Humans have progressed in the last thousand years
from animal powered transport on land and wind powered ships on water to
vehicles that are sufficiently sophisticated to allow travel beyond the
Earth into the solar system.
Scientists have drawn on advances in areas
such as aeronautics, materials science, robotics, electronics, medicine
and energy production to develop viable spacecraft. Perhaps the most dangerous
parts of any space mission are the launch, re-entry and landing. A huge
force is required to propel the rocket a sufficient distance from the
Earth so that it is able to either escape the Earth’s gravitational pull
or maintain an orbit. There are many factors to be taken into account
in choosing the time of day for a rocket to be launched. These include
consideration of: the weather predictions for the launch date; whether
there is an expectation that the craft will rendezvous with another orbiting
body; and whether the landing site for an aborted mission is appropriate.
Following a successful mission, re-entry through the Earth’s atmosphere
provides further challenges to scientists if astronauts are to return
to Earth safely.
Rapid advances in technologies over the past
thirty years have allowed the exploration of not only the Moon, but the
Solar System and, to an increasing extent, the Universe. Space exploration
is becoming more viable. Information and research undertaken in space
programs have impacted on society through the development of such things
as personal computers, advanced medical equipment, communication satellites,
improved weather forecasting and accurate mapping of natural resources.
Speculation continues as we consider where
humans will be travelling in the next one thousand years. Meanwhile, space
research and exploration of space increase understanding of the Earth’s
own environment, the Solar System and the Universe.
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
- define the change in gravitational potential
energy as the work done to move an object from a very large distance
away to a point in a gravitational field, E=G m1 m2
Many factors have to be taken into account
to achieve a successful rocket launch, maintain a stable orbit and return
- perform an investigation and gather
information to determine a value for acceleration due to gravity using
pendulum motion, computer assisted technology and/or other strategies
and explain possible sources of variations from the value 9.8 ms-2
- gather secondary information to identify
the value of acceleration due to gravity on other planets
- analyse information using the expression
F=mg to determine the weight force for a body on Earth and the weight
force for the same body on other planets
A java applet which simulates a swinging
pendulum, allowing the student to calculate the acceleration due to
gravity from T = 2 p
root(L/g). The length of the pendulum and height of the swing
can be varied. A more advanced version, which allows one to also
vary the mass of the bob and the acceleration due to gravity, can be
found at http://www.phy.ntnu.edu.tw/java/Pendulum/Pendulum.html.
However this is probably too complicated to be worth using.
The concepts in this part of the syllabus
can be explained through teaching the physics behind the following formulae:
F = mg = GMm / R2.
E = KE + PE = 1/2 mv2 - GMm/R
From v2/R = GM/R2 then
PE = -2 KE, so that E = -GMm/2R
Also, to escape must have E=0, which gives
Acceleration due to gravity on other planets
found from above. Calculated values shown in the table below.
However, to compare how much heavier/lighter you may be on another planet
(a standard exam question!), all you have to do is calculate (M1/R12)/(M2/R22).
Table also shows Kepler's 3rd law (T2/R3).
To calculate mass of Sun we actually have T2=4p2
A demonstration of reduced gravity on the
Moon can be seen from video clips of the Apollo astronauts walking about
the surface. For instance, in this movie
clip of the Moon Rover from Apollo 16 observe how long it takes
on the Moon for dirt to fall. At first you think this is all because
dust falls slowly due to air resistance - but then you remember there
is no air on the Moon! In fact if you look carefully you see that
everything falls at the same rate, as of course it should do
in a vacuum. Note the Moon dust has been made through grounding
down rocks by micro-meteorite bombardment over the past 4.5 billion
years and not by weathering!
