including light) are self-propagating waves (no medium)

Describe and evaluate the Michelson-Morley attempt to measure the relative velocity through the aether.

Conducted by Michelson and Morley in 1887:

AIM:

To measure the velocity of the Earth relative to the aether.

METHOD:

 A beam of light emitted by a light source was split by a half-slivered mirror and sent at 90o

to one another towards two different mirrors

 They were reflected back and combined, such that both rays travelled the same distance to reach a detector at the end of their journey.

 The whole apparatus was floated on liquid mercury which enabled a smooth rotation of the entire experiment.

RESULTS:

 If the light rays were being influenced by an Aether „flow,‟ (across/upstream) the rays would strike the detector at different times, producing an interference pattern.

 Also, as the experiment was rotated, the aether wind was expected to slow or hasten the speed of light in a particular direction, thus causing a changing interference pattern.  Despite extensive testing and repetition, no interference

pattern was observed and the experiment was a null result.

CONCLUSION:

 The null result did NOT disprove the theory immediately: scientists were forced to reconsider the model and create ad-hoc explanations (aether drag.)

 The result was later used by Einstein to support his theory of relativity and to disprove the aether model. Although it was a failure, the conclusion drawn from the null result was both valid and reliable and changed scientific theory dramatically, making it one of history‟s most important experiments.

Gather and process information to interpret the results of the Michelson-Morley experiment

 The Michelson & Morely experiment was based upon the presumption that aether remained stationary while earth moved through it. They expected to detect this motion of the earth through the aether by observing how much the light was influenced when it travelled through the ‘aether wind’

 In much the same way that two boats travel the same distances, one up the current and the other across the current, the light rays were expected to arrive at different times according to whether they were moving against the aether or across it, as earth moved through the aether.

 The table upon which the experiment was conducted floated upon a pool of mercury, allowing the entire experiment to be rotated. M&M were looking to detect any differences in velocity or interference patterns when they altered the direction at which the light moved through the aether.

 No such change in interference pattern resulted, therefore providing a null result.

o There is no stationary background medium (aether) in space moving relative to the earth o All moving objects (frames of reference) receive light travelling at the same speed in a

vacuum in all directions.

 Since the Earth was known to move, the aether model was pronounced flawed, later to be disproved by Einstein, who used these results in confirming his theories of the constancy of the speed of light.

 The experiment supported Einstein‟s theory that light remains constant, and refuted the aether model Outline the nature of inertial frames of reference

 A frame of reference is an environment from which an observer can conduct an observation  Einstein proposed that there are two distinct frames of reference:

Inertial Frames of Reference

 An inertial frame of reference is an environment or system travelling with uniform velocity  In an inertial frame of reference, all of Newton‟s laws are obeyed (e.g. addition of velocities)  No observation can be made within an inertial frame of reference to determine whether the

frame is moving or at rest. (e.g. if there were no windows in a train travelling at uniform velocity, the passengers would not be able to detect the train‟s motion by any means.)

Discuss the principle of relativity.

 There is no absolute frame of reference in the universe, as everything is in motion. All motion is simply relative to other motion (e.g. when still, we are stationary relative to earth‟s surface)  In 1905, Einstein published a paper proposing a “Special Theory of Relativity.” This theory

superseded Newtonian Relativity.

Special relativity is based upon two fundamental principles:

1. The laws of physics are the same for all inertial frames of reference.

2. The speed of light (c) is constant for all observers regardless of their velocity  These principles inferred the following visible implications for observers:

o Length contracts in the direction of motion

o Time dilates (object appears to slow as the seconds lengthen) o Mass increases with velocity

Length, Mass and Time distort to keep the speed of light constant for all observers The speed of light (c) is the only thing that remains constant in the universe

 Einstein‟s theory of special relativity, in conflict with the popular scientific theory of aether, was revolutionary and hesitantly received. The theory was based upon thought

Describe the significance of Einstein’s assumption of the constancy of the speed of light.  Special relativity assumes that the speed of light remains constant for all observers (c)  This means that all observers will measure the speed of light travelling at the same speed  This idea is in conflict with Newtonian logic, which implies that light will exceed the value of c

when light is emitted from a fast-moving object – according to vector addition

 Employing the logic of Einstein‟s relativity, we can accurately determine how objects behave at relativistic velocities (e.g. time dilates, length contracts, mass increases)

 There exists a space-time continuum, in which any event has 4 dimension: 3 spacial coordinates and 1 time coordinate

Analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and reality.

Einstein had two main thought experiments:

 Looking at himself in a mirror on a train moving at the speed of light  Bouncing light from the roof to the floor and back in a moving train

TRAIN-MIRROR THOUGHT EXPERIMENT:

 Einstein wondered whether he would be able to see his face normally in a mirror he held in front of his face if the train was travelling at the speed of light.

 He decided that he would be able to, because he was in an inertial frame and should have no way to determine he was moving at c.

 But with vector addition, a stationary observer would see light travelling away from Einstein‟s face at c, but as the train was also moving at c, the observer would see light travel twice the distance in the same amount of time.

o Einstein‟s interpretation of this was that the time observed for light to travel that distance had changed (increased), so that a stationary observer would see light travelling at c.

