hsc physics space

Space

Module 9.2 Part 2

Image: New Horizons satellite at Pluto in June 2015 Artist’s impression

Syllabus 9.2.3

Mass and Gravitational Fields• The gravitational field around a

massive object is radial in shape, with the direction of the field being towards the massive body

• The strength of the gravitational field obeys an inverse square law i.e. the gravitational field strength decreases in proportion the the reciprocal of the square of the distance from the object’s centre of mass

• describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

Mass and Gravitational Fields

• describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

The gravitational field of the Earth is not uniform...

… unless just a small region of the total field is considered

The gravitational field of a massive body such as the Earth causes objects near the surface to undergo projectile motion, and more distant objects to undergo orbital motion

uniform field

Factors Affecting the Gravitational Force• The strength of the gravitational force

between two masses is– proportional to the mass of each object– inversely proportional to the square of the

distance between the centres of mass of the two objects

• The force is also dependent on the Universal Gravitational Constant - it is believed that this is a fixed quantity for our Universe

• present information and use available evidence to discuss the factors affecting the strength of the gravitational force

F Gm1m2

d2

Newton’s Law of Universal GravitationEvery particle in the universe attracts every other particle in the universe with a force that is proportional to the product of the masses and inversely proportional to the square of the distance between the particles.

• define Newton’s Law of Universal Gravitation

Good referenceshttp://www.physchem.co.za/Motion/Gravity.htm#Reasoninghttp://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l3c.html

F Gm1m2

d2

Newton’s Law of Universal GravitationCalculate the gravitational force between the Earth and the Moon.The mass of the Moon is 7.3483 x 1022 kg and the mass of the Earth is 5.98 x 1024 kg.The distance between the Earth and the Moon is 384,402 km.G = 6.67300 x 10-11 m3 kg-1 s-2

m M

mEd

FGm1m2

d2

• solve problems and analyse information using… [Newton’s Universal Law of Gravitation]

Newton’s Law of Universal Gravitation


mEarth = 5.97 x 1024 kg mSun = 1.99 x 1030 kg

distance from the Sun to the Earth = 150 million km

What is the gravitational force between the Earth and the Sun?

FGm1m2

d2

6.67 10 11 1.99 1030 5.97 1024

(1.5 1011 )2

3.52 10 22 N



FGm1m2

d2

m1 = 65 kg m2 = 20 000 000 kg

distance between neighbours = 2000 m

6.67 10 11 65 20000000

(2000)2

2.2 10 7 N

What would be the gravitational force between you and and a 20 000 tonne ship 2 km away?



F Gm1m2

d2

What is the gravitational force between you and the person sitting closest to you? [G = 6.67 x 10–11]

Answer ~ 3 x 10–7 N

Brain Break

What is a law?State an example of a law.

Outline three ways in which laws are validated.

About LawsWhat is a law?

State an example of a law.

Outline three ways in which laws are validated.

A law is a concise statement of how …

Newton’s laws of motion and his law of universal gravitation are examples of laws.

Answers

Laws are validated through being…

1. Being consistent with observations of phenomena to which the law applies.

2. tested and confirmed using controlled experiments designed to test the law.

3. able to make predictions than can be tested and verified.

Newton’s Law of Universal Gravitation• Do exercises at the website below

• solve problems and analyse information using

http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l3c.html

FGm1m2

d2


• discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites

r3

T 2 GM

4 2



FGm1m2

d2

Newton’s Law of Universal Gravitation•Isaac Newton proposed the Law of Gravity – a universal force that governed both projectile motion on the Earth, the motion of the Moon around the Earth and the motion of the planets around the Sun

•Newton’s three laws of motion apply to planetary motion as they do to motion on the Earth’s surface

• Law of inertia• F = ma• Forces act in pairs


Newton’s Law of Universal Gravitation• Before Newton, nobody understood

what force kept the planets moving in their orbits.