- describe the trajectory of an object
undergoing projectile motion within the Earth’s gravitational field
in terms of horizontal and vertical components
- describe Galileo's analysis of projectile
- explain the concept of escape velocity
in terms of the:
- gravitational constant
- mass and radius of the planet
- discuss Newton's analysis of escape
- use the term ‘g forces’ to explain the
forces acting on an astronaut during launch
- compare the forces acting on an astronaut
during launch with what happens during a roller coaster ride
- discuss the impact of the Earth's orbital
motion and its rotational motion on the launch of a rocket
- analyse the changing acceleration of
a rocket during launch in terms of the:
- Law of Conservation of Momentum
- forces experienced by astronauts
- analyse the forces involved in uniform
circular motion for a range of objects, including satellites orbiting
- compare qualitatively and quantitatively
low Earth and geo-stationary orbits
- discuss the importance of Newton's Law
of Universal Gravitation in understanding and calculating the motion
- describe how a slingshot effect is provided
by planets for space probes
- account for the orbital decay of satellites
in low Earth orbit
- discuss issues associated with safe
re-entry into the Earth’s atmosphere and landing on the Earth’s surface
- identify that there is an optimum angle
for re-entry into the Earth’s atmosphere and the consequences of failing
to achieve this angle
- solve problems and analyse information
to calculate the actual velocity of a projectile from its horizontal
and vertical components
- solve problems and analyse information
using v=u+at, vx2=ux2,
+ 1/2ayt2 in relation to projectile motion
- perform a first-hand investigation,
gather secondary information and analyse data to describe factors,
such as initial and final velocity, maximum height reached, range,
time of flight of a projectile, and quantitatively calculate each
for a range of situations by using simulations, data loggers and computer
- identify data sources, gather and process
information from secondary sources to investigate conditions during
launch and use available evidence to and explain why the forces acting
on an astronaut increase to approximately 3g during the initial periods
of the launch
- identify data sources, gather, analyse
and present information on the contribution of Tsiolkovsky, Oberth,
Goddard, Esnault-Pelterie, O'Neill or von Braun to the development
of space exploration
- perform an investigation that demonstrates
that the closer a satellite is to its parent body, the faster it moves
to maintain a stable orbit
- solve problems and analyse information
to calculate centripetal force acting on a satellite undergoing uniform
circular motion about the Earth
- solve problems and analyse information
using r3/T2 = GM/4p2
- plan, chose equipment or resources for,
and perform an investigation to model the effect that removal of the
Earth’s gravitational force would have on the direction of satellite
- plan, chose equipment or resources for,
and perform a first-hand investigation to model the effect of friction
and heat on a range of materials, including metals and ceramics
The Java applet at http://zebu.uoregon.edu/nsf/cannon.html
(from the University of Oregon) allows an investigation of the trajectory
of a projectile to be made, while varying the inclination, speed and
the acceleration due to gravity. A simplified version at http://zebu.uoregon.edu/nsf/cannon2.html
only allows the angle of launch and the speed to be changed. It
is also possible to look at the effects of air resistance and wind speed,
though you probably will want to leave these options turned off.
The aim is to see how far a cannon goes by altering these input variables,
and then to hit a target by appropriate choice. A suggested learning
exercise has the student varying the acceleration due to gravity, then
examining the relation between PE and KE, then altering the angle of
launch, before trying to hit the target. The basic relations can
perhaps be derived mathematically first. The exercise is as follows
(though you may only wish to have your students do the first two parts,
before attempting to hit the target in the absence of air resistance):
(Note: Hit the "more" button
when you run out of ammo!)
Conservation of energy:
1.Set the angle of the cannon
to 45 degrees.
2.Set the velocity to 30.
3. Shoot the cannon and note
4. Double the gravitational
acceleration (e.g.. move it so it reads -19.6).
5. What must the velocity
be set to, in order to cover the same distance as the previous shot?
Change the velocity, shoot the cannon until you have determined this.
6. Now reset the gravitational
acceleration back to -9.8.
7. Set the velocity to 40
and the cannon angle to 70.
8. Repeat steps 3 through
9. What is the relation between
kinetic energy and gravitational acceleration as determined by this
Angles, Angles, Angles:
1.Set gravity to -9.8.
2.Set velocity to 50.