LIGHT BOUNCING THOUGHT EXPERIMENT:

 Inside the moving train, the light is seen to travel straight up and down from the roof to floor and back again.

 From a stationary observer however, the light is seen to travel a much longer path, but in the same amount of time, which would result in a changed speed of light (going against Einstein‟s theory)

 Again his interpretation was that time had slowed (dilated) so that c remains constant.

RELATIONSHIP BETWEEN THOUGHT AND REALITY:

 Thought experiments (gedankens) can be useful tools to „perform‟ experiments that cannot be performed in reality, such as a train moving at c, and to make meaningful conclusions as Einstein did.

 However, it is very easy to misinterpret thought experiments, either through flawed logic of failing to take into account other factors that would influence a real-life experiment.

Identify that if c is constant then space and time become relative.

In traditional physics, the behaviour of light had to adapt to the motion of the observer. With the light of speed being a constant under Einstein‟s theory, the dimensions involved in motion have to adapt to light. This means that space and time become relative to velocity so that c is always constant.

Explain that length is defined in terms of time

A metre was once defined as of the circumference of the Earth, and then later as the distance between two lines on a platinum-iridium bar, which provided the standard measure of the metre. However, today the metre is defined as the distance light travels in

seconds. This means that

distance is calculated with respect to time – a unit of distance measure in terms of how much distance light travels in a period of time. (like a light-year, the distance light travels in one year)

Analyse information to discuss the relationship between theory and evidence supporting it, using Einstein’s predictions based on relativity that were made many years before evidence was available

Scientific hypotheses cannot be proven/disproven (become theory) without evidence or experimental procedure. For this reason, Einstein’s hypothesis regarding the constancy of light was initially regarded with caution amongst the scientific community. In recent years, as new technology has become

available, scientists have experimentally proven what Einstein theorised about light and relativity:

 Atomic Clocks have been raced around the world in extremely fast jets to test

Einstein’s prediction of time dilation. The results showed that the precision atomic

clocks aboard the jets had slowed by a few nanoseconds, hence time dilates at high

velocities.

 A muon is a particle similar to an electron, but heavier. When stationary it has a half

life of around 2 microseconds, but when accelerated in a particle accelerator to

speeds up to 0.9994c, it was found their observed half life was around 60

microseconds – confirming Einstein’s theory.

Explain the consequences of special relativity in relation to the relativity of simultaneity…

A number of consequences and equations have arisen from Relativity:

SIMULTANEITY:

 Events observed to be simultaneous in one frame may not be simultaneous in another  This idea of simultaneity is dependent on the frame from which events are observed

EXAMPLE: Consider a train moving at a relativistic velocity

o A light source emits light that travels from the centre to the two ends of the carriage. o From an observer inside the carriage, the light will reach the ends simultaneously as the

distance travelled is equal.

o For a stationary observer however, the distance for the light to travel initially is the same, but the motion of the train means that the light reaches the rear of the carriage first as the front of the carriage is moving away from the light.

o Therefore the event does not happen simultaneously for both frames.

T

v

=

√

LENGTH CONTRACTION:

 A stationary observer sees a moving object contract in the direction of relativistic motion  The moving observer sees the stationary observer contract in the direction of motion

TIME DILATION:

 Seconds measured by the stationary observer seem longer than those measured by the moving observer

 Seconds measured by both observers seem to remain the same but the clocks in the other frame of reference (either faster or stationary) seem to run slower in comparison.

 All clocks, biological or mechanical run slower because time itself is passing more slowly

MASS DILATION:

 When an object travels at relativistic velocities, the mass of the object increases  This has implications for the limiting velocity that can be achieved by an object:

NO OBJECT CAN TRAVEL FASTER THAN THE VELOCITY OF LIGHT (c) (i.e. 3x108 ms-1)

All of these observations are true only when the frame being observed and the frame of observation are both inertial frames of reference. Note also that these changes are actual changes in the properties of space-time.

MASS & ENERGY:

 This equation shows the “rest energy” of an object and also the amount of energy released if matter is destroyed and converted into pure energy. (e.g. nuclear reactions, fission, fusion etc;)

Length, Time and Mass all change in proportion to keep the speed of light constant

Discuss the implications of mass increase, time dilation and length contraction for space travel. TIME DILATION:

 Allows travel into the future at high speeds, but not back to the past.

 Astronauts travelling in a relativistic spacecraft will age slower than people back on earth, which means they can comparatively live longer during space travel and people on earth will pass away

before they return. (Twin paradox)

LENGTH CONTRACTION:

 As a space craft speeds up, the apparent distance to objects ahead decreases. This means trips on a relativistic spacecraft will appear to cover less distance to observers in the spacecraft.

 Could possibly allow travel to distant stars etc.

MASS DILATION:

 As the speed of a spacecraft increases to the speed of light, its mass will increase up to infinity and hence restricting the velocity it is able to achieve.

L

v

= L

o

√

E = mc

2

M

v

=

√

 Travelling at a constant velocity (constant thrust), mass increases causing acceleration to decrease as the thrust becomes less and less effective requiring more fuel.