• Newton realised that the same force of gravity governed the motion of projectiles on the Earth and the motion of planets around the Sun

• Gravitational forces act between all objects having mass


The gravitational pull of the Sun provides the required centripetal force

FGMm

r2 mv 2

r

Newton’s Law of Universal Gravitation• Outline the views held about

motion of objects on the Earth’s surface and motion of celestial objects prior to Newton. (2M)

• Identify the major advance in scientific understanding brought about by Newton’s universal law of gravitation. (1M)

• Evaluate the importance of Newton’s law of universal gravitation in changing the nature of scientific thinking. (5M)

H1. evaluates how major advances in scientific understanding and technology have changed the direction or nature of scientific thinking

• Prior to Newton, people believed that celestial motion was governed by different laws to those that determined the motion of objects on the Earth’s surface. Ideas about the causes of celestial motion were not based on scientific thinking that related causes and effects.

• Newton advanced scientific understanding by deducing that planetary motion and motion of objects on the Earth’s surface were both determined by gravity

The Slingshot EffectAfter flying past Venus at an altitude of 16,000 km on February 10, 1990, the Galileo spacecraft swung past Earth at an altitude of 960 km on Dec. 8, 1990. That flyby increased Galileo's speed enough to send it on a two-year elliptical orbit around the Sun.The spacecraft returned for a second Earth swing-by on Dec. 8, 1992, at an altitude of 303 km. With this, Galileo left Earth for the third and final time and headed toward Jupiter.

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

The Slingshot EffectThe Cassini spacecraft was launched in 1997, flew twice by Venus, and then passed 1200 km from the Earth. On Dec. 30th 2000, it passed Jupiter, and finally arrived at Saturn in July 2004.Cassini, increased its speed by 5.5 kilometres per second as it passed Earth. And the total effect of the probe's four planetary flybys was 21.44 kilometres per second.


The Slingshot EffectThe slingshot effect is used to increase - or sometimes to decrease - the the speed, and to change the direction of motion of an interplanetary spacecraft.

Three bodies must always be involved for the slingshot effect to operate.

The satellites (usually a planet and an artificial one) must both be in orbit around a third central body.

As a result of the slingshot effect, the satellite gains momentum relative to the central body


See: SlingshotEffectSattEarth.mov

Successive positions of the Earth and a passing satellite interacting gravitationally.

T1 shows the path of the satellite altered by the slingshot effect. T2 shows the path had there been no interaction.

The Slingshot Effect• The momentum gained by the

satellite is not transferred back to the planet after the satellite-planet interaction.

• Momentum is transferred between the two because of the gravitational interaction between them.

• To gain momentum the satellite must approach the planet so that it passes on the side of the planet away from the Sun.


The Slingshot Effect• Interplanetary satellites use the

slingshot effect to reach their destinations without requiring large amounts of fuel.

• Looping orbits take the satellite close to the planet from which momentum is transferred, increasing the velocity.

• The trade-off is a journey which takes a long time, since several orbits around the Sun may be necessary to achieve the final goal.


The Slingshot Effect• Voyager 2 left the Earth at about 36 km/s

relative to the Sun. Moving away from the Sun, it loses much of the initial velocity the launch vehicle provided. Nearing Jupiter, its speed is increased by the planet's gravity, and the spacecraft's velocity exceeds solar system escape velocity.

• Voyager departed Jupiter with more Sun-relative velocity than it had on arrival. The happened at Saturn and Uranus.

• Diagram courtesy Steve Matousek, JPL.


The Slingshot Effect - New Horizon• In January 2006 a satellite

called New Horizons was launched from Earth on a 10-year journey to Pluto (due to arrive June 2015)

• The large rocket used propelled it away from the Earth at 15 km/s - the fastest ever

• It reached the distance of the Moon’s orbit in just 9 hours

• It will undergo a slingshot manoeuvre at Jupiter in 2008

The Slingshot Effect - Dawn Asteroid Mission• In September 2007 the Dawn satellite was

launched from Earth on a, 4.8-billion km journey to the asteroids Ceres and Vesta

• Dawn will make use of ion propulsion engines using xenon gas during its journey

• Dawn's will carry out measurements and observations of the asteroid Vesta in 2011 and the dwarf planet Ceres in 2015.

• Use the diagram to describe some aspects of the mission in words.