3. Determine the cannon angle
which produces the maximum horizontal distance of the shot.
4. What is this angle and
why do you think it has this value?
The effects of Drag:
1.Set gravity to -9.8.
2.Set velocity to 66.
3. Shoot the cannon to hit
4. Now turn on the atmosphere
by clicking the button that says drag.
5. Set the windage to -10
and shoot the cannon and note how far the shot falls from the target.
6. Set windage to -20,-30,-40
and repeat. Plot the distance from target versus wind velocity.
The effects of projectile
1. Keep drag turned on and
set windage to -20.
2. Keep velocity at 66; set
density to 1.2.
3. Shoot the cannon and note
4. Decrease the density of
the projectile by a factor of 2 (e.g. 0.6) and shoot the cannon and
note the density.
5. Now decrease density to
0.3 and then 0.15 shooting the cannon at each new value for density.
6. Plot the decrease in distance
as a function of density.
7. Repeat steps 2-6 for windages
of -10 and -40.
In each case you have 4 chances
to hit the target:
1. Turn off drag if its on.
2.Set the gravitational acceleration
3. Hit the target (and record
the correct velocity and angle).
4. Turn on drag.
5. Set windage to -50.
6. Set density to 0.6.
7. Hit the target in 4 tries
and record the settings.
8. Leave drag on.
9. Set gravity to -2.
10. Set windage to -10.
11. Set density to 1.2.
12. Hit the target in 4 tries
and record the settings.
The Java applet at http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html
(from Michael Fowler) allows an investigation of Newton's classical
thought experiment of firing cannon balls from a mountain top to find
what speed is needed to achieve orbit - ie when the projectile is continuously
falling at a rate which matches the curvature of the Earth. Unfortunately
the speeds are in mph not kph!
Let a ball roll from a fixed height down
a groove in an inclined ramp. Keep the bottom of the ramp parallel
to the ground so that the ball is launched into the air with a fixed
velocity, v, horizontally. Mark where the ball strikes the ground
and measure its horizontal distance from the launch point, x.
Then raise the height of the ramp, y, above the ground and repeat.
Plot x vs y - should get a parabola: y = 1/2 gt2 and x =
vt so that y = gx2/2v2.
The Table above (showing planetary data)
also demonstrates Kepler's Third Law, r3/T2 =
and this can usually be applied by just showing that r3/T2
= constant. For instance, when measured in AU (1 Astronomical
Unit = Earth - Sun distance) and Years, then applying the formula to
other planets shows directly either how much further from the Sun they
are, or how many times longer their year is.
The Java applet at http://www.physics.nwu.edu/ugrad/vpl/mechanics/planets.html
(from North Western University in Chicago) illustrates Kepler's Laws
in action for the orbit of two objects around one another. The
orbits and speeds can be viewed as (i) the relative mass of the planets,
(ii) the orbital period, (iii) the step-time interval and/or (iv) the
eccentricity are varied. By selecting "show area", Kepler's Second
Law can be demonstrated (equal areas in equal times). The trajectories
can be viewed from the centre of mass frame, or from the frame of either
The link at http://home.cvc.org/science/kepler.htm
by Bill Drennon from a Californian high school provides animated images
demonstrating the first two of Kepler's Laws and shows how the planetary
orbits obey the Third Law. There is also some background history
on Johannes Kepler and Tycho Brahe, from whose diligent observations
Kepler deduced his laws.
Also known as gravity-assist, or gravity-boost,
this is a way of adding velocity to a spacecraft as it passes by a planet.
It is used for interplanetary travel to reduce journey times and minimise
fuel demands. Essentially the satellite undergoes a "collision"
with a planet, gravitationally interacting. Gravity is a conservative
force, so the collision is elastic. Since the planet is so massive
its velocity is effectively unaffected.
Consider an encounter where a spacecraft
passes Jupiter, arriving in the opposite direction to Jupiter's orbit
and leaving in the same direction as the orbit. Momentum
and energy conservation gives (an exercise for the Teacher!), with a
little algebra, vpi - vsi = -(vpf -
vsf) where p is for planet, s for satellite,
i for initial and f for final. Suppose the approach speed, before
encounter, is 10 km/s. Jupiter's orbital speed is 13.1 km/s.
Thus, -13.1-10 = -(-13.1-vsf). Re-arranging gives vsf
= -36.2 km/s - ie the satellite leaves with a speed more than 3 times
faster than the approach!
Satellite Tracking - NASA's J-Track Software
J-Track is a fantastic resource which allows
you to see the location of all satellites orbiting the Earth.
The paths of satellites can be seen in 2D, projected onto a map of the
world, or in 3D showing their actual distribution in space. The
latter version, in particular, can be used in a highly educative way
to illustrate a number of features of spaceflight, and the different
functions of spacecraft.
It works using Java applets, so should work
on your machine once you download the database. In particular, you can
find out where the Hubble Space Telescope, the Mir space station, the
Space Station and the Space Shuttle (during missions) are right now,
watch their progress across the surface of the Earth and see when they
will next be visible from your location. The 3D version is particularly
useful for illustrating orbital mechanics, by studying the varying distributions
of satellite orbits, which reflect the purposes for which the satellites
are used for. Some background material on the different types
of satellites in use can be found by consulting John Graham's on-line
book on "Space
Exploration: from talisman of the past to gateway for the future"
, particularly chapters 24-27.
Shows Satellite location over Earth map.
Future space travel and exploration will
entail a combination of new technologies based on current and emerging knowledge.
|Click on craft
||Change orbital data in lower right
|Ctrl+Click on craft
||Toggles on/off ground trace
|Shift+Click on craft
||Goes to web page about craft
|Click+hold on map
||Display when first visible at longitude
For instance, use the software to find when
the Space Station will next be visible at night, and what trajectory
it will take across the sky, and then go out and watch it pass overhead!
Shows 3D distribution of satellites
|Click on satellite
|Click in list
||Rotate in 3d
Under "Satellite", then "Select" choose
the following options for illustrative viewing:
Select a satellite, and find what its orbital
radius, period and speed are (under "View" then "Satellite Position"),
showing that the faster it moves the closer it is to the Earth, and also
demonstrating Kepler's Third Law.
- Astronomy - IUE, HST, ROSAT, Chandra,
XMM - a variety of orbits, some highly elliptical in order to get
a long way from the Earth for much of the orbit - to minimise radiation
from Earth, but HST is in LEO.
- Communications - Geostationary orbits
- fixed above one location -e.g. Inmarsat with global phone
coverage, but requires high power.
- Human Crew - all in LEO (Low Earth Orbit).
- Iridium - Low Earth Polar Orbit for
low power phones, with global coverage.
- Military- GPS - full-earth coverage
from circular orbits - fix your position precisely.
- Weather- GOES - geostationary
orbits but several older satellites now oscillating above and below
equatorial plane - can be used for communication at the South Pole
(e.g. GOES 3)!
Rocketry, Launch, Re-entry and Orbital
The fundamental principle for rocketry is
Newton's Third Law, for every action there is an equal and opposite
reaction, together with the conservation of momentum. Ejection
of propellant at high speed through a nozzle in a direction opposite
to that desired will propel a spacecraft forward. Moreover, this
works in a vacuum, as well as an atmosphere (better in fact) (unlike
Following the basic force-energy relations
(see earlier), to achieve orbit, v2/R = GM/R2 so
v = root(GM/R) = 7.9 km/s. To escape vesc= root(2GM/R)
= 11 km/s. Launch is helped using an equatorial location, where
the Earth's rotational velocity of 0.5 km/s, in an eastward direction,
reduces the energy requirements a little.
During launch the maximum acceleration reached
by human-crewed spacecraft is 3g. A description of the experience
is given on this NASA
Q&A fact sheet. This is toward the end of the burn in
which nearly 2000 tons of fuel is used, 7 minutes after launch.