• Dawn will take 17 months to reach Mars, where it will undergo a gravity assist (slingshot) manoeuvre. Four years after launch it will reach Vesta where observations will be carried out for 9 months. It will then travel for 33 more months to study Ceres for 5 months.

• Ref: dawn-launch.pdf

Slingshot effect – Mercury Messenger

Slingshot effect – Mercury Messenger

KEY EVENTS:

• August 3, 2004 -- MESSENGER Launch• August 2005 -- Earth flyby• October 2006 -- Venus flyby• June 2007 -- Venus flyby• January 2008 -- Mercury flyby• October 2008 -- Mercury flyby• September 2009 -- Mercury flyby• March 2011 -- Yearlong science orbit of Mercury begins

The Slingshot Effect - Dawn Asteroid Mission• By studying both asteroids, scientists more accurately can compare and

contrast the two.• Dawn's science instrument suite will measure elemental and mineral

composition, shape, surface topography, and tectonic history, and will also seek water-bearing minerals.

Would you trust these people to put you in space?

Syllabus 9.2.4a

Syllabus 9.2.4b

Introduction to the Theory of Special Relativity

Prior to Einstein, length, mass and time were thought to be absolute quantities.

This meant that it was thought that the the properties of space and time were fixed, and in no way depended on the location or state of motion of the observer.

Einstein demonstrated that length, mass and time are not absolute quantities. This is relativity

Albert Einstein

2005 Happy 100th Anniversary!

Brain Break!

The Nature of LightTwo Models• Isaac Newton proposed in the 1600s

that light was a stream of particles - this model successfully explained the observed behaviour of light such as reflection and refraction.

• The alternative wave theory of light, proposed by the Dutch Christian Huygens, also explained reflection and refraction.

• There was no clear argument or phenomenon to exclusively support either model of light.

The Triumph of the Wave ModelDiffraction and interference• In the 1800s new phenomena

were discovered, diffraction and interference, that could not be explained with the particle model of light

Diffraction

Inte

rfer

ence

Young’s Experiment Confirms Wave Theory

Light interference was demonstrated by Thomas Young in the 1800s

Light passed through two very narrow slits produced two sets of waves waves.

Superposition of the waves on a screen resulted in the production of an interference pattern.

Unless light was a wave, no interference pattern could ever be observed on the screen - the particle theory of light could not explain the pattern.

Wave vs Particle 1-0• In the latter half of the19th century, the wave model became the

accepted model used to understand the observed properties of light

• The wave theory became successful because it successfully explained the phenomena of diffraction and interference, which could not be explained using the alternative particle model.

Problems for the Wave Theory• All other types of waves require

a medium for their propagation • It had been deduced from

experiments studying the interference of light that light had to be a transverse waveHowever, transverse waves could not travel through the body of a liquid or gaseous medium — recall that sound which can travel through liquids and gases is a longitudinal wave.

The Aether Model for Light TransmissionHypothesis• there was medium throughout

all of space through which light travelled

• The medium was called the luminiferous aether* (or light carrying aether) or simply aether

• outline the features of the aether model for the transmission of light

Scientists were at the time also trying to understand James Clerk Maxwell’s theory that light propagated like a wave - the aether model could help with this understanding (above - Maxwell’s famous electromagnetism equations)

* sometimes spelled ether

The Aether Model for Light TransmissionProperties of the Aether

• The aether either had to be a solid, or at least have the elastic properties of a solid - since only solids could transmit transverse waves.

• To account for the enormous speed of light, the aether had to be more rigid than steel!

• The Earth and other planets had to move through the aether in space

• The aether had to penetrate all matter through which light travelled.

• outline the features of the aether model for the transmission of light

The Aether, Newton and Relative MotionNewton• Newton realised that the motion of an

object had to be described relative to another object - there appeared to be no universal reference frame against which all motion could be measured.

• The realisation, coming from Newton’s work, that all bodies in the Universe were in motion, resulted in the uncomfortable idea that there was no absolute frame of reference against which motion could be measured.

• The existence of the aether was an hypothesis eagerly embraced because it provided a possible frame of reference against which all motion could be measured

The Michelson-Morley Experiment

• A paradigm shift in scientific thinking was precipitated by one of the most famous experiments in science…

• The purpose of the Michelson-Morley experiment was to detect and measure the relative motion of the Earth through the aether

• The Michelson-Morley experiment relied upon the interference of two rays of light travelling paths perpendicular to each other

• describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether

An experiment that didn’t work… as expected

The Michelson-Morley experiment

The Michelson-Morley Experiment

• The rays of light travelling paths A and B produced an interference pattern, seen by the observer

• It was predicted, using proven principles, that if the Earth was moving through the aether, that when the apparatus was rotated about a vertical axis, the interference pattern would change


Measuring the Earth’s Motion Through the Aether


Rotating the apparatus would allow the direction of the aether wind to be deduced

The Michelson-Morley ApparatusMichelson and Morley, despite careful experimental design and months of work were unable to detect any change in the interference pattern produced by their apparatus.

Brain Break

Consequences of moving through the aether

• If the device is at rest relative to the ether, a particular interference pattern will be seen by the observer and this pattern will be independent of the orientation of the apparatus

• However, if the device is actually passing through the aether...


Observer


… then it was predicted that light requiring different times to travel the two different paths, A and B, would result in a different interference pattern

As the velocity relative to the aether changes with the Earth’s motion around the Sun, a different interference pattern would be observed.


Observer



Michelson and Morley thus developed their experiment, using the wave properties of light to detect and measure the motion of the Earth through the

aether using the interference pattern from two beams of light

The interference pattern would change if the paths of the light beams relative to the aether changed due to the apparatus being rotated and due to the Earth’s

motion around the Sun

The known speed of the Earth in its orbit around the Sun enabled Michelson and Morley to accurately calculate the predicted effect of this motion on the

interference pattern


Interpreting the Michelson-Morley Results

• the Earth drags the aether along with it• there is no aether• motion through the aether distorts the apparatus,

cancelling out light path length differences

Conclusions

The null result of the Michelson-Morley experiment was bewilderingAttempts were made to explain the unexpected result including …

This all happened in 1887

These all had problems which caused them to be rejected

Question Time

• Describe the apparatus set up by Michelson and Morley to detect the motion of the Earth through the aether.

• Remember Mr Pitt’s deefer rule…

• D for describe - D for diagram!

Question Time

• Outline the physical phenomenon on which the Michelson-Morley experiment was based.


Evaluating the Experiment• The aether hypothesis was based on sound science - that light was

transverse wave and, at the time, all transverse waves were known to require a medium through which to propagate

• The Michelson-Morley experiment was of great value because its careful design would enable the existence of the hypothetical aether could be confirmed using well-understood principles involving relative motion of the Earth through the aether and interference of light

• It was also of great value because the conclusion that there was no measurable motion of the Earth through an “aether” ultimately led to the rejection of the aether model

• The Michelson-Morley result was consistent with Einstein’s 1905 postulate that the speed of light was not dependent on the relative motion between the source of light and the observer


Evaluating the Experiment

The experiment to measure the Earth’s motion through the aether was carefully designed:

– The well-understood wave phenomenon of interference was the principal on which the motion through the aether would be detectable

– The magnitude of the effect of the relative motion of the Earth through the aether was calculated and its effect on the interference pattern predicted

– The experiment was meticulously designed to produce and measure the predicted variation of the light interference pattern caused by Earth’s motion through the aether

– Experimental variables were identified and controlled– Variables that would affect the results adversely were identified and eliminated - e.g.

floating the apparatus in mercury to eliminate vibrations


Evaluating the Experiment• The experiment was repeated

meticulously at different times/places as the Earth orbited the Sun (this is to establish that the results were reliable)

• Attempts were made to account for the predicted changes in the interference pattern and because none of these were ultimately acceptable…

• It led ultimately to the conclusion that there was no aether

The Michelson-Morley Experiment• The Michelson-Morley

experiment demonstrated that the speed of light is independent of the motion of observer or the source.

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

The Michelson-Morley Experiment• The theories

– Aether model– Theory of relativity– [Maxwell’s electromagnetic theory]

• Although Einstein did not know about the Michelson-Morley experiment until after he’d proposed his theory of relativity, the results of the MM experiment were consistent with the theory of relativity and inconsistent with the aether theory

• discuss the role of the Michelson-Morley experiments in making determinations about competing theories

Inertial Frames of Reference• Consider the situation in which a coin is dropped inside a moving car.