Once thrust is cut, however, weightlessness follows as the spacecraft
is now in orbit, with everything in it continuously "falling".
To return to Earth the orbital velocity
must be reduced to zero. Firing rockets in the opposite direction
to the orbital velocity reduces the speed, decreasing the total energy,
and putting the spacecraft into an elliptical orbit which will intersect
the Earth's atmosphere. The primary reduction in speed, however,
comes from aerodynamic drag with the atmosphere (otherwise spacecraft
would have to carry enormous fuel tanks to return to Earth). Both
through compression of the air and through friction, substantial heat
is produced (spacecraft are travelling at Mach 25 at re-entry).
This must be radiated away to avoid melting the spacecraft! The
most efficient means is through a shock wave (think about the bow wave
caused by a high speed boat on a river - much of the energy for powering
the boat goes into driving this wave). This is produced best through
a blunt shape to the craft (ie exactly the opposite to what's needed
at launch!). It is also essential for the craft to radiate heat
away as quickly as possible - hence the special tiles on the underbelly
of the Shuttle - to dissipate heat. These are made of ceramic
material, with a porous structure.
If the angle of approach is too steep, frictional
heating will be too fast and burn the spacecraft up. If the angle
of approach is too shallow the spacecraft will skip off the atmosphere
into a highly elliptical orbit which will take it far from the Earth
(think about skipping a stone across a pond). There is thus an
optimum angle for re-entry.
For satellites in Low Earth Orbit there
will be some residual friction with the atmosphere (space is not a perfect
vacuum!), which will continually work to reduce the energy of the satellite.
Since E = -GMm/2R the orbital radius will decrease, increasing the frictional
drag. Thus the orbit gradually decays until the frictional heating
with the atmosphere becomes too great and the satellite burns up.
Demonstration of Rocketry Principle
Blow up a balloon and let the air escape
before tying it up! Newton's Third Law propels the balloon forward,
and conservation of momentum determines the velocity.
Demonstration of the Effect of Removing
Gravitational Field on Orbit
Attach a ball to a piece of string or ribbon.
Swing it around, say about your head or even around a globe of the Earth
(thus simulating a orbit). Cut or let go of the ribbon at your
hand. The ball with continue in a straight line with the ribbon
streaming out behind it, showing its path, and illustrating Newton's
First Law (ie state of uniform motion).
Some Notes on Historical Figures
in the Development of Space Exploration
- Russian mathematician.
- "Father" of astronautics.
- Proposed to escape Earth's gravity through
launching from top of tower reaching from Earth to geostationary orbit
(36,000 km high). Wrote book called "Beyond the Planet Earth"
about life in a spindle-shaped spacecraft at this position.
- Conceived idea of the rocket - continuous,
propellant driven vehicle to escape the Earth, giving precise control
of acceleration and orbit.
- Conceived of fundamental formula for
rocket motion, essentially applying Newton's Third Law to derive the
quantity of "specific impulse" (impulse is F/Dt).
- However his work was virtually unknown
outside even his home town (Kaluga) - Oberth and Goddard developed
similar principles independently.
- German (actually Transylvanian by birth).
- Wrote key book in 1923 on "The
Rocket into Planetary Space" out of his PhD dissertation.
- Book inspired rocket societies to spring
up all over the world, one of which lead directly to the development
of the V2 rocket.
- Book covered manned and unmanned rocket
flight, liquid fuel rocket construction, propulsion, inertial guidance
and navigation, aerodynamics, thermodynamics, flight mechanics, pre-testing,
life-support systems, spaceflight hazards and their remedies, bio-astronautics,
re-entry and recovery techniques, telescopic tracking and applications
of rocket technology to spaceflight. All in 87 pages!
- Described the basic theoretical principles
for thrust and determining the most favourable velocity to reach a
- Conducted practical experiments in rocketry.
- Determined they worked better in vacuum
than in air (when most people mistakenly believed air was necessary
for the rocket to push against).