Observer in car: coin drops straight to the groundObserver outside car: coin follows a parabolic trajectory

• Both frames of reference are inertial frames, and the coin takes the same time to fall to the floor from both frames of reference.

• outline the nature of inertial frames of reference

Inertial Frames of ReferenceConsider a ball dropped from a height of one metre

• outline the nature of inertial frames of reference

On the surface of the Earth In a lift moving at constant speed

The ball takes the same time to fall for both observers. There is no way the person in the lift can determine, using the observations of the falling ball, whether he is stationary or moving at a constant speed.

Both reference frames are inertial

Non-inertial Reference Frames

• perform an investigation to help distinguish between non-inertial and inertial frames of reference

An accelerating lift is an example of a non-inertial frame of reference

scales

scales

FR

mgF = maTaking “up” as +ve

FR - mg = ma

FR = m(g + a)If a = 0 then FR = mg normal weight

If a is positive then FR = m(g + a) weight increases

If a is negative then FR = m(g - a) weight decreases

FR is reaction force

= reading on scales

Non-inertial Reference Frames• If this apparatus is set up in a lift

the reading measured by the force sensor is greater than the weight of the object when the acceleration is upwards and less than the weight of the object when the acceleration is downwards

• Question: How can the acceleration be downwards if the lift is travelling upwards?


Non-inertial Reference Frames• Results - weight of 200 g mass in ascending lift• The lift is a non-inertial frame of reference


Non-inertial Reference Frames• Other examples of non-inertial

reference frames (and evidence for this fact)

• A car travelling at uniform speed around a roundabout (an accelerometer sensor shows that there is a constant magnitude acceleration towards the centre; a pendulum swings away from the centre and maintains a constant angle to the vertical)


Non-inertial Reference Frames• Other examples of non-inertial reference frames (and evidence for this

fact)• A car that is increasing its speed uniformly in the forward direction (a

pendulum hanging in the car swings towards the back of the car and makes a constant angle to the vertical)


Acceleration of car

Relativity (UNSW Website)• www.phys.unsw.edu.au/einsteinlight/

• http://www.cell-action.com/einstein/index.html[Excellent animated presentation]

• http://www.wyp2005.org/

• Einstein said..

"Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity."

Principle of Relativity• The special theory of relativity deals with events that are observed and

measured from inertial reference frames

• Inertial reference frames can be described as ones in which Newton’s first law - the law of inertia - is valid

Newton’s First Law: If an object experiences no net force it remains at rest or it continues in motion at constant velocity

• Relativity principle states that the laws of physics are the same in all inertial reference frames.

• In classical (Newtonian) physics, mass, space and time are considered absolute, their measurement does not change from one reference frame to another.

• discuss the principle of relativity

Question TimeEinstein developed two theories of relativity!

The theory ofSpecial Relativity

and the Theory of General Relativity

QuestionWhat is special about“Special Relativity”?

Special relativity deals only with motion in inertial frames of reference - that is, ones that are not accelerating.[Einstein’s Theory of General Relativity - not in this course - deals with accelerated frames of reference and gravity]

Postulates of the Special Theory of Relativity

1. Absolute uniform motion cannot be detected.

2. The speed of light is independent of the motion of the source.


The second of these postulates is contrary to our everyday experience

It must be accepted, since it is based on observational evidence.The postulate’s consequences completely change the way we perceive the Universe!

At different velocities, distances and times take on different values!Length, mass and time all depend on the motion of the observer!

The Principle of Relativity

The speed of light is measured to be the same in all frames of reference.

This is a startling statement!


The Principle of Relativity

The speed of a light flash emitted by the space station is measured to be c by observers on both the space station and the rocket ship.


gasp

Albert Einstein

• describe the significance of Einstein’s assumption of the constancy of the speed of light

A billboard in Paris

Einstein and the Speed of Light• Eighteen years after the

Michelson-Morley experiment in 1905, Einstein published a paper in which he presented the consequences of his startling proposition that…


Einstein and the Speed of Light…

Light travels at the same speed in all reference frames and that the speed of light does not depend on the relative motion of the source and the observer

Electromagnetic waves did not require a medium through which to travel!