- Developed solid and liquid-propellant
rockets, with first successful flight with liquid in 1926.
Esnault-Pelterie (main work 1912-1930)
- Calculated trajectories to the planets.
- Analysed significance of relativity
theory to spaceflight, assessed probabilities for extra-terrestrial
- Investigated nuclear propulsion.
- Coined the word "astronautics".
- Conceived plans for space colonies at
stable Lagrangian points between Earth-Moon (L5) - wrote book on this
called "The High Frontier".
- Devised concept of "mass-driver" and
"electromagnetic slingshot" to accelerate cargoes into orbit from
the Moon (eg after mining) and towards catcher ships.
von Braun (1912 - 1977)
- German, then American.
- Developed V2 rocket in WW2.
- Devised concept of space-station.
- Devised concept of the space-shuttle.
- Devised first comprehensive scenario
for reaching Mars (and inter-planetary travel).
- Directed NASA's space-flight program
in the 1950s and 1960s.
- discuss the limitation of current maximum
velocities being too slow for extended space travel to be viable
- describe difficulties associated with
effective and reliable communications between satellites and earth
- van Allen radiation belts
- sunspot activity
Extended Space Travel
- gather, process, analyse and present
information to compare the use of microwave and radiowave technology
as effective communication strategies for space travel
Pioneer 10, 11, Voyager 1 and 2 are now heading
for interstellar space at speeds of 10-17 km/s. Will travel 1 light
year in ~30,000 years. Nearest star is 4 light years away (Alpha
Centauri) - so an impracticable method for travel to the stars.
Some possible methods of interstellar transportation (all well beyond
our current technology) include:
Drive Now! There is no such thing as warp drive, but in this
site NASA scientist Marc Millis assesses the prospects for achieving propulsion
breakthroughs that would make interstellar travel possible. Particularly
relevant to the HSC is his discussion on why interstellar
travel is so tough.
- Nuclear fusion, ejecting stream of
ionized gas, accelerating to ~0.1c. However only ~0.4% mass
released as energy - require stupendous fuel loads.
- Antimatter rockets - react antimatter
with matter, and eject debris through nozzle. Much more efficient,
might only need a few kg of antimatter - however we cant make antimatter
- Light sails - using momentum carried
by photons. Sunlight too weak except for miniature payload,
so would need to construct and direct enormous laser (with telescope
several hundred km in diameter in order to focus it!) at sails several
km across and billions of kms away.
- Interstellar ram-jet, scooping up
interstellar matter and fusing - would need scoop several 1000 km
across - magnetic confinement?
- World ships, taking human colonies
that live for several generations, to reach destination.
Using current technology to accelerate ship.
- Relativistic time dilation. The Lorentz
= 1/root(1-v2/c2) = 2.3 for v=0.9c, 7 for
v=0.99c and 22 for v=0.999c. This is the factor by which time
is slowed for the space travellers. Need high Lorentz factors
to be practicable!
- Suspended animation - over hundreds
Light Travel Time
Light travels at 300,000 km/s. Thus,
the following delays are encountered for communication within our Solar
|Mars (closest approach)
||80 million km (0.5 AU)
||150 million km (1 AU)
|Jupiter (closest approach)
||630 million km (4 AU)
|Pluto (closest approach)
||6 billion km (39 AU)
|Alpha Centauri (nearest star)
||4 million, million km
Thus light travel time is significant in
our own Solar System; cf operation of Pathfinder spacecraft on Mars
or Galileo spacecraft at Jupiter - need robotic operation. Time
delay even noticed in long distance telephone calls, especially if the
call is routed through more than one geostationary satellite.
Communication Disruptions with Satellites
Van Allen belts are where charged particles
from the Sun are trapped in the Earth's magnetic field. Two doughnut-shaped
rings surrounding the Earth - inner and outer belts. Produce currents
which flow along magnetic field lines. As particles collide with
upper atmosphere they create aurorae by exciting the atoms and molecules
to excited energy levels. Produces strong radio emission from
synchrotron - charged particles spiralling about the Earth's magnetic
field. Increases in times of Solar Storms, with the extra flux
of charged particles from the Sun. Sunspot activity, associated
with magnetic fields on the Sun's surface, are sites for solar flares
and mass ejections of particles. Communication disruptions will
be caused when satellites pass through the radiation belts, eg the South
Microwave and Radiowave Communication
Technology for Space Communication
I am afraid I do not understand what the
syllabus writer intends with this concept point.
Current and emerging understanding about
time and space has been dependent upon earlier models of the transmission
- outline the features of the aether model
for the transmission of light
- describe and evaluate the Michelson-Morley
attempt to measure the relative velocity of the Earth through the
- discuss the role of critical experiments
in science, such as Michelson-Morley's, in making determinations about
- outline the nature of inertial frames
- discuss the principle of relativity
- identify the significance of Einstein’s
assumption of the constancy of the speed of light
- recognise that if c is constant then
space and time become relative
- discuss the concept that length standards
are defined in terms of time with reference to the original meter
- identify the usefulness of discussing
space/time, rather than simple space
- account for the need, when considering
space/time, to define events using four dimensions
- explain qualitatively and quantitatively
the consequence of special relativity in relation to:
- the relativity of simultaneity
- the equivalence between mass
- length contraction
- time dilation
- discuss the implications of time dilation
and length contraction for space travel
- perform an investigation and gather
first-hand or secondary data to model the Michelson-Morley experiment
- perform an investigation to help distinguish
between non-inertial and inertial frames of reference
- analyse and interpret some of Einstein’s
thought experiments involving mirrors and trains and discuss the relationship
between thought and reality
- 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
- solve problems and analyse information
using: Lv = L0 root(1-v2/c2)
and tv = t0 / root(1 - v2/c2)
- gather, process, analyse information
and use available evidence to discuss the relative energy costs associated
with space travel
- 1792 the new Republic of France defined
the metre as one ten-millionth the distance from the North Pole to
- Not very practicable, so re-defined
as the distance between two scratches on a platinum-iridium bar in
the International Bureau of Weights and Measures in Paris at STP.
- Awkward, so new standard defined
based on wavelength of light.
- In 1960 re-defined as 1,650,763.73 wavelengths
of an orange-red line emitted by Kr86 in a gas discharge
- Available everywhere, repeatable.
- Re-defined again in 1983 as even this
was not proving accurate enough for high precision.
- Now defined in terms of the speed of
light: 1 metre is the path travelled by light in a vacuum during a
time interval of 1/299,792,458 of a second.
- This now defines the speed of light
as 299,792,458 m/s!
- The mass standard is currently a particular
block of metal, but this will eventually be re-defined in terms of
the mass of an atom.
Relativity Teaching Thoughts
A possible route to to follow when teaching
Relativity Simulations on the Web
- There are two key concepts to get across,
the Postulates of Special Relativity:
- Laws of Physics are the same everywhere
in inertial frames.
- Speed of light constant for all observers.
This is the one which causes all the apparent paradoxes!
- Concept of measuring an event, and placing
space-time co-ordinates to it.
- Simultaneity no longer holds, as it
takes time for information about an event to reach an observer!
- By looking at the same event from two
reference frames we then find that different observers perceive different
time intervals for that event.
- It is important to compare measurements
to the "Proper Time", t0, which is the time interval for
an observer who sees the event at the same place. Time dilation
occurs for observers moving with respect to this frame of reference,
tv = t0 / g,
= root(1 - v2/c2). ie the moving observer
sees the event go more slowly (takes longer).
- Similarly, comparing the length of an
object to the "Proper Length", L0, the length
measured in the reference frame where the object is at rest, we get
Lv = L0 g.
The object has contracted for the moving observer.
- This is probably was far as you will
wish to take your students. However, if you wish to introduce
E=mc2, and do more than just state the result, you will
have to introduce the concept of relativistic momentum, as in the
next two points:
- Momentum conservation still holds
if we now consider relativistic momentum, gmv,
instead of just mv.