Einstein and the Speed of Light

The speed of a light flash emitted by the ambulance is still measured to be ‘c’ by observers in the car in front.


gasp

The Ultimate Speed Limit

Consequences of the constancy of cIf the speed of light does

not vary…

then mass, length and time are cannot be absolute

quantities!!!

Measured lengths and times depend on the relative motion between the observer and the

event being observed

• identify that if c is constant then space and time become relative

Consequences of the constancy of c

From the sprinters frame of reference, the track is less than 100 metres in length.

During the race, the sprinter’s watch, seen by the stationary race timer, ticks off less than 10 s.

The difference is not significant at speeds of 10 m s–1. But near light speed it is a very significant effect.

• identify that if c is constant then space and time become relative

The athletic track is 100 m long and the stationary race timer records a time of

10 s for the race

Einstein’s Thought Experiments

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

It was impossible to achieve the kinds of speeds necessary to test his ideas (especially while working in the patent office…), so Einstein used Gedanken experiments or Thought experiments.

Young Einstein

Gedanken (Thought)

experiments


A light clock

The light will bounce back and forth between the parallel mirrors, each

journey back and forth "ticking off" equal intervals

of time.



What happens when the clock moves?


In this imaginary clock, the flash goes off, light bounces off the mirror, is detected at the photocell, triggering a “tick” sound and another flash.

photocell flash

mirror

1.5 m


What happens when the clock moves?


photocell flashbulb

mirror

1.5 m

This clock shouldproduce a tick

every how manyseconds?

td

v

m

m s

2 15

3 108

( . )

/

t = 10-8 s


How did the photon get

here?

Einstein’s Thought Experiments• Einstein carried out a thought experiment involving a clock in a box car• A modern version could involve a flash of light and a photocell detector

• An observer (a) moving with the space ship observes the light flash moving vertically between the mirrors of the light clock.

• An observer (b) who is passed by the moving ship knows the flash of light must have moved along a diagonal path, since in the time it takes the light to go across and back, the ship moves forward.



The longer distance taken by the light flash in following the diagonal path must be divided by a correspondingly longer time interval to

yield an unvarying value for the speed of light.


How did the photon get

here?

Einstein’s Thought Experiments• Einstein carried out a thought experiment involving a clock in a box car• A modern version could involve a flash of light and a photocell detector

Since the speed of light is the same in both frames of reference, the clock on the train (the moving clock), as seen by the stationary observer, must

be ticking more slowly than the stationary clock.


Time Dilation

All moving clocks appear to run slow. This stretching out of time is called time

dilation, which has nothing to do with the mechanics of clocks, but instead arises

from the nature of time itself.

Movie: Relativity.car.avi

Brain Break

What does all this mean?


To a stationary observer, moving clocksappear to be ticking more slowly!

And the faster the clock is moving,the more slowly it appears to tick!

Although we used a light clock, the type ofclock used in this experiment is immaterial

It really is time itself that is moving atdifferent rates for the two observers!

Brain Break!


• Relativity predicted1. Time dilation2. Length contraction3. Mass increase

• 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

• Evidence supporting1. Atomic clock on plane and

GPS atomic clocks2. Particle accelerators - path

length from frame of reference of high-speed particle is shorter

3. Particle accelerators - magnetic fields used to control moving particles have to factor in the increased particle mass due to relativistic effects


• 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

GPS navigation is a application of physics which has had a significant impact on society, making travel by ship and plane safer, and used in cars, GPS adds to the safety and ease of navigation, improving travel times for drivers. With GPS, companies can track delivery vehicles, improving efficiency.

Einstein Through the Eyes of Time

Defining the Metre• In contrast to the original definition

of the metre…• one ten-millionth of the length of the

earth's meridian along a quadrant (one-fourth the polar circumference of the earth)

• The following definition now applies…

• The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second

• discuss the concept that length standards are defined in terms of time in contrast to the original metre standard

Simultaneity• A boxcar moves with uniform

velocity• Two lightning bolts strike the

ends• The lightning bolts leave

marks (A’ and B’) on the car and (A and B) on the ground

• Two observers are present: O’ in the boxcar and O on the ground

explain qualitatively and quantitatively the consequence of special relativity in relation to: (a) the relativity of simultaneity (b) the equivalence between mass and energy (c) length contraction (d) time dilation (e) mass dilation

Simultaneity• Observer O is midway between the

points of lightning strikes on the ground, A and B

• Observer O’ is midway between the points of lightning strikes on the boxcar, A’ and B’

• The light reaches observer O at the same time

• He concludes the light has travelled at the same speed over equal distances

• Observer O concludes the lightning bolts occurred simultaneously


Simultaneity• By the time the light has reached observer

O, observer O’ has moved• The light from B’ reaches the observer O’

before the light from A’ reaches her• The two observers must find that light

travels at the same speed• Observer O’ concludes the lightning struck

the front of the boxcar before it struck the back (they were not simultaneous events) because O’ knows that the distance travelled by the light is the same (since he is in the middle of the train) and therefore, because he saw the strike from B’ first, he deduces that that event happened first

• http://www.youtube.com/watch?v=wteiuxyqtoM• See Simultaneity Einstein TOR.mov


SimultaneitySummaryTwo events that are simultaneous in one reference frame are in general not simultaneous in a second reference frame moving relative to the firstThat is, simultaneity is not an absolute concept, but rather one that depends on the state of motion of the observerIn the thought experiment, both observers are correct, because there is no preferred inertial reference frame


Mass–energy Equivalence• Mass and energy are inter-

convertible- Nuclear fission / fusion- Particle / antiparticle annihilation

E = mc2


Length Contraction• In figure A, the rocket is at rest

relative to the Earth and distances measured from either frame of reference on the other are the same

• In figure B, the observer on Earth sees the rocket moving away and because of the relative motion, the rocket appears shorter, lv, than it was at rest, lo


lv l0 1 v2 / c2

Length Contraction• In figure C, the observer on

rocket sees the Earth moving away, and because of the relative motion, the Earth appears flattened along the axis of motion

• lo is the diameter of the Earth as seen by the observer at rest and lv is the contracted diameter of the Earth (along the axis of motion)


lv l0 1 v2 / c2

Length Contraction


A fast-moving plane at different speeds.

[view this live!]

v = 10% c

v = 80% c

v = 99.9% c

v = 99% c

Length Contraction and Muon Decay


Cosmic Ray Muons: Muons are produced in the upper atmosphere in collisions between ultra-high energy particles and air-molecule nuclei. But they decay (lifetime t = 2.2 ms) on their way to the Earth’s surface:

No relativistic correction

With relativistic correction

Top of the atmosphere

Now time dilation says that muons will live longer in the Earth’s frame, that is, t will increase if v is large.

And their average velocity is 0.994c !


From our reference frame on the Earth’s surface, the lifetime of the moving muon is much longer than the lifetime in the muon’s frame of reference.

Applying the time dilation formula to a muon travelling at say 2.99995 x 108 m s–1, results in the muon’s lifetime of 2.2 ms dilating to 380 ms.

At this speed, given the lifetime of the muon observed from our frame of reference, the muon can travel a distance

d = vtd = 2.99995 x 108 x 380 x 10–6 = 114 km


tv to

1 v2

c2

Length Contraction and Muon Decay• Muons are created in the upper atmosphere when high energy cosmic rays strike atoms


g

gg

g

g

gg

g

g

g

• In the laboratory, this decay occurs in an average time of t = 2.2 µs

• Two types of muons decay into electrons and positrons as shown below: [not needed for HSC]

• Travelling at the top speed available (c), the muons should decay in a distance ct = 660 m

• In fact, observations on mountains indicate that the muon flux only drops by a factor of two after d = 6000 m

ee

ee



• The muons’ decay time as measured in our reference frame is thus

t’ = d/c = 20

• This time dilation implies that the muons must be travelling so fast that

t’/t = 9.1

cv 994.0

The observed behaviour of muons is consistent with the predictions of special relativity. This fact helps to validate the theory of relativity. (H2)

Length ContractionThe Tevatron at Fermilab in Chicago accelerates protons and antiprotons to almost 1000 GeV, or one teraelectron volt (1 TeV). At this speed, they are travelling only 300 kilometres per hour slower than the speed of light, the protons and antiprotons circle the Tevatron in opposite directions. The beams ultimately collide with each other at creating bursts of new particles.