- Further, by defining the total energy
of a particle as gmc2
= mc2 + K where K is the relativistic kinetic energy,
we end up with the famous E=mc2.
There are many sites devoted to Relativity
on the web, both Special and General. However they are generally
at too high a mathematical level to be useful for the HSC. Here
are some sites you might like to try, even if only for your own edification.
Relativity Notes and Paradoxes
Visualisation Sites No longer works - let me know if
you find the new link so that I can correct this! A starting point
for searching for Relativity on the web. Broken down into popular
science sites, visualisation sites and tutorial sites.
Relativity An extensive site from Andrew Hamilton in Colorado
with a number of illustrations for Special Relativity, but at a level
above the HSC. However the graphics depicting time
dilation might be useable.
from John Walker offers some spectacular images showing how Special
Relativity appears to distort our view, by ray-tracing images
of the effects seen from a space-ship travelling at relativistic speeds
through the Galaxy. Effects like the Lorentz Contraction, Time
Dilation, Doppler Shift and the Aberration of Light are all illustrated.
Unfortunately, most of this is at too advanced a level.
Light Cone A tutorial on Relativity, leading you through all the
concepts of Relativity, and setting the scene with the historical
background. Extensive animated graphics illustrating the concept
of the light cone.
First Year Physics lecture notes, from Joe Wolfe, in pdf format.
A succinct summary of Special Relativity.
Twin Paradox. Further notes from Joe Wolfe on this well-known
paradox involving time dilation.
Pole Paradox. Yet more notes from Joe Wolfe on this well-known
paradox involving length contraction.
Relativity FAQ. Frequently asked questions and answers about
Relativity. Includes discussion on the paradoxes such as the Pole
& Barn and the Twins, amongst many other topics. A good
place to find answers to those curly questions your students might
have thrown up! Incidentally there is no point in your trying
to disprove relativity by arguing that special relativity doesn't
actually explain the Twin Paradox (as some people are want to do),
as SR doesn't deal with acceleration correctly. Yes, it is true
that General relativity needs to be taken into account to study the
apparent paradox fully, but this is way beyond the level of
HSC. The simple thought experiment, without any consideration
of how one accelerates and decelerates, is more than sufficient for
HSC level, and if you want to look further for your own edification
then look at one of the references above - but you will need to wade
through the mathematics!
Hawking's home page. OK, its not in the syllabus, but everyone
seems to want to know about Hawking. His work is in GR, not
to Einstein talking about E=mc2.
101. The most readable discussion on the physics of relativity
I have come across, by Patricia Schwarz of Cal Tech. The level
is about right (at least for the teachers!) and there are some easy-to-understand
animated graphics illustrating key concepts through thought experiments.
I suggest looking at the first two sections; (i) what is space-time
and (ii) why was relativity needed. In latter sections you might
look at some of the graphics but ignore the maths.
The Michelson-Morley Experiment
Possibly the most important null experiment
in Physics history. Designed to measure our motion with respect
to the aether, the postulated medium for light. Found no
result from observing the difference in travel times from two orthogonally
directed beams, whatever was tried. Pushed the experimental technique
to the limits. The conclusion: the aether cannot be detected,
which is another way of saying there is no medium needed for the passage
of light. Some websites devoted to discussion on the subject include:
Inertial Reference Frames
Frames that move at constant velocity with
respect to one another. Rotating frames are not inertial reference
frames. Strictly speaking, the Earth is not an inertial
frame of reference, but this only really manifests itself on large-scales,
such as weather systems and ocean currents.
Experimental Tests for Inertial Reference
- Hang a pendulum in a car or train.
Mark position of stationary bob on a table. When in motion if
bob moves away from this position the system is non-inertial - eg
when accelerating, rounding a corner.
- Place ball on merry-go-round (or rotating
table). As ball is rolled along a radial line if it veers away
from that line the frame is non-inertial, as occurs when its rotating.