Question

The speed of light = 299 792 458 m / s

1. Deduce the speed of the protons in the Tevatron.

2. If the path length that the protons follow at this speed is 6.44 km relative to a scientist working at the Tevatron, what distance do the protons travel in their frame of reference?

1. v = 299 792 458 - 83.3 = 299 792 374.7 m / s

2.

lv lo 1v 2

c 2 6.44 12997874582

2997924582 0.037 km

Time DilationTime passes more slowly in a frame of reference moving relative to an observer.This real effect is called time dilation.


tv t0

1 v 2 /c 2

Galileo - Newton Einstein

Time DilationTime passes more slowly in a frame of reference moving relative to an observer.This real effect is called time dilation.


tv t0

1 v 2 /c 2

Einstein - Station F.O.R. Einstein - Train F.O.R.

Time Dilation - Twin Paradox


The Set-upMary and Frank are twins. Mary, an astronaut, leaves on a trip many light years (ly) from the Earth at great speed and returns; Frank decides to remain safely on Earth.

The ProblemFrank knows that Mary’s clocks measuring her age must run slow, so she will return younger than he. However, Mary (who also knows about time dilation) claims that Frank is also moving relative to her, and so his clocks must run slow.

The ParadoxWho, in fact, is younger upon Mary’s return?

Time Dilation - Twin Paradox Resolution


Frank’s clock is in an inertial system during the entire trip. But Mary’s clock is not. As long as Mary is traveling at constant speed away from Frank, both of them can argue that the other twin is aging less rapidly.

• But when Mary slows down to turn around, she leaves her original inertial system and eventually returns in a completely different inertial system.

• Mary’s claim is no longer valid, because she doesn’t remainin the same inertial system. Frank does, however, and Mary ages less than Frank.

x

t

Time Dilation - Atomic Clock Validation


Two planes travelled east and west, respectively, around the Earth as it rotated. Atomic clocks on the planes were compared with similar clocks kept at the US Naval Observatory to show that the moving clocks in the planes ran slower.The results of this experiment validated Einstein’s theory.

Travel Predicted Observed

Eastward -40 ± 23 ns -59 ± 10 ns Traveling twin

Westward 275 ± 21 ns 273 ± 7 ns Stay-at-home twin

Mass Dilation• Objects moving relative to the observer

increase in mass compared with their masses when at rest relative to the observer.

• Calculate the mass of a proton at its maximum speed in the Fermilab Tevatron.

Proton rest mass is 1.67262158 × 10-27 kg.v = 299 792 374.7 m / sc = 299 792 458

The mass increases by a factor of 1341 times the rest mass.


mv m0

1 v 2 /c 2

Special Relativity


Relativity Video• Watch the Ustinov video clip . . .

Einsteins Universe Relativity.mov

Special Relativity

solve problems and analyse information using

Special Relativity

solve problems and analyse information using

c = 299 792 458 m s-1

(a) What will be the mean life time of a muon measured in a laboratory if it is travelling at v = 0.6c with respect to the laboratory? Its mean life time at rest is 2.2 x 10-6 s.

(b) How far does a muon travel in the laboratory, before decaying?

Solution (a) tv to

1v2

c2

2.2 10 6

1 (0.6c)2

c2

= 2.75 x 10-6 s

Solution (b) s = vt = 0.6 x c x 2.75 x 10-6 s = 494.7 m

Special Relativity• See Space notes for

extended discussion

discuss the implications of mass increase, time dilation and length contraction for space travel

Galaxies

A word from the creator

This PowerPoint presentation was prepared by Greg Pitt of Hurlstone Agricultural High School.

Please feel free to use this material as you see fit, but if you use substantial parts of this presentation, leave this slide in

the presentation.